Summary with the 3rd edition of Fundamentals of Corporate Finance by Hillier

What is corporate finance? - Chapter 1

Key Notations:

Corporate finance = The study of ways to answer the questions ‘What long term investments to make?’, ‘Where to get the long-term financing to pay for the investment?’ and ‘How to manage everyday financial activities?’.

The financial manager would be in charge of answering the three questions as described above. In most organizations the chief financial officer would answer directly to the executive director, whom reports directly to the board of directors. The chief financial officer manages the Treasurer (finance function) and the controller (accounting function). Accounting functions take all financial information and data of the firm, and attempt to present this information in such a way that management can assess the performance and risk of their firm, and such that management can take proper decisions based on the information. Finance functions use the information and output of the accounting functions, and include the three general questions, and decisions around those three questions.

What sort of financial management decisions are there?

The financial management decisions as discussed below are in line with the three questions in the Corporate Finance definition.

1. Capital Budgeting

The planning and managing of long-term investments. The investments are judged on size, timing and the risk of future cash flows. The firm has to find investments that create value, so the value has to be more than the costs of the asset.

2. Capital Structure

The firm’s mixture of long-term debt and equity. Firms have to determine how they want to finance its long-term investments. They also have to find the best capital structure; the one with the least expensive sources of fund.

3. Working Capital Management

Contains the firm’s short-term assets and its short-term liabilities. Managing the working capital is a day-to-day activity. The working management deals with questions like: How much cash and inventory? Sell on credit? How do we obtain short-term financing?

What are the goals of financial management?

The main goal is to add value for the owners; to make money. Some possible goals:

1. Survive
2. Bankruptcy avoidance
3. Beat the competition
4. Maximize sales or market share
5. Minimize costs
6. Maximize profits
7. Maintain the steady earnings growth

You can divide these goals in two classes. The first is earning or increasing profits. The second group relates to controlling risk. It isn’t really possible to maximize the safety and the profit, because making profit often brings some risk. Therefore we thought of a better goal, an appropriate goal. This is the goal from a shareholder’s point of view. The financial manager has to make decisions that increase the equity value. So the goal of the financial manager would be: “The goal of financial management is to maximize the current value per share of existing equity”.

So we have to learn how to discover good investments and financial arrangements that increases the value of the equity. The more general goal is: maximize the market value of the existing owners’ equity.

What are financial markets?

Bringing buyers and sellers together involves the following cash flows:

• Cash to the firm from financial markets for securities issued (A)

• Cash flow within the firm to invest in assets (B), cash from the firm to pay taxes (C) to the government (D), cash reinvested in the firm (E), cash to financial markets as dividends and debt payments (F)

• Cash to financial markets from households (G) or financial institutions (H)

Financial markets function as both primary and secondary markets for debt and equity securities:

Primary markets = The corporation sells and thereby raises money for the corporation. There are two types of transaction: public and private offerings.

Secondary markets = One owner or creditor sells to another. This means transferring the ownership of corporate securities. The secondary market has two types:

• The auction markets: Has a physical location, matches sellers and buyers. For example NYSE Euronext, NASDAQ, these are organized auction markets.

• The dealer markets: Connected electronically, over-the-counter (OTC) markets. Buying and selling done by the dealer.

How are ownerships and corporate governance organized? - Chapter 2

What are the legal classifications of businesses?

There are several legal classifications of businesses, each with its advantages and disadvantages. A key observation is that as a firm grows, the advantages of the corporate form outweigh the disadvantages.

• First, the sole proprietorship. The business is owned by one person. This is the easiest way to create a business. The advantage in terms of finance is that the owner can make all decisions and gets all the profit. However, he also pays all the bills and his personal assets are included in the property (unlimited liability). Also, the business dies when the owner dies before he has sold his business to someone else.

• Second, the partnership. The business is owned by at least two persons. They can be general partners, so they operate the daily business together. They can also be limited partners, these only operate part of the business, or silent partners, who just invest and do not operate daily business. This form also mixes up personal and private property (unlimited liability), except for the limited partner. It is difficult to change partners, because a new agreement has to be set up.

• Third, corporations. Here, the company is a legal entity so that there is only limited liability. To set up a corporation, articles of incorporation are required. The shareholders are the owners, and they select a board of directors. This board chooses the main corporate officers. Ownership can be transferred easily (by selling shares). It is easier to borrow money. A disadvantage is that the corporation pays taxes on profits and then the owners pay taxes on their income, so there is double taxation.

These corporate forms of organization can have many variations around the world. The names also differ throughout the world, in the Netherlands there is for example a "Besloten Vennootschap" (BV) and "Naamloze Vennootschap" (NV) form, in the UK comparable forms would be a "Limited" and a "Public Limited Company".

What is the agency problem?

Financial managers act in the best interests of the shareholders by taking actions that increase the value of the company’s equity. In very large corporations, especially the UK and the US, ownership can be spread over a huge number of shareholders, meaning that management controls the firm and not the owners. One might ask the question, will management necessarily act in the best interests of the shareholders? In Europe, a different type of problem exists. Many European firms have one dominant shareholder that directs corporate objectives at the expense of smaller shareholders.

Type I agency problem is the possibility of conflict of interest between the shareholders and the management of the firm.

A simple example could be the decision of whether to invest or not; investing may increase share value, but may also turn out badly, causing managers losing their jobs.

Agency costs = Costs of conflict of interest between shareholders and management

• Direct agency costs = Corporate expenditures that benefit management but cost shareholders and Expenses that come from the need to monitor management actions

• Indirect agency costs

Whether or not management acts in the best interests of the shareholders depends on two factors; How closely are management goals aligned with shareholder goals and Can managers be replaced if they do not pursue shareholder goals. There are a number of reasons to think that management has a significant incentive to act in the interests of the shareholders, because:

• Managerial compensation; Increasing equity’s value may be in managements’ best interests because managerial compensations very often rely on financial performance in general. Also, better performers within the firm will tend to get promoted

• Control of the firm; Control of the firm rests with shareholders. They elect the board of directors, who hire and fire managers

• Shareholder rights; Single-tier board countries > Shareholders elect directors. Two-tier board countries > Supervisory board (main shareholder representatives, major creditors and employee representatives) elects directors. General idea = one share, one vote (80 shares, 80 votes). Two different voting procedures;

1. Cumulative voting = A procedure in which a shareholder may cast all votes for one members of the board of directors. If there are N directors, then 1/(N+1) per cent of the shares plus one share guarantees you a seat.
2. Straight voting = A procedure in which a shareholder may cast all votes for each member of the board of directors. The only way to guarantee a seat is to own 50% plus one share
3. Staggering = Only a fraction of the directorships are up for election at a particular time. It makes it more difficult for a minority to elect a director when there is cumulative voting and takeover attempts become less likely to be successful.

If only two directors are up for election, it takes 1/(2+1) = 33.33% of shares plus one share to guarantee a seat

• Proxy voting; A proxy = A grant of authority by a shareholder allowing another individual to vote his or her shares

• Classes of shares; A class A share may give you 1 vote, whereas a class B share may give you 10 votes. Creating such shares has to do with the control of the firm

• Other rights; The right to share proportionally in dividends paid, The right to share proportionally in assets remaining after liabilities have been paid in liquidation and The right to vote on shareholder matters of great importance such as mergers
  Pre-emptive right = The right to share proportionally in any new equity sold. This right is not straightforward

• Dividends; A dividend = Payments by a corporation to shareholders, made in either cash or shares

Type II agency problem = The possibility of conflict of interest between controlling and minority shareholders.

Stakeholders = Someone, other than a shareholder or creditor, who potentially has a claim on the cash flows of the firm.

Is corporate governance the solution?

Corporate governance is a term that describes the way a company does its business and how it monitors whether the right procedures and behavior are used while conducting business. The SOX, or the Sarbanes-Oxley Act was established to ensure more ethical behavior in businesses. It says that the CFO and the CEO will sign a paper which says that the financial report is fair. Moreover, it says that there should be a good internal control on financial reporting. Lastly, auditors and the company monitor whether the controls were effective the last fiscal year. Managers can be replaced. That can be done by the board of directors. Members from the board of directors can be voted out by shareholders. Also, legal action can be taken.

So finance should be studied because as an employee, you will be able to increase your contribution to the company if you know how financial decisions are made. Furthermore, it helps you to assess trade-offs you will face in your personal life.

How to analyze and use financial statements? - Chapter 3

Key Notations:

1. b: Retention ratio

2. NWC: Net working capital

3. P/E ratio: Price-earnings ratio

4. PPE: Property, plant and equipment

5. ROA: Return on assets

6. ROE: Return on equity

This chapter treats financial statements, taxes and cash flows. The goal of the chapter is not to be able to prepare a financial statement, but to recognize key relevant data that is needed to make decisions in the field of finance. Particular attention is paid to two important differences: (1) the difference between accounting value and market value; (2) the difference between accounting income and cash flow.

What is an annual report?

There are three financial statements in the annual report:

1: Balance sheet

Shows a firm’s accounting value on a particular date. Also called the statement of financial position.

• Assets [Left Side]; Assets can be classified as being current or non-current. Non-current assets stay in the firm for a rather long time (>12 months). Current assets usually are inventory and cash. Non-current assets can be both tangible (computers, trucks) or intangible (patents or goodwill)

• Liabilities and Owners’ Equity [Right Side]; Liabilities can also be classified as being either current or non-current. Like current assets, current liabilities are in the firm for less than 12 months. Trade payables, for example, are a current liability. The difference between the total value of assets and the total value of liabilities is the shareholders’ equity (if the firm would sell all its assets and uses that money to pay off debts, whatever is residual belongs to the shareholders)
  In other words: Assets = Liabilities + Shareholders’ equity

• Net Working Capital: Current assets – Current liabilities, so the cash that is left as soon as the firm paid all of its bills. A healthy firm has NWC

• Market Value versus Book Value; The values shown in the balance sheet for the firm’s assets are the book values, which usually do not represent the asset’s actual worth. Under International Accounting Standards (IAS), financial statements can show assets in two ways

  • Historical cost model; assets are valued a what the firm paid for them

  • Revaluation model; presents an asset’s value as what it is worth in the market today

2: Income statement

Income statement which summarizes a firm’s performance over a period of time.

Revenues – Expenses = Income. This is the EBIT, earnings before interest and taxes. After paying the interest and taxes, we get the net income. The net income is often expressed in earnings per share (EPS).

Non-cash items are expenses, but they don’t affect the cash flow (depreciation costs for example).

Corporate tax rate = The tax rate that corporations have to pay.

Average tax rate = Your tax bill / your taxable income

Marginal tax rate = If you earn one more euro, the tax that you have to pay over that euro. The new tax flows.

3: Statement of cash flows

The cash flow identity:

Cash flow from assets = cash flow to creditors + Cash flow to shareholders.

The total cash flow is the sum of:

• Cash flow from operating activities: day-to-day activities of producing and selling.

• Cash flow from investing activities: firm’s long-term investments.

• Cash flow from financing activities: debt and equity choices.

What is ratio analysis?

A ratio analysis can be done in order to analyze and compare the financial ratios to see how healthy a company is.

1. Short-term solvency or liquidity measures

• Current ratio = A high current ratio indicates liquidity, but it also may indicate an inefficient use of cash and other short-term assets:

Current ratio = Current assets / Current liabilities

• Quick ratio = This ratio is regarding the inventory of a firm:

Quick ratio = (Current assets – Inventory) / Current liabilities

• Cash ratio = This ratio is interesting to short-term creditors.

Cash ratio = Cash / Current liabilities

2. Long-term solvency measures (leverage ratios)

• Total debt ratio = Takes into account all debts of all maturities to all creditors.

Total debt ratio = (Total assets – Total equity) / Total assets

There are two useful variations on the total debt ratio:

• Debt-equity ratio = Total debt / Total equity

• Equity multiplier = Total assets / Total equity

• Times interest earned ratio = This is also often called the interest coverage ratio. This ratio measures how well the company has its interest obligations covered.

Times interest earned ratio = Operating profit / Interest (TIE ratio)

• Cash coverage ratio = The TIE ratio is based on the operation profit, but this isn’t a good measure of the cash available to pay interest. This is because of the fact that depreciation and other non-cash expenses have been deducted out. So we define the interest with the cash coverage ratio:

Cash coverage ratio = (Operating profit + Non-cash deductions) / Interest

EBITDA (= Operating profit + non cash deductions) means earnings before interest, taxes, depreciation and amortization

3. Asset management (turnover measures)

Describes how efficiently, or intensively, a firm uses its assets.

• Inventory Turnover = The higher this ratio is, the more efficiently we are managing inventory. How fast we can sell our product.

Inventory turnover = Cost of goods sold / Inventory

If we know the inventory turnover, we can figure out how long it took on average to turn it over. This is the average days’ sales in inventory:

Days’ sales in inventory = 365 days / Inventory turnover

• Receivables Turnover = How fast we can collect on sales.

Receivables turnover = Sales / Trade receivables

Days’ sales in receivables = 365 days / Receivable turnover

Often called the average collection period (ACP).

• Payables Turnover = How long it takes to pay for supplier purchases.

Payables turnover = Credit purchases / Trade payables

Days’ purchases in payables = 365 days / Payables turnover

Often called the average payment period (APP).

• Asset Turnover Ratios = ‘Big picture’ ratios.

The net working capital turnover measures how much ‘work’ we get out of our working capital.

NWC Turnover = Sales / NWC

PPE Turnover = Sales / Property, plant and equipment

Total asset Turnover = Sales / Total assets

4. Profitability measures

Measure how efficiently a firm uses its assets and manages its operations. The focus is on the net income.

• Profit margin = A high profit margin is desirable.

Profit margin = Net income / Sales

• Return on assets (ROA) = This is a measure of profit per unit cash of assets.

Return on assets = Net income / Total assets

• Return on equity (ROE) = A measure of profit per asset value, a kind of measure of performance.

Return on equity = Net income / Total equity

These ratios are accounting rates of return. They are also called return on book assets and return on book equity.

5. Market value measures

• Earnings per share (EPS) = Net income / Shares outstanding

• P/E ratio = Prices per share / Earnings per share

Whether a P/E ratio is high or low depends on the expected future earnings growth rate. So that’s the PEG ratio.

PEG ratio = Price-earnings ratio / Earnings growth rate (%)

• Price-sales ratio = Price per share / Sales per share

• Market-to-book ratio = Market value per share / Book value per share

• Tobin’s Q = This ratio focuses on what the firm is worth today relative to what it would cost to replace it today. The market-to-book ratio focuses on the historical costs.

Tobin’s Q = Market value firm’s debt and equity / Replacement cost firm’s assets

What is the Du Pont Identity, or ROE?

The difference between ROE and ROA is a reflection of the use of debt financing.

Before proceeding to the explanation of the Du Pont Identity, the definition of ROE and ROA:
Return on equity = Net income / Total equity
Return on assets = Net Income / Total Assets

We can multiply ROE by Assets/Assets without changing anything (Assets/Assets equals one, and multiplying something by one has no effect at all):

Return on equity = (Net Income / Total Equity)
Return on equity = (Net Income / Total Equity) * (Assets/Assets)

rewriting this formula results in;
Return on equity = (Net income / Assets) x (Assets / Total equity)
This final equation results in the exact same outcome as the first and the second. It is just using mathematics to rewrite the formula in a different way.

Now that we have expressed the ROE as the product of two other ratios, ROA and the equity multiplier:

ROE = ROA x Equity multiplier = ROA x (1 + Debt-equity ratio)

The difference between ROE and ROA can be enormous, especially when a firm borrowed a lot of money. If we multiply the top and bottom by total sales we decompose ROE further (again, multiplying by (Sales / Sales) has the exact same effect as multiplying by 1):
ROE = (Sales / Sales) * (Net income / Assets) * (Assets / Total equity)
ROE = (Net income / Sales) * (Sales / Assets) * (Assets / Total Equity)

The ROA is now partitioned into its component parts: profit margin and total asset turnover. The last expression of the preceding equation is the Du Pont Identity, this is defined as:

ROE = Profit Margin * Total Asset Turnover * Equity Multiplier

The return on equity (ROE) is thus affected by three things:

• Operating efficiency (measured by the profit margin)

• Asset use efficiency (measured by the total asset turnover)

• Financial leverage (measured by the equity multiplier)

How does one use financial statement information?

The primary reason for looking at accounting information is that we don’t have, and can't reasonably expect to get, market value information. Firms will compare their performance via the ratios as discussed above. Financial statement information can be used for;

• Internal uses; Performance evaluation. Managers, for example, are frequently evaluated and compensated on the basis of accounting measures of performance such as profit margin and return on equity. Another example is that firms with multiple divisions use financial statements to compare the performance of those divisions. Is one outperforming the other? Why? Another important internal use is planning for the future, what can we expect?

• External uses; Financial statements are also very useful to parties outside of the firm, including creditors and potential investors. Financial statement information can also be used to analyze competitors, what happens if we launch a new product? Does our main competitor have the resources to step in and imitate us immediately? Finally, financial statement information can be useful when planning to acquire another firm.

Choosing a benchmark

When we evaluate a division or a firm based on its financial statements, we need a benchmark, or a standard of comparison. Some ways are:

1. Time trend Analysis, using history as a standard. For example; Did the company make changes that could allow it to use its current assets more efficiently?

2. Peer group Analysis, by identifying similar firms.

Problems with Financial Statement Analysis

When comparing firms, some events can give misleading signals. These days the major competitors and the natural peer group members in an industry are scattered around the globe. Therefore it’s difficult to compare financial statements across national border.

Different standards and procedures:

• Accounting procedures

• The end of the fiscal years

• Unusual or transient events

This chapter treats financial statements, taxes and cash flows. The goal of the chapter is not to be able to prepare a financial statement, but to recognize key relevant data that is needed to make decisions in the field of finance. Particular attention is paid to two important differences: (1) the difference between accounting value and market value; (2) the difference between accounting income and cash flow.

What is the present and future value of money? - Chapter 4

Key Notations:

• FV = Future value

• FVIF(r,t) = Future interest fator for a sum of money invested at r percent for t periods

• PV = Present value

• r = Interest rate or discount rate

• t = Number of periods

A very common problem faced by financial managers is how to determine the value today of cash flows expected in the future. The time value of money refers to the fact that money in your hand today is worth more in the future. One possible explanation for this phenomenon is the fact that you can earn interest over your money.

How does future value and compounding work?

When we want to know the value of a specific amount of money in, let’s say, 10 years, we want to know the future value.

We will start with a simple example, the single-period scenario. That is, I have a certain amount of money now, for instance €100, and put it in a savings account that gives me 5% interest. At the end of the year I will have €105. So the principal (what I had at the beginning) times the interest rate is what I will earn on my investment. Here, the bank borrows money from me, so I am the lender. The €105 in the future is a lump-sum payment. I am paid just once (my original deposit and the interest earned).

FV = principal * interest rate = 100 * 5% = 100 * 0.05 = 105

Now we will discuss the multiple period scenario. Consider the case we had in the single-period scenario; at the end of the year, I have €100 (my original deposit) and €5 (the interest earned). So in the next year, I will receive interest on both the €100 and the €5.

FV = principal * interest rate = 0.05 * €100 + 0.05 * €5 = €5.25

Compound interest = The interest earned on interest. To calculate the future value then, you have to multiply the initial amount you put on your account times the interest plus one for every year that you keep the money in your account. We assume that you do not add money in that time. The formula is:

Future value = deposit * (1 + r) * (1 + r), etc.

We will now make a simple equation for this. Therefore we use the FV (future value), the PV (present value), r (interest rate), and n (the number of time periods).

FV = PV * (1+r)ⁿ

To take the first example again, we get 5% interest over our principal of €100 for 6 years

FV = 100 * (1.05)⁶ = 134.0095 … ≈ 134.01

r is also described as the growth rate. The last part of the equation, (1+r)ⁿ is the FVIF (future value interest factor), which combines the time periods with the interest rate. You can use a table (Appendix A Table A.1) to look up the appropriate FVIF.

In the first example, the FVIF was (1.05)⁶ = 1.34009 … ≈ 1.34

How does present value and discounting work?

Now we want to know how much a certain amount in the future would be worth today. We start again with the single-period scenario. I want to buy a new laptop for €500 next year. How much should I put aside now to be able to have the money then? So we want to find the present value of the €500. Instead of the growth rate, we now need the discount rate. We can make the following equation:

PV = FV / (1+r)

In order to buy the laptop, and given that the interest rate is 6%, I need
PV = 500 / (1.06) = 471.69811

So instead of multiplying the amount we have now by the interest rate to know what we have in the future, we divide the amount we need in the future by the interest rate to know what we need now to get that amount.

For the multiple-period scenario we just have to add the n again: PV = FV * 1 / (1+r)ⁿ

The last part is the PVIF (present value interest factor), which can also be found in a table (Appendix A Table A.2)

Determining the discount rate

The basic PV equation; PV = FV_t / (1+r)^t

There are four parts in this equation [PV, FV, r, and t]. Given any of these (3 values known) the fourth can always be found. See Examples 4.9 – 4.12 on pages 90-92.

Example: We have an investment of 100 pounds that will double that amount in eight years. To see if this is a smart investment to make, we have to find the implicit discount rate, and compare that with the discount rate of similar investments. How?

Known is that we have a PV of 100 pounds, a FV of 200 pounds, and eight periods.

PV = FV_t / (1+r)^t

100 = 200 / (1+r)⁸

(1+r)⁸ = 200 / 100

(1+r)⁸ = 2

Three ways to solve for r

1. Use a financial calculator or a spreadsheet

2. Take the eighth root of both sides and then solve the equation, or raise to the power 1/8, which is the same thing
   The eighth root of (1+r)⁸ is (1+r), the eighth root of 2 is 2^(1/8) = 9%

3. Use a future value table. The Future Value Factor after eight years equals 2 (the amount doubles). If you look across the row corresponding eight periods in Appendix A.1, you will see that a future value factor of 3 corresponds to the 9% column

To put solution number two into a simple equation: r = (FV / PV)^1/n - 1

Finding the number of periods

Today you have €25.000 and you want to know how long it takes to get €50.000. Again:

The basic PV equation; PV = FV_t / (1+r)^t

There are four parts in this equation and given any of these (3 values known) the fourth van always be found. See Example 4.13 on page 92.

n = [ln(FV / PV)] / [ln(1+r)]

What are annuities and perpetuities? - Chapter 5

Key notations

• APR = Annual percentage rate

• C = Cash flow

• EAR = Effective annual rate of return

• g = Growth rate

• m = Number of times interest is compounded a year

• PVIFA = Present value interest factor for annuities

• q = Quoted rate

• r = Interest rate or discount rate

• t = Number of periods

How do calculations with multiple cash flows work?

The examples in chapter 4 all included a single cash flow; one amount of money that grew over time because of interest payments. This chapter examines multiple cash flows; depositing money each month (for example) on an account with interest payments.

Future value with multiple cash flows

Suppose you deposit €2000 at the end of each of the next 5 years. The current balance is zero, interest rate is 10%.

• Draw out a timeline.

• Nothing happens until the end of year 1, when the first €2000 investment is made. This investment earns interest for the next four years, not five. Also note that the last (fifth) investment is made at the end of year five so that it earns NO interest. In order to make a clear overview for yourself, it may be useful to draw a timeline and write calculations under each year. This may prevent you from being lost or missing details

• The amount additions should be added per year, including the interest per year.

Present value with multiple cash flows

As with future cash flows, there are two possible ways to calculate the present value of multiple cash flows.

1. Discount back one period at a time

You need €1000 in one year and €2000 in two years. If the interest rate is 9%, how much money do you need to day to cover these amounts in the future?
PV of 2000 = 2000/1.09² = 1638.36
PV of 1000 = 1000/1.09 = 917.43
Total PV = 1683.36 + 917.43 = 2600.79

2. Calculate present values individually and add them up
   You can earn €1000 every year with an investment, what is the present value?
   PV = (1000/1.06) + (1000/1.062²) + (1000/1.062³) + (1000/1.062⁴) + (1000/1.062⁵)

A small note about timing: As you may have seen, it is very critical when the cash flows occur. Unless stated otherwise, you should assume that cash flows occur at the end of a period.

What are annuities and perpetuities?

In the previous chapter we discussed how much one payment now will be worth in the future or how much one payment in the future will be worth now. But what if we put €100 in our savings account every year instead of only once? We use T₀ for now, T₁ for in one year, etc.

Present value

Suppose, you have an asset promising €500 at the end of each of the next three years. These cash flows, thus, are in the form of a three-year €500-annuity. If the interest rate is 10%, how much would we offer for this annuity? But what if there are 300 payments in total? Calculating present values individually and adding them up is not that efficient in that case. There is an easier way;

Annuity PV = PMT * [(1-(1+r)^t)/r] or Annuity PV = PMT * [(1/r) – (1/r(1+r)^t)]

The term PMT is multiplied with a factor that is called the Present Value Interest Factor for Annuities (PVIFA). Like the PVIF, this PVIFA can also be found in Appendix A, but now in Table A.3

Finding the payment

Suppose you want to repay your €100.000 loan in five payments. The interest rate is 18%, how much will each payment be? You can solve this very easily by just changing the already existing formula a bit. You know the Annuity PV (€100.000), the number of payments (5) and the interest factor (0.18). An example of a calculation for finding the payment is displayed below.

If Annuity PV = €100.000, then:

PV = C * [(1 – Present value factor) / r]

PV = C * {[1 – (1/1.18⁵)]/0.18}

PV = C * [(1 – 0.4371)/0.18]
PV = C * 0.31272
C = 100.000/3.1272
C = €31.978

Finding the rate

Take an insurance company telling you to pay you €1000 per year for 10 years if you will pay €6710 up front. In order to know if this is a good investment to make, you have to find out what rate is implicit in this 10-year annuity. If you know the implicit rate, you can very easily compare this investment to similar ones. Again, you can solve this very easily by just changing the already existing formula a bit. You know the Annuity PV (€6710), the number of payments (10) and the cash flows (€1000).

Solving an equation to find r (like we did in previous similar example) mathematically is impossible to do. Therefore, you should calculate the PVIFA, and then use the number of payments in order to find r.

6710 = 1000 * [(1 – Present value factor) / r]

6710 / 1000 = 6.71

PVIFA is 6.71. When looking up this factor in the row of 10 periods, you find 6,71 at 8%.

Future value

Sometimes it might be handy to know a shortcut for calculating the future value of an annuity.

FV = PMT x [(1+r)ⁿ – 1] / r

Where PMT is the periodical cash flow. The last part of the equation is the FVIFA (future value interest of an annuity). So FVIFA = [(1+r)ⁿ – 1] / r

When the payment is made at the end of the period, it concern an ordinary annuity. When it is made at the beginning, it is an annuity due. For the annuity due, the equation is slightly different:

FV = PMT x [(1+r)ⁿ – 1] / r x (1+r)

Perpetuities

When an annuity goes on forever, it is called a perpetuity. See Example 5.6 for an important example of a perpetuity. Because a perpetuity has an infinite number of cash flows, we can’t compute its value by discounting each one. The equation is the following:

PV = PMT / r

Growing annuities and perpetuities

Annuities very often have payments that grow over time at factor g. Take a lottery payout over a 20-year period and each year, the payment grows by 5%.

Growing annuity PV = PMT * [1 – (1 + g / 1 + r)^t / r – g]

How can you compare the rates?

At times, interest rates are quoted in deliberately deceptive ways to mislead borrowers and investors.

Effective annual percentage rates and compounding

If a rate is quoted at 10% compounded semi-annually, this actually means the investment pays you 5% each 6 months. But is 10% a year the same as 5% each half year? > €1 * 1.1 = €1.10 and €1 * 1.05² = €1.1025, making the actual rate 10.25% a year.

Nominal interest rate = The interest rate expressed in terms of the interest payment made each period. Also known as the stated or quoted interest rate

Effective annual percentage rate (EAR) = The interest rate expressed as if it were compounded once per year.

Calculating EAR

Suppose you have to choose what’s best among bank A 15% compounded daily, bank B 15.5% compounded quarterly and bank C 16% compounded annually. By calculating EAR, you know the interest rate per year for each of the banks.

EAR = [1 + (Quoted rate/m)]^m – 1

So EAR for bank A = [1 + (0.15/365)]³⁶⁵ – 1 = 16.18%

Annual percentage rate (APR) = The harmonized interest rate that expresses the total cost of borrowing or investing as a percentage interest rate.

What sort of loan types are there?

Discount loan = Simplest form of loan. The borrower receives money today and repays a single lump sum at some time in the future. Pure discount loans are common when the loan term is short – a year or less. You calculate the amount you can borrow as follows:
Suppose you are able to repay 25.000 in 5 years, and you want a 12% interest rate:
PV = 25.000 / 1.12⁵

PV = 25.000 / 1.7626

PV = 14.186

Interest-only loan = Pay interest each period, and repay the entire principal (the original loan amount) at some point in the future. If there is just one period, a discount loan and an interest-only loan are exactly the same. With a three-year, 10%, interest-only loan of €1000; the borrower pays 1000*0.1 = 100 at the end of the first and the second year. At the end of the third year, he borrower pays back the principal amount of 1000 and another 100 interest for the third year.

Amortized loan = With an amortized loan, the lender may require the borrower to repay parts of the loan amount over time. A simple way to do so would be to have the borrower pay the interest each period, plus some fixed amount. This approach is common with medium-term business loans. If you want to make calculations with amortized loans, make a amortization schedule. Suppose, you have a €5000, five-year loan at 9% interest, where you pay back €1000 each year. A schedule will look like this and helps you organize your data and prevents you from getting lost.

Determining the payment of an amortized loan

Determining the payment of the amortized loan is useful when the borrower has to make a single, fixed payment every month, which includes both interest and pay-back.

Again, a €5000, five-year loan at 9% interest loan.

Using the PV formula:

5000 = C * {[1 – (1 / 1.09⁵)] / 0.09}
5000 = C * [(1 – 0.6499) / 0.09]
C = 5000 / 3.8897
C = 1285.46

Now make an amortization schedule again. Here, you already know your total payment, instead of the principal paid in the first case.

What are bonds (in corporate finance)? - Chapter 6

Key notations

• C: Coupon

• FV: Face value of the bond

• h: Inflation rate

• PV: Present value

• r: Interest rate or discount rate

• t: number of periods

• YTM: Yield to maturity

What are bonds and what is bond valuation?

A bond is an interest-only loan, meaning the borrower will pay the interest every period, but none of the principal will be repaid until the end of the loan. Some terminology;

Coupon = The stated interest payment made on a bond

Face value = The principal amount of a bond that is repaid at the end of the term. Also called par value.

Coupon rate = The annual coupon divided by the face value of a bond.

Maturity = The specified date on which the principal amount of a bond is paid.

Bond values and yields

As time passes, interest rates change in the marketplace. To determine the value of a bond at a particular point in time, you need to know the number of periods remaining until maturity, the face value, the coupon and the market interest rate for bonds with similar features.

Yield to maturity = The rate required in the market on a bond

Suppose, the market interest rate gets higher than the bond interest rate >> The value of the bond drops, as investing money in something else than a bond is more attractive. The market interest rate gets lower than the bond interest rate >> The value of the bond rises, as investing money in a bond is more attractive than investing somewhere else.

So, in short:

Selling at discount means that the bond sells for less than its face value, the market rate (YTM) is higher than the coupon rate. Selling at premium means that the bond sells for more than its face value, the market rate (YTM) is lower than the coupon rate. In case of selling at discount, investing in bonds is less attractive than investing in similar projects in the market. In case of selling at premium, the opposite holds. Refer to pages 137 and 138 of the book for examples that illustrate the difference between selling at discount and selling at premium.

Now we can write a general expression for the value of a bond;

Bond value = C * [ (1 – 1 / (1 + r)^t) / r ] + F / (1 + r)^t, where

C * [ (1 – 1 / (1 + r)^t) / r ] is the present value of the coupons and F / (1 + r)^t is the present value of the face amount. The present value of the coupons reflect whether the market interest rate is higher or not. If the bond value is lower than its face value, the market interest rate was higher and vice versa.

Interest rate risk

Interest rate risk = Arises for bond owners from fluctuating interest rates. How much risk depends on how sensitive a bonds’ price is to interest rate changes. This depends on two things; time to maturity and coupon rate. Also, keep in mind;

• All other things being equal, the longer the time to maturity, the greater the risk.

• All other things being equal, the lower the coupon rate, the greater the risk

Finding YTM

Finding YTM actually comes down to ‘plug and chug’. If you know the par value of a bond is €1000 and the real price is €955,14 and the coupon rate is 8%, you know that the YTM has to be higher than 8% (bond value < face value, see above).

955.14 = 80 * {[1 – 1 / (1 + r)⁶] / 6} + [1000 / (1 + r)⁶]

In order to find the correct YTM, you have to do trial and error. Just plug in 9, 10 or 11 into the formula to get to your answer.

What else is there to know about bond features?

Securities issued by corporations can be either debt securities or equity securities. From a financial point of view, there are three main differences between debt and equity:

1. Debt is not an ownership of interest in a firm

2. The corporation’s payment of interest on debt is considered a cost of doing business, and is fully tax deductible. Dividends are not tax deductible

3. Unpaid debt is a liability of the firm. If not paid, creditors can claim the assets of the firm. This possibility does not hold when equity is issued

Indenture = The written agreement between corporation and the lender detailing the terms of the debt issue. It generally includes the following provisions:

• Terms; Corporate bonds usually have a face value in multiples of €1000. Registered form = The form of bond issue in which the registrar of the company records ownership of each bond; payment is made directly to the owner of the record. Bearer form = The form of bond issue in which he bond is issued without record of the owner’s name; payment is made to whomever holds the bond

• Security; Debt securities are classified according to the collateral and mortgages used to protect the bondholder. Collateral is a term that means securities that are pledged as security for payment of debt. Mortgage securities are secured by a mortgage on the real property of the borrower. The property involved usually is real estate – land or buildings.

  1. Unsecured bond = An unsecured debt security, usually with a maturity of 10 years or more

  2. Note = An unsecured debt security, usually with a maturity under 10 years

• Seniority; Indicates preference in position over other lenders

• Repayment; Bonds can be repaid at maturity, at which time the bondholder will receive the stated or face value of the bond. Sinking fund = An account managed by the bond trustee for early bond redemption

• The call provision = An agreement giving the corporation the option to repurchase a bond at a specified price prior to maturity.

  1. Call premium = The amount by which the call price exceeds the par value of a bond

  2. Deferred call provision = A call provision prohibiting the company from redeeming a bond prior to a certain date

  3. Call-protected bond = A bond that, during a certain period, cannot be redeemed by the issuer

• Protective covenants = A part of the indenture limiting certain actions that might be taken during the term of the loan, usually to protect the lender’s interest. Can be classified in two types:

  1. Negative; ‘thou shall not’. It limits or prohibits actions the company might take [the firm cannot pledge any assets to other lenders | the firm cannot merge with another firm]

  2. Positive; ‘thou shalt’. Specifies an action the company agrees to take, or a condition the company must abide by [the company must maintain its working capital at or above some specified level | the firm must maintain any collateral or security in good condition]

What are bond ratings?

Firms frequently pay other firms to have their debt rated. The three leading bond-rating firms are Moody’s, Standard & Poor’s (S&P) and Fitch. The debt ratings are an assessment of the creditworthiness of the corporate issuer. Definitions of creditworthiness used are based on how likely the firm is to default, and on the protection that creditors have in the event of a default. Refer to Table 6.3 on page 145 for bond ratings.

What different types of bonds are there?

The thus far discussed bonds are corporate bonds. But there are more types of bonds.

Government bonds

The biggest borrowers in the world are governments. The thing with government bonds is that you always get your money back, as governments cannot go bankrupt.

Zero coupon bonds

Zero coupon bonds = A bond that makes no coupon payments and is thus initially priced at a deep discount. Also called pure discount bonds. Zero coupon bonds use semi-annual periods to be consistent with coupon bond calculations.

Floating rate bonds

With floating rate bonds the coupon payments are adjustable. They have the following features;

• The holder has the right to redeem the note at par on the coupon payment date after some specified amount of time (put provision)

• The coupon rate has a floor and a ceiling, meaning that the coupon is subject to a minimum and a maximum (these minimum and maximum are called the collar)

Other types of bonds

Catastrophe bonds = Issued at a large discount to par value and lose all their value if there is a major specific catastrophe in a stated region.

Warrant = Gives the buyer of a bond the right to purchase shares of equity in the company at a fixed price.

Income bonds = Similar to conventional bonds, except that coupon payments depend on company income.

Convertible bond = Can be swapped for a fixed number of shares of equity any time before maturity at the holder’s option.

Put bond = Allows the holder to force the issuer to buy back the bond at a stated price.

What are inflation and interest rates?

Real rates = Interest rates or rates of return that have been adjusted for inflation.

Nominal rates = Interest rates or rates of return that have not been adjusted for inflation

Inflation affects how much you can buy with your money. 5% inflation means that everything became 5% more expensive.

An investment with a present value of €100 and a future value of €115,50 has a 15.5% rate of return. Adjusted to inflation, however, 115,50/1,05=€110, meaning that real return is 10%.

The Fisher effect

Fisher effect = The relationship between nominal returns, real returns and inflation.

R = nominal rate, r = interest rate, h = inflation rate

1 + R = (1+r) * (1+h)

R is approximately equal to r+h

Inflation and present values

Always make sure that you discount nominal cash flows at a nominal inflation rate, or discount real cash flows at a real rate. As long as you are consistent, you will get the same answer. See the example at pages 157 and 158.

What are the determinants of bond yields?

There are many determinants of a bond’s yield. The yield reflects a variety of factors. Some of them are common to all bonds, some of them are very specific to the issue under consideration.

The term structure of interest rates

Generally speaking, short-term and long-term interest rates are different. Sometimes, short-term rates are higher than long-term rates, sometimes lower.

Term structure of interest rates = The relationship between nominal interest rates on default-free, pure discount securities and time to maturity. In other words: the pure time value of money for different lengths of time. Long-term rate > short-term rate; term structure is upward sloping. Short term rate > long-term rate; term structure is downward sloping. What determines the term structure? Three basic components:

1. Real rate of interest; the compensation that investors demand for forgoing the use of their money

2. Rate of inflation; future inflation may erode the value of cash that will be returned
   Inflation premium = The portion of a nominal interest rate that represents compensation for expected future inflation

3. Interest rate risk; this has to do with the life of a bond. A long-term bond has much greater risk of loss resulting from changes in interest rates than do shorter-term bonds
   Interest rate risk premium = The compensation investors demand for bearing interest rate risk

The yield curve

Treasury yield curve = A plot of the yields on Treasury notes and bonds relative to maturity. Figure 6.4 on page 149 shows the yield curve for the UK and the Eurozone late 2013, you can use this as an example. The Treasury yield curve and the term structure of interest rates (previous section) are almost the same thing. The term structure, only, is based on pure discount bonds, whereas the Treasury yield curve is based on coupon bond yields. The Treasury yield curve relies on the same three basic components as does the term structure of interest rates.

Treasury notes and bonds have three very important features: they are default-free (except for Eurozone countries), taxable, and highly liquid. This is not true of bonds in general. The following three components contribute to yields:

1. Credit risk, or the risk of default. Investors know that in most countries, issuers other than the Treasury may or may not make all the promised payments on a bond. Default risk premium = The portion of a nominal interest rate or bond yield that represents compensation for the possibility of default.

2. Government bonds are tax-free and have much lower yields than taxable bonds. Investors demand the extra yield on a taxable bond as compensation for the unfavorable tax treatment. Taxability premium = The portion of a nominal interest rate or bond yield that represents compensation for unfavorable tax status.

3. Bonds also have varying degrees of liquidity. There are enormous numbers of bond issues, meaning if you wanted to sell quickly, you would probably not get as much of a price as you could otherwise. Liquidity premium = The portion of a nominal interest rate or bond yield that represents compensation for lack of liquidity.

What is equity valuation? - Chapter 7

Key Notations

• D: Dividend

• P: Share price

• g: Growth rate

• r: Interest rate or discount rate

• t: number of periods

What is share valuation?

It is more difficult to value share prices than bond values. Cash flows are not known in advance, the life of a share is forever and there is no easy way to observe the rate of return.

Current share price: P₀ = (D₁ + P₁) / (1 + R). Where P₁ is the price in one period. R is the required return on the investment. The problem is, we have to find out P₁ and that’s difficult. If we fill in P₁ and P₂ we get:

P₀ = [D₁ / (1+R)¹] + [D₂ / (1+R)²] + [D₃ / (1+R)³] + [P₃ / (1+R)³]

We can push the problem of finding the share price off into the future forever, in the example above we pushed the problem to year three, so we assume that the share is sold in year three. What we see is that the share price today (P₀) is equal to the present value of all of the future dividends. The element [P₃ / (1+R)³] is added, because if you assume that you sell your share in the third year, you have to add your yield of selling the share as well.

Pattern of future dividends

• Zero growth rate
  In the case of zero growth, the dividend is always the same, so the share price can be viewed as an ordinary perpetuity with a cash flow equal to D every period, that in theory can go on forever.

The per-share value; P0 = D / R.

• Constant growth rate

The dividend t periods in the future; Dt = D0 x (1 + g)t. A growing perpetuity is an asset with a constant growth rate forever.

With the dividend growth model we can get the share price at any point in time;

Pt = (Dt x (1 + g)) / (R – g).

We can also calculate Pt in a different way, for example P4 = P0 x (1 + g)4.

• Non-Constant growth

1. Make a time line and watch when the growth is constant and when it’s non-constant. Notice when constant growth starts.

2. Use the constant growth model; determine the price at the end of the non-constant growth. For example; P3 = D3 x (1+g) / (R-g)

3. Now we can calculate the total value of the equity;

P0 = [D1 / (1+R)1] + [D2 / (1+R)2] + [D3 / (1+R)3] + [P3 / (1+R)3]

This is the present value of the first three dividends plus the present value of the price at P3.

• Two-Stage growth

• The dividend grows first at a rate of g1 for t years and then at a rate of g2 thereafter forever.

• First stage: Pt = [D0 x (1+g1)t x (1+g2)] / (R - g2)

• Second part: present value of the share price when the second stage begins at time t.

P0 = (D1 / R-g1) x [1 – ((1+g1) / (1+R)t)] + (Pt / (1+R)t)

Required return = The required return (R) consists of two components; the dividend yield and the capital gains yield. We can calculate the required return, R= (D₁ / P₀) + g%

This equation tells us that R has two components: D₁ / P_0, the dividend yield = An equity’s expected cash dividend divided by its current price and g, the capital gains yield = The dividend growth rate, or the rate at which the value of an investment grows. An example to illustrate this:

Suppose, we have an equity worth €20 per share. The next dividend will be €1 per share. You expect dividends to grow at 10% per year more or less indefinitely. What is the return of this equity if this is correct?

R = dividend yield + capital gains yield

R = D₁ / P₀ + g

R = 1/20 + 10%

R = 5% + 10%
R = 15%

This answer can be verified by calculating P₁ and using the 15% as R

P₁ = D₁ * (1 + g) / (R – g)

P₁ = 1 * 1.1 / (0.15 – 0.10)
P₁ = 1.10 / 0.05

P₁ = €22

This €22 is 20 * 1.1, so the share price has grown 10%, like expected.

Table 7.1 on page 179 offers a summary of equity valuation.

The price-earnings ratio

The P/E-ratio is the share price divided by earnings per share. P/E ratios are used by analysts to compare equity values across an industry, and they are used to complement other methods of equity valuation. The dividend growth model tells us that share values increase with growth rates, and so it implies that companies with high growth opportunities will have higher P/E ratios.

What are ordinary and preference shares?

Ordinary equity = Equity without priority for dividends or in bankruptcy. Preference shares differ from ordinary equity. The holders of preference shares hold equity with dividend priority over ordinary shares, normally with a fixed dividend rate, sometimes without voting rights.

States value

Preference shares have a stated value, with the cash dividend being described as a percentage of the stated value.

Cumulative and non-cumulative dividends

Preference share dividends are not like interest payments on bonds. The board of directors may decide not to pay the dividends on preference shares, and their decision may have nothing to do with the current net income of the corporation. Dividends payable on preference shares are cumulative or non-cumulative.

Cumulative dividends = If not paid in a particular year, they will be carried forward as an arrearage. Both the accumulated (past) preferred dividends and the current preferred dividends must be paid before the ordinary shareholders receive anything.

Note: unpaid dividends are not debts of the firm.

How do stock markets work?

Shares of equity are bought and sold on various stock exchanges. The stock market consists of a primary market and a secondary market.

Primary market = The market in which new securities are originally sold to investors. Here, companies sell securities to raise money.

Secondary market = The market in which previously issued securities are traded among investors.

Securities transactions involve dealers and brokers. A dealer has an inventory, for example a car dealer. He can buy and sell his products at any time. A broker brings buyers and sellers together. He doesn’t have an inventory. An example is a real estate broker. The bid price is the price a dealer is willing to pay, and the selling price is the ask price. The difference between those two prices is the spread, this can be the dealers profits.

What are investment criteria? - Chapter 8

Key Notations

• AAR: Average accounting return

• IRR: Internal rate of return

• NPV: Net present value

• PI: Profitability index

• R: Discount rate

What is net present value?

When judging a potential investment, we look at the effect that the investment has on the value of the firm’s shares. We do this with the net present value approach. An investment has to be worth more than it costs to acquire. The management has to add value. They have to think ahead of time, will the investment be worth more in the marketplace?

Example: Suppose you buy a wooden table at a thrift shop for €50. The table is in poor condition and you decide to buy some tools and paint for €60 to get it back in its proper shape. In total, you paid €110 for the table. When its finished, you decide to sell the table on the market, and someone offers you €150. The net result is that you created €40 in value, this is your value added. This is what capital budgeting is all about- trying to determine whether a proposed investment will be worth more than it costs once it is in place.

Net present value (NPV) = investment’s market value – its cost. This is a measure of the value created or added. Firms have to search for investments with a positive net present value.

Estimating the net present value

You can’t always estimate the future market value. So we must also be able to estimate the value by other means. We can estimate the future cash flows of the investment. Then we discount the cash flows to estimate the present value. We discount the cash flows with the discounted cash flow valuation.

Example: Revenues from a project will be €20.000 per year, assuming everything goes as expected. Costs of the project will be €14.000 per year. The project life time is 8 years. Plant, property and equipment have a salvage value of €2000 and the project costs €2000 and the project costs €30.000 to launch. 15% discount rate is used. 1000 shares of equity outstanding, what is the effect on the share price of taking this investment?

Net cash inflow: 20.000 – 14.000 = 6.000 per year

Single lump-sum inflow in 8 years = 2.000

Present value = 6000 * [1 – (1/1.15⁸)] / 0.15 + (2000 / 1.15⁸) >> How to solve problems like these is discussed in chapter 5
Present value = (6000 * 4.4873) + (2000/3.0590)

Present value = 26924 + 654

Present value = €27.578

The costs made were €30.000, so:

NPV = -30.000 + 27.578 = - €2422

Conclusion: This is not a good investment.

Present value = cash inflow x [1 – (1/(1+R)^t)] / R + (single lump-sum inflow / (1+R)^t.

NPV = the cost of the investment + the present value of future cash flows.

After calculating the NPV we can calculate the impact of taking the project on the value per share. Loss of value per share in the previous case: 2422/1000 = €2.42 loss per share.
The net present value rule is thus: An investment should be accepted if the net present value is positive, and rejected if it is negative.

What is the payback rule?

Another way of estimating whether an investment should be made or not is using the payback rule.

Example: Initial investment is €50.000. In year 1, €30.000 is recovered. In year 2, the remaining €20.000 is recovered. This investment ‘pays for itself’ in two years.

Payback period = The amount of time required or an investment to generate cash flows sufficient to recover its initial costs.

The payback rule: An investment is acceptable if its calculated payback period is less than some pre-specified number of years.

It is also possible that a payback period is, let’s say, two years and eight months.

Example: Initial investment is €60.000, cash flows are €20.000 in year one and €90.000 in year two. The cash flows over the first two years are €110.000, meaning the project pays itself back somewhere in year two. If the initial amount was €60.000, and after year 1 €20.000 is recovered, €40.000 is left to be recovered. €40.000 is 40.000/90.000 = 4/9 of the amount of year 2’s cash flow. The investment pays for itself after 1 4/9 years.

You can also use the payback rule to investigate different projects. Table 8.1, for example, illustrates 5 projects, with year 0 being the costs, or the initial investment, of each project. See for yourself which project is best as a way to practice. The answer is given on page 202 of the book.

Shortcomings of the payback rule are that it is:

• Ignoring the time value of money

• Ignoring any risk differences

• Ignoring cash flows beyond the cut-off date (date that the investment pays for itself)

• Pushing us towards short-term investments.

Positive features:

• Low cost of analyzing, easy to understand

• Biases us towards short-term projects, so towards liquidity

• Later cash flows are probably more uncertain

What is a discounted payback?

A shortcoming of the payback rule was that it ignores the time value of money. This problem is fixed by the discounted payback period.

Discounted payback period = The length of time required for an investment’s discounted cash flows to equal its initial cost.

The discounted payback rule: An investment is acceptable if its discounted payback is less than some pre-specified number of years.

Example: The required rate of return on new investments is set at 12.5%. The new investment costs €300 and has cash flows of €100 for five years. It shows both the discounted and the undiscounted cash flows. The regular payback is exactly three years. The discounted cash flows total €300 after four years. Using the discounted payback method, we get the money of our investment, and the interest we could have earned elsewhere if we wouldn’t have invested the money after four years.

Negative features:

• May reject positive NPV investments

• Ignores cash flows beyond the cut-off date

• Against long-term projects

Positive features:

• Time value of money included

• Easy to understand

• Won’t accept a project with a negative NPV

• Biased towards liquidity

What is the average accounting return?

The average accounting return (AAR) = Average net income / Average book value.

AAR rule: A project is acceptable if its AAR exceeds a target average accounting return.

Some steps for calculating the AAR:

• The average book value = (the initial investment + the residual value) / 2.

• The average net income = the sum of the net income in the depreciation years / number of years.

• AAR = Average net income / Average book value.

A big advantage of the AAR is that is can almost always be computed. The information needed for this calculation is almost always available.

Weaknesses:

• Ignores time value

• Lack of an objective cut-off period

• Doesn’t look at the right things. Net income and book value are poor substitutes of cash flow and market value.

What is the internal rate of return?

The most important alternative to the NPV is the internal rate of return.
Internal rate of return = The discount rate that makes the NPV of an investment zero.

IRR rule: An investment is acceptable if the IRR exceeds the required return. Otherwise it should be rejected.

The IRR is related to the NPV. An investment is taken when the NPV is equal or higher than zero. When the NPV is zero the investment is a break-even proposition.

Example: We have a simple investment of €100 that pays €110 in one year. The IRR on this investment obviously is 10% (100 * 1.1 = 110). If we want to calculate NPV for this simple investment:
NPV = -100 + [110 / (1 + R)]

To find the IRR we have to set the NPV equal to zero and solve it to find the discount rate. We need to use trial and error, so try to find the discount rate where the NPV is zero by filling in some numbers.

NPV = 0 = -100 + [110 / (1 + R)]

100 = 110 / (1 + R)

1 + R = 110 / 100 = 1.1

R = 10%

So: the IRR on an investment is the required return that results in a zero NPV when used as the discount rate.

For an investment with multiple cash flows, the trial and error method as already discussed in chapter 4 should be used in order to find the correct rate.

The relationship between the IRR and the NPV can be illustrated in a net present value profile.

Net present value profile = A graphical representation of the relationship between an investment’s NPV and various discount rates.

On the horizontal side the R (%) and on the vertical side the NPV. Where the curve cuts through the x-axis, the NPV is equal to zero and IRR can be found.

Do IRR and NPV rules always lead to identical decisions? Yes. As long as two very important conditions are met:

1. The project’s cash flows must be conventional, meaning the first cash flow is negative and all the rest are positive

2. The project must be independent, meaning that the decision to accept or reject the project does not affect the decision to accept or reject any other.

When these conditions aren’t met, problems arise:

Non-Conventional cash flows

When the cash flows are non-conventional (after the first negative cash flow, another negative cash flow follows), we can get the multiple rates of return problem. This is when there is more than one discount rate that will make the NPV of an investment zero. Even though you might wonder which one is right, the answer is that they both are.

Mutually exclusive investments

Two investments are mutually exclusive means that you have to choose between the investments, you can’t have both. So we have to find out which one is the best. The best investment is the one with the largest NPV. A problem with this is that the NPV depends on our required return. The IRR can be misleading because it tells us the discount rate where the NPV is zero. But at other discount rates the NPV of another project can be higher. So instead of looking at the IRRs we have to look at the relative NPVs. We can use the investments’ NPV profiles.

Investing or Financing?

• Investment-type cash flows: the higher the discount rate, the smaller the NPV.

• Financing-type cash flows: the higher the discount rate, the higher the NPV. You first buy the investment and later pay for it. Only take a project with financing-type cash flows if it is an inexpensive source of financing. And if its IRR is lower than your required return.

Advantages and disadvantages IRR

Advantages:

1. IRR is closely related to NPV, often leading to identical decisions

2. IRR is easy to understand and communicate

Disadvantages:

1. IRR may result in multiple answers, or not deal with non-conventional cash flows

2. IRR may lead to incorrect decisions in comparisons of mutually exclusive investments

Modified internal rate of return (MIRR)

To address some of the problems that arise with standard IRR, it is often proposed that a modified one can be used, MIRR.

• Discount approach: Before calculating the IRR, we discount all negative cash flows to the present at the required return and add them to the initial cost.

• Reinvestment approach: Before calculating the IRR, we compound all cash flows (except the first one) to the end of the project’s life. We don’t take the cash flow out of the project, but we reinvest them.

• Combination approach: This is a combination of the discount and the reinvestment approach. The negative cash flows are discounted to the present, the positive cash flows are compounded to the project’s end.

What is the profitability index?

The profitability index is also called the benefit-cost ratio. It measures the value created per cash unit invested.

PI = Present value future cash flows / initial investment.

If projects are mutually exclusive, pick the one with the highest NPV. This is the same ranking problem as we had with the IRR.

Advantages of the Profitability Index:

• Often leading to identical decisions as with the NPV

• Easy to understand

• Useful when available investment funds are limited

A disadvantage of the PI is that it may lead to incorrect decisions when we have mutually exclusive investments.

How does capital budgeting work in practice?

When evaluating a project, the NPV can be estimated. But the true NPV is unknown. So we have to seek for clues to help us judge if the estimated NPV is reliable. So firms use multiple criteria when evaluating a proposal. When we have a project in which we have little confidence, it’s good to do some more analysis.

Investment criteria summary

Discounted cash flow criteria:

1. Net present value

2. Internal rate of return

3. Modified internal rate of return

4. Profitability index

Payback criteria

• Payback period

• Discounted payback period

Accounting criterion

• Average accounting return

Decisions on capital investment? - Chapter 9

Key Notations

• AAR: Average accounting return

• EAC: Equivalent annual cost

• EBIT: Earnings before interest and taxes

• NPV: Net present value

• OCF: Operating cash flow

What are project cash flows?

What is a relevant cash flow for a project? Relevant cash flows are changes in the firm’s overall future cash flow that comes about as a direct consequence of the decision to take a certain project. The relevant cash flows for a project are incremental cash flows.

Incremental cash flows = The difference between a firm’s future cash flows with a project and those without the project.

Once the effect of undertaking the proposed project on the firm’s cash flows is identified, a focus on the project’s resulting incremental cash flows is needed. This is the stand-alone principle.

What are incremental cash flows?

Some things to consider when you make a project analysis:

• Sunk costs = A cost that has already been incurred and cannot be removed, and which therefore should not be considered in an investment decision. So when analyzing a project, be sure to exclude the sunk costs
  Example: You hire a consultant to evaluate if you should launch a project. Whether you launch or not, you will have to pay for the consultant.

• Opportunity costs = The most valuable alternative that is given up if a particular investment is undertaken.
  Example: A firm has excess space that it can rent to another firm, in order to earn something on the space. The firm with excess space does not have to buy anything, it already owns the room, but still there are costs involved; what if the firm would have sold the excess space instead of renting it? These are opportunity costs

• Side effects; A project can have side, or spillover, effects. These effects can be good and bad. Erosion = When the new project has a negative effect on an existing project. The erosion is only relevant when the sales wouldn’t be lost if the new project wasn’t accepted, as sales can also decrease as a result of competition.
  Example: HP used to sell printers for €500-600, but this price declined to below €50 by 2014. Instead of being concerned, HP realized that the big money is in the consumables that printer owners buy to keep their printers going, such as inkjet cartridges, laser toner cartridges, laser toner cartridges and special paper. The profit margins for these products are substantial

• Projects usually require firms to invest in net working capital in addition to long-term assets. A project generally requires to have some cash on hand to pay expenses.

• Financing costs. We don’t include interest paid in the analysis of a proposed investment. This is because we are interested in cash flow generated by the assets of a project. Interest isn’t a component of cash flow from assets.

• Measure cash flow when it occurs, not in an accounting sense.

• Always interested in after-tax cash flow

What are pro forma financial statements and how do they relate to project cash flows?

With the help of pro forma financial statements, projected cash flows from the project can be developed. Once cash flows are present, the value of the project can be estimated, with techniques that were described in chapter eight.

Pro-forma financial statements = Financial statements projecting future years’ operations. In order to prepare these statements, estimates of quantities are needed.

Format of a projected income statement

Sales

Variable costs -

Gross profit

Fixed costs

Depreciation -

Profit before taxes

Taxes (%) -

Net income

Format of projected capital requirements

Net working capital

Net non-current assets +

Total investment

To develop cash flows from a project, we need the cash flows of three components: cash flows from operating activities, financing activities, and investing activities. The cash flows attributable to a project are those cash flows that arise directly as a result of making the investment.

Project cash flow = Project operating cash flow – Project capital spending.

Thus, we ignore the financing activities because we are only interested in the cash flows from the project.

Project operating cash flow = Net income + Depreciation – Increase (or + Decrease) in Net Working Capital.

Net working capital and capital spending = Total investment. The number of the changes in NWC has to appear at some time in the future.

What else is there to know about project cash flow?

Net Working Capital examined

In calculating the operating cash flows, the fact that some of the sales or purchases can be on credit was not considered. These sales and purchases on credits are the ‘Trade Receivables’- and ‘Trade Payables’ – accounts. Given this information,

Total cash flow = Operating cash flow – Change in NWC – Capital spending

Cash inflow = Sales – Increase in Trade Receivables

Cash outflow = Costs – Increase in Trade Payable

Cash flow = Cash inflow – Cash outflow

Depreciation

Accounting for depreciation is a non-cash deduction. Depreciation has cash flow consequences only because it influences the amount of taxes payable. The way assets are depreciated is thus of great importance.

Straight-line depreciation = (initial value – residual value) / life in years

Reducing-Balance depreciation = A depreciation method allowing for the accelerated write-off of assets under various classifications.

Here the asset is depreciated with a percentage per annum.

1. Initial value year 1 – Depreciation (%) = Written-down value year 1.

2. Initial value year 2 (= Written-down value year 1) – Depreciation (%) = Written-down value year 2.

3. Etc.

At the end of the life the rest of the value minus residual value is depreciated.

For an example of the Reducing-Balance depreciation, refer to the table on page 238.

Book value vs. Market value

The book value of an asset as a result of the method of depreciation can differ from the actual market value of an asset. In the case of a market value exceeding the book value, taxes have to be paid over the difference between the sale price (market value) and the book value, because of the simple fact that the asset in this case is over-depreciated, which is beneficial for the company.

What are alternative definitions of operating cash flow?

There exist different approaches to operating cash flow that all measure the exact same thing. Not one approach is better or less than the other.

The kind of approach you use is determined by the circumstances.

• Basic approach:

OCF = EBIT + Depreciation – Taxes, with
EBIT = Sales – Costs – Depreciation
Taxes = EBIT * T

• The bottom-up approach:

OCF = Project net income (= EBIT-Taxes) + Depreciation

This calculation is only correct when there is no interest expense.

• The top-down approach:

OCF = Sales – Costs – Taxes

• The tax shield approach:

OCF = (Sales – Costs) x (1 – T) + Depreciation x T

The OCF consists of two components. The project’s cash flow and the depreciation tax shield. Depreciation tax shield = The tax saving that results from the depreciation deduction, calculated as depreciation multiplied by the corporate tax rate. The tax saving arises because depreciation expenses are not a cash outflow, but do reduce taxable income

What is discounted cash flow analysis?

There are three common cases that require a discounted cash flow analysis. The first involves investments aimed at improving efficiency and cutting costs, the second case comes up when a firm is involved in submitting competitive bids, the third arises in choosing between equipment options with different economic lives.

1. Evaluating cost-cutting proposals
   Example: We want to automate some part of an existing production process, which is going to cost €80.000 to buy and install necessary equipment. The automation will save €22.000 per year. The equipment has a five year life and is depreciated with the straight line method to zero, but will actually be worth €20.000. Tax rate = 34%; discount rate = 10%. Should we automate? In order to make this decision, you have to calculate the Operating Cash Flow and the Net Present Value.

2. Setting the bid price
   This situation occurs when a competitive bid should be submitted to win a job. The winner is whoever submits the lowest bid. In this case, you have to decide on what the lowest price is you can possibly charge in order to remain profitable. This requires you to evaluate costs, determine your required rate of return and calculate the amount of sales you need.

3. Evaluating equipment options with different lives
   Here, the most cost-effective alternative should be chosen. The approach here is necessary only under two special circumstances. The first is that the possibilities under evaluation have different economic lives. The second is that we shall need whatever we buy more or less indefinitely. In this case, you have to calculate the present value of the costs of the alternatives, which are the equivalent annual costs. Calculating EAC involves finding an unknown payment amount, by first calculating the annuity factor (how you find an annuity factor is thoroughly discussed in earlier chapters), and then solve the following equation:
   PV of costs = EAC * Annuity factor

How to analyze and evaluate projects? - Chapter 10

Key Notations:

• D: Depreciation

• DCF: Discounted cash flow

• DOL: Degree of operating leverage

• FC: Total fixed cost

• NPV: Net present value

• P: Price per unit

• Q: Total quantity of output

• S: Total sales = P x Q

• T: Tax rate

• TC: Total cost

• v: Variable cost per unit

• VC: Total variable cost

How can you evaluate the NPV estimates?

We can estimate cash flows only on what we know today. So we don’t know the exact cash flows in the future and we can’t know the exact NPV.

So we have a forecasting risk. This is the possibility that some errors lead to incorrect decisions. We can also call this the estimation risk. This can happen when we are overly optimistic about the future. As a result the projected cash flows don’t reflect realistically the future cash flows.

We have to discover the areas with potential errors. Try to assess the economic ‘reasonableness’ of the estimates we make.

When we have estimated the NPV to be positive. We need to find why it’s positive, the source of value. Also consider the degree of competition in that market and the potential competition (success attracts imitators and competitors). When the competition is very high, it’s rare to have a positive NPV.

What is the What-if analysis?

Assess the degree of forecasting risk and identify the most critical components of success or failure of an investment.

First we make a base case. This is the estimated NPV, which is based on the projected cash flows. Then we put an upper and lower bound on the components of the project. It’s unlikely that the true average of the possible values is outside the range.

Scenario analysis

We ask what-if questions and then investigate the changes in the NPV estimates. We will find the worst-case and the best-case scenario. These two scenarios tell us the minimum and the maximum NPV of the project. We can better call these scenarios optimistic and pessimistic.

Scenario analysis tells us what could happen, but it doesn’t tell us if we should take a project.

Sensitivity analysis

To discover how sensitive the estimated NPV is to the changes in one variable. When the NPV is sensitive to small changes in the value of a project’s component, then that forecasting risk is high. We can calculate this sensitivity on components by comparing the base case scenario with the worst and best case scenarios.

The bigger the difference between these scenarios, the bigger the sensitivity. A sensitivity analysis is useful for seeing which variables need the most attention. The higher the sensitivity of the NPV to changes in a variable, the higher the degree of forecasting risks.

Simulation analysis

A combination of a sensitivity analysis and a scenario analysis is called a simulation analysis. Not only the different variables change (as with a scenario analysis), but also the values changes (as with a simulation analysis). This gives a large number of possible outcomes, therefore preferably a computer program should be used. Interpreting the results and basing decisions on these results can be difficult, but computers are getting better and better at doing so.

What is a break-even analysis?

The sales volume is a crucial variable for a project. To analyse the relationship between profitability and sales volume we use the break-even analysis. We can compare this analysis with the payback period.

• Variable costs (VC): Depends on the quantity of output. When production is zero, the variable costs are zero.

Total variable cost = Total quantity of output x Cost per unit of output.

VC = Q x v

• Fixed costs (FC): Don’t change during a particular time, a quarter or a year. We can see the fixed costs as sunk cost, because we have to pay it no matter what.

• Total costs (TC): TC = VC + FC.

Marginal (or incremental) cost is the change in costs as a result of a small change in output.

Accounting break-even

This is the sales level where the project net income is zero. So this is when revenues are equal to the total costs.

Calculate the break-even point: Q = (FC + D) / (P – v)

Why we should use the accounting break-even:

1. Easy to calculate and explain

2. If a project doesn’t break even, it reduces total earnings

3. If a project just breaks even, it loses money because of financial or opportunity cost

Cash flow and accounting break-even

When a project breaks even, the cash flow will equal the depreciation. When a project does better than break even, the payback is shorter than the project’s life and it has a positive rate of return.

When a project breaks even on an accounting basis it has a negative NPV and a zero return.

What is the relationship between sales volume and operating cash flow?

We can see the relationship of between operating cash flow and sales volume through the following formula:

OCF = (P – v) x Q – FC

When we will in some number we get: (40-20) x Q – 500 = - 500 + 20 x Q

So the relationship is: A straight line with a slope of 20 and a y-intercept of – 500.

Different break-even measures:

1. General break-even.

Q = (FC + OCF) / (P – v)

2. Accounting break-even = when net income is zero.

Q = (FC + D) / (P – v).

3. Cash break-even = when operation cash flow is zero.

So we put a zero for OCF: Q = (FC + 0) / (P – v)

4. Financial break-even = when the NPV of a project is zero.

Q = (FC + OCF*) / (P – v)

OCF* is the level of OCF that results in a zero NPV. OCF* can be calculated as follows: Investment = OCF x (n year annuity factor at % return on its investment)

What is operating leverage?

The degree to which a firm or project is committed to its fixed costs. A firm with high operating leverage is said to be capital intensive.

When evaluating a project, it’s important to measure the operating leverage. When a firm has a high degree of operating leverage, they have to deal with the potential danger from the high forecasting risk. It’s important for projects to have a lowest possible degree of operating leverage.

The degree of operating leverage (DOL) is the percentage change in OCF relative to the percentage changed in the quantity sold.

DOL = 1 + FC / OCF

When evaluating a project; compare the change in NPV and the change in DOL. If the DOL is lower in the new scenario, consider the project.

What is capital rationing?

The situation that a firm has profitable investments available, but can’t find the necessary financing.

• Soft rationing: The corporation as a whole isn’t short of capital. If the management want to, it can raise the money to finance the projects.

• Hard rationing: The business can’t raise the needed capital for the project under any circumstances. This can happen when the company experiences financial distress.

How do Capital Markets operate? - Chapter 11

Key Notations

• D: Dividend

• P: Share price

• R: Return

• R: Average return

• SD(R) or σ: Standard deviation of returns

• T: Number of historical returns

• Var(R) or σ2: Variance of returns

What are cash returns?

Return on your investment = dividend income + capital gain or capital loss on the equity.

Selling equity: Total cash = initial investment + total return. When you don’t sell the equity you can still see the capital gain (or loss) as part of your return.

Percentage returns

Return in percentage terms. Percentage return = dividend yield + capital gains yield.

Dividend yield = Dt+1 / Pt.

Capital gains yield = (Pt+1 – Pt) / Pt.

What were the historical rates of return?

In some (European) countries stock exchanges have been open for hundreds of years. A big change in recent history was in 2007, it became clear that the financial market was based on borrowing and therefore unsustainable. From 2009 and onwards, the stock market indexes in various rates.

What are average returns?

Average returns is the sum of the years divided by the number of years.

• Geometric average return is the average return earned per year, compounded annually.

= [(1 + R₁₎) x (1 + R₂) x ... x ( 1 + R_t )] ^{1 / r}

• Arithmetic average return is what you have earned in an average year. Use if you know the true value.

= (R₁ + R₂ + ...+ R_t ) / T

Combining the two averages with the Blume’s formula:

R(T)= (T-1)/(N-1)*Geometric Average + (N-T)/(N-1)* Arithmetic Average

Forecasting, which to use:

• Up to a decade: arithmetic

• A few decades: split the difference between geometric and arithmetic

• Many decades: geometric

Risk

When an investment is risky, the investor often gets a risk premium. A risk premium is a reward for bearing the risk. The greater the risk, the greater the excess return. The excess return is the difference between very risky returns and risk-free returns.

What is the variability of returns?

Variance = the average squared difference between actual return and average return.

1. Actual return

2. Average return

3. Deviation (actual return – average return)

4. Squared deviation

5. Var(R) = 1/(r-1) [R₁ - R)² +... + (R - R₂)^2]

Standard deviation = the square root of Var(R). The greater the standard deviation, the more volatile the investment.

SD(R) = σ = √σ ²

Normal distribution is a bell-shaped figure that gives the probability of a return ending up in a given range.

How do average returns work?

Geometric average return answers the question: what was your average compound retrun per year over a particular period?
Arithmetic average return answers the question: What was you return in an average year over a particular period?

Geometric average return = [(1+R₁) x (1+R₂) x ... x (1+R_T)]^1/r - 1

What is market efficiency?

A market is efficient when prices adjust to new information. When new information arrives, the market can have an efficient market reaction, a delayed reaction or an over-reaction.

The efficient markets hypothesis says that actual capital markets are efficient. This is because of the competition among investors, mispriced equities will become fewer and fewer. All the investments are zero-NPV investments.

EMH: Efficient markets hypothesis, the hypothesis that actual capital markets are efficient.

Market efficiency forms

• Weak-form efficient, share prices are based on the equity’s past prices.

• Semi-strong-form efficient, the public information is reflected in the share prices.

• Strong form efficient, all information is reflected in the share prices.

How does return, risk, and the security marketline work? - Chapter 12

Key Notations:

• CAPM: Capital asset pricing model

• E (R): Expected return

• R_f : Risk-free rate of return

• R_p : Portfolio return

• β: Beta or systematic risk

• β_p : Portfolio beta

• σ: Standard deviation of returns

• σ²: Variance of returns

From previous chapters we know that people get a premium for bearing risk, a risk premium. We also know that this risk premium is larger for riskier investments.

What are future returns and their associated probabilities?

Expected return

The expected return (E) = Sum of the possible return rates multiplied by their probabilities.

Example: We have equities A and B, which both have different characteristics. Equity A is expected to have a return of 25%, equity B is expected to have a return of 20% for the same period. Why, now, would anyone want to hold B? B has a lower expected return. Now suppose the economy booms, where we expect equity A to have a 70% return and equity B 10%. In case of an economic recession, we expect equity A to have a -20% return and equity B a 30% return. This example is depicted in Table 12.1 on page 268. Also suppose that a boom and a recession are equally likely to happen (50-50 chance). Now refer to Table 12.2 for the calculations of the expected returns E(R)

E(R)_b = 0.5 * 30% + 0.5 * 10% = 20%
E(R)_a = 0.5 * -20% + 0.5 * 70% = 25%

The risk premium (money for bearing the risk) = Expected return – Risk-free rate (R_f).

If risk-free investments currently offer you 8%, risk premiums for A and B are:
Risk premium A = 25% - 8% = 17%

Risk premium B = 20 – 8% = 12%

Variance

Calculating the variance (σ²) in three steps:

• Determine the squared deviations from the expected return.

• Multiply each possible squared deviation by its probability.

• Add these up

σ is the standard deviation; this is the square root of the variance.

The lower the variance and the standard deviation, the less risky the project.

Take equity B again, which had an expected return of 20%. In a given year it will return either 30% or 10%. The possible deviations: 30 – 20 = 10% and 10 – 20 = -10%

Variance = σ² = 0.5 * (10%)² + 0.5 * (-10%)² = 0.01

Standard deviation = √0.01 = 0.1 = 10%

What are portfolios?

Investors have a portfolio of different assets, for example equities and bonds. The portfolio weight = the value of the asset divided by the total portfolio’s value. The weights have to add up to 1.00 in total. So if you have an asset 1 of €50 and asset 2 of €150, asset 1 weighs 50 / (50 + 150) = 0.25 and asset 2 weighs 150 (50 + 150) = 0.75, together they weigh 1.00.

Portfolio expected returns

Consider equities A and B again. You put half of your money in each. The portfolio weights thus are 0.5 and 0.5. The portfolio expected returns in case of a recession are:
R_p = 0.5 * -20% + 0.5 * 30% = 5%

Table 12.5 on page 272 summarizes the remaining calculations, including what happens in a boom and the total expected returns (the average of returns in a boom and returns in a recession, with the probability of each being 0.5).
Portfolio expected returns, E(R_p) = X₁x E(R₁) + X₂x E(R₂) + … + X_nx E(R_n); with X_n being the percentage of money in Asset i.

Portfolio variance

Table 12.6 on page 334 summarizes the relevant calculations for calculating the variance of the portfolio. You use the same procedure as you do for a single equity.

What are announcements, surprises and expected returns?

There (almost) always exist deviations between actual and expected return. Why do these deviations exist?

Expected and unexpected returns

The return on any equity traded in a financial market is composed of two parts:

1. The normal, or expected, return from the equity, which is the part of the return that shareholders in the market predict or expect

>> Based on the market’s understanding today of the important factors that will influence the share price in the coming year

2. The uncertain, or risky, part. The portion that comes from unexpected information revealed within the year. Possible sources of such information;

   • Government figures released on gross domestic product

   • The results from the latest arms control talks

   • A sudden, unexpected drop in interest rates

Total return = Expected return + Unexpected return

R = E(R) + U, U is the unexpected return, which is a surprise and can be either negative or positive.

Announcements and news

The effect of news items on the return of an asset has to be dealt carefully with. The impact of certain news item depends on how new the information is. Rises in GDP, for example, can influence the share price. It is widely known that rises in GDP influence share prices, so investors already predict GDP to some extent and take this into account. An announcement isn’t news if the market already ‘discounted’ the announcement. If, for example, the actual GDP strongly deviates from the expected GDP, investors really learned something. The difference between the actual result and the forecast is called the innovation, or the surprise.

To summarize: an announcement can be broken into two parts:

Announcement = Expected part + Surprise

What is risk?

Systematic risk = Has influence on a large number of assets, also called market risk.

Example: uncertainties about general economic conditions (interest rates or inflation).

Unsystematic risk = Has influence on a small number of assets, also called unique.

Example: announcement of an oil strike by a company.

So we have to adjust the total return formula:

R = E(R) + Systematic portion + Unsystematic portion

R = E(R) + m + ε

What is diversification?

Portfolio diversification can be put in a graph with the number of equities in a portfolio on the x-axis, and the average annual standard deviation (%) on the y-axis. The benefits in terms of risk reduction from adding securities drops off as more equities are added in the portfolio. Than learns us two important lessons:

1. Some of the riskiness associated with individual assets can be eliminated by forming portfolios. This is what is called the principle of diversification.

Diversification = Spreading an investment across different assets. The principle of diversification says that spreading an investment will eliminate some risk. If the number of securities increases then the standard deviation declines.

2. There is a minimum level of risk that cannot be diversified. This is called the non-diversifiable risk. It is at the height of the point at which benefits from risk start to stagnate.

We can eliminate the unsystematic risk by diversification. The value of a single equity fluctuates because of company-specific events. But this doesn’t matter because we can have different assets. So the effects of the fluctuations will cancel each other out. So this risk is also called diversifiable risk. The systematic risks can’t be eliminated by diversification. This is because those risks affects almost all assets. So we can call this risk non-diversifiable.

What is systematic risk and how does beta relate to it?

The systematic risk of an investment determines the reward for bearing risk. Because we can eliminate systematic risk, the expected return on an asset only depends on that asset’s systematic risk. This is the systematic risk principle.

Measuring systematic risk

The beta coefficient (β) = Stands for the amount of systematic risk present in a particular risky asset relative to that in an average risky asset. The larger the beta, the greater the systematic risk and the greater the expected returns. An asset with a beta of 0.5, for example, has half as much systematic risk as an average asset; an asset with a beta of 2.0 has twice as much. An average asset has a beta of 1.0 by itself.

We can calculate the portfolio beta in the same way as the portfolio expected return. Multiply each asset’s beta by its portfolio weight. The sum of those results is the portfolio’s beta.

A risk-free asset has no systematic risk, so is has a beta of zero.

When having risky and risk-free investments in your portfolio, we have to calculate the E(R_p) and the β_P this way:

1. E(R_P) = Weight R_Ax E(R_A) + (1 – weight R_A) x R_f.

2. β_P= Weight R_Ax β_A+ (1 – Weight R_A) x 0

Also make other combinations of expected returns and betas, percentage of portfolio.

What is the security market line (SML)?

Shows the relationship between the beta and the expected return. Refer to the table on page 344. With investing more in a risky asset, and less in a risk-free asset, both expected return and beta go up.

Reward-to-risk ratio

Refer to Figure 12.2 on page 345, which depicts portfolio expected returns and betas for assets A, B, and C. the slope of these straight lines is the reward-to-risk ratio, and can be calculated as follows:

Slope (%) = [E(R_A) – R_f] / β_A

This means that R_A has a risk premium of … % per ‘unit’ of systematic risk.

When deciding which investment is better, look at the reward-to-risk ratio. The higher this ratio, the better. So take the investment with the highest ratio. In an active and competitive market, the reward-to-risk ratio must be the same for all the assets in the market, because if, for example, A has a higher reward-to-risk ratio than B, all investors would be attracted to A and away from B. As a result, asset A’s price would rise and asset B’s price would fall. Because prices and returns move in opposite directions, asset A’s returns would fall, and asset B’s returns would rise. This buying and selling continues up until the point the two assets are on the same line, and

(E(R_A) – R_f) / β_A = (E(R_B) – R_f) / β_B holds. The reward-to-risk ratio must be the same for all the assets in the market.

Security market line = A positively sloped straight line displaying the relationship between expected return and beta.

Market portfolios

A portfolio that consists of all of the assets in the market. The expected return on the market portfolio is E(R_M). The beta is 1 because the portfolio is representative of all the assets in the market, and thus must have average systematic risk. So we could express the SML slope as: (E(R_M) – R_f)/ β_M= E(R_M) – R_f/ 1 = E(R_M) – R_f

E(R_M) – R_f is what is called the market risk premium. Market risk premium = The slope of the SML – the difference between the expected return on a market portfolio and the risk free rate.

Capital asset pricing model (CAPM)

The expected return on a risky asset has three components:

• The time value of money, as measured by the risk-free rate; the reward for merely waiting for your money, without taking any risk (R_f)

• The reward for bearing systematic risk, as measured by the market risk premium. This is the reward the market offers for bearing an average amount of systematic risk in addition to waiting [E(R_M) – R_f)]

• The amount of systematic risk, as measured by the beta for that asset. This is the amount of risk present in a particular asset or portfolio, relative to that in an average asset (β_i)

So the expected return on asset i:

E(R_i) = R_f+ [E(R_M) – R_f) x β_i

What is the cost of capital and the SML?

The cost of capital: the minimum required return on a new investment. This is the minimum a what should be earned for a firm to break even on an investment or project. Chapters 13-16 will discuss this subject.

What are costs associated with capital? - Chapter 13

Key Notations:

• D: Dividend

• D: Market value of debt

• E: Market value of equity

• f_A: Weighted average flotation cost

• f_D: Debt flotation cost

• f_E: Equity flotation cost

• g: Growth rate

• NPV: Net present value

• P: Share price

• PV: Present value

• R: Discount rate

• R_D: Return on debt

• R_E: Return on equity

• R_f: Risk-free rate of return

• R_M: Market return

• SML: Security market line

• T_C: Corporate tax rate

• V: Market value of firm

• WACC: Weighted average cost of capital

• β: Beta of systematic risk

What is the cost of capital?

In determining whether or not an investment to make, you look for a discount rate that results in a return that exceeds what the financial markets offer on investments of similar risk. This minimum required return is what is called the cost of capital associated with a particular project.

Example: A required return of 10% on an investment usually means that the investment will have a positive NPV only if the actual rate of return exceeds 10%. Put differently: the firm must earn 10% on the investment just to compensate investors for the use of the capital needed to finance the project >> 10% is the cost of capital associated with the investment. The cost of capital for a risk-free investment equals the risk-free rate.

Note that the key fact to grasp is that the cost of capital associated with an investment highly depends on the risk involved. “The cost of capital depends primarily on the use of the funds, not the source”

What is the cost of equity?

A firm’s overall cost of equity = The required return on the investments in the firm of equity investors.

Two approaches to determining the cost of equity: the dividend growth model approach and the security market line approach.

The dividend growth model approach

Recap from chapter 7. Given a constant growth rate g, the share price (P₀) can be written as

P₀ = [D₀ * (1 + g)] / R_E – g

P₀ = D₁ / R_E – g

This formula can be rearranged in order to get to R_E

R_E= D₁/ (P₀+ g)

Because R_E is the return that shareholders require on equity, it can be interpreted as the firm’s cost of capital.

Example: Dividends paid on Great Country Public Service shares are €4 per share; the equity currently sells at €60 per share. You estimate that g will be 6% per year into the indefinite future. What is the cost of capital?

D₁= D₀x (1+g)

D₁ = 4 * 1.06

D₁ = €4.24

Given this, R_E is

R_E= D₁/ (P₀+ g)

R_E = (4.24 / 60) + 0.06

R_E = 13.07%

How to estimate g?

• Using historical growth rates

• Using analysts forecasts of future growth rates

• Calculate the average growth rate for a given number of years, 7 for example if you have growth data of the past 7 years. Calculate growth per year (new dividend – old dividend) / old dividend, sum the calculated growth years up and divide them over 7

The advantage of the dividend growth model is that it’s easy to use.

Disadvantages: The model is only applicable to companies that pay dividends; The dividend must grow at a constant rate; The dividend growth rate approach doesn’t explicitly consider risk.

The Security Market Line approach

The required, or expected, return on a risky investment depends on three things (Recap from chapter 10):

1. The risk-free rate R_f

2. The market risk premium. E(R_M) – R_f

3. The systematic risk of the asset relative to average, which we called its beta coefficient, β

Using SML, we can calculate expected return as follows:

R_E= R_f+ β_Ex (R_M – R_f)

where β_E is the estimated beta.

Example: In order to effectively use the SML approach, the risk-free rate, an estimate of the market risk premium, and an estimate of the relevant beta are needed. An estimate of the market risk premium (based on UK equities) is about 4%. Treasury bills paid around 2.2%, so we take that as a risk-free rate. Beta coefficients for publicly traded companies are widely available, ITV plc, for example, had an estimated beta of 1.9 in 2013.

R_E = R_f + β_ITV * (R_M – R_f)

R_E = 2.2% + 1.9 * 4%

R_E = 9.80%

Advantages: Adjusts for risk. Also applicable to companies that don’t pay steady dividend.

Disadvantages: Requires the estimates of risk premium and beta coefficient. Relies on the past.

What is the cost of debt and what are preference shares?

The cost of debt (R_D) = The return lenders require on the firm’s debt. We can calculate these costs as the yield to maturity on the outstanding debt, sine the cost of debt is the interest rate the firm must pay on new borrowing. The coupon rate is irrelevant, as this rate only tells what the firm’s cost of debt was when the bonds were issued.

Cost of preference shares (R_P) = Preference shares have a fixed dividend paid every period forever, meaning a single preference share is a perpetuity.

R_P = D / P₀

What is the weighted average cost of capital (WACC)?

The capital structure weights

Total market value = Equity + Debt

V = E + D

The market value of the firm’s equity can be calculated by multiplying the number of shares outstanding by the share price. The market value of the firm’s debt can be calculated by multiplying the market price of a single bond by the number of bonds outstanding (this holds for long-term debt).

If we divide both sides by V, we can calculate the percentages of the total capital represented by the debt and equity;

100% = E/V + D/V

These percentages are called the capital structure weights.

Taxes and WACC

As discussed earlier, interest paid by corporations is tax deductible. Payments to shareholders aren’t. in determining an after-tax discount rate, we have to distinguish between pre-tax and after-tax cost of debt.

Example: A firm borrows €1 million at 9% interest. Corporate tax rate is 34%. What is the after-tax interest rate on this loan?

Interest costs; 1000000 * 0.09 = €90.000

Tax bill reduced by; 90000 * 0.34 = €59.400

After-tax interest rate; 59400/1000000 = 5.94%

Generally speaking, the after-tax interest rate is the pre-tax rate multiplied by 1 minus the tax rate, after tax rate = R_D * (1 – T_C), with T_C being the corporate tax rate. Using the numbers from the previous example;

After-tax rate = 9% * (1 – 0.34) = 5.94%

Now, to calculate the firm’s overall costs of capital, multiply the capital structure weights by their associated costs, and add them up:

WACC = the weighted average of the cost of equity and the after-tax cost of debt.

• WACC = (E / V) x R_E+ (D / V) x R_Dx (1 – T_C)

• In case the firm uses preference shares:

WACC = (E / V) x R_E+ (P / V) x R_P+ (D / V) x R_Dx (1 – T_C)

Refer to page 377, where the WACC is calculated for the European energy supplier, RWE AG.

What are divisional and project costs of capital?

Using WACC as the discount rate for future cash flows is only appropriate when the proposed investment is similar to the firm’s existing activities.

The SML and the WACC

When evaluating investments with risks that are substantially different from those of the overall firm, the use of the WACC will most likely lead to poor decisions. Refer to Figure 13.1 on page 380. The SML is plotted based on an all-equity firm, a risk-free rate of 7%, a market risk premium of 8%, and a beta of 1. If the firm would use WACC to evaluate all investments, and WACC would be 15%, the firm would accept any investment with a return greater than 15% and reject investments with a return smaller than 15%. Take point A, which is a project with a beta of 0.60 and an expected return of 14%. This would result in a required return of 11.8%, which is desirable, but will be rejected because the firm uses WACC as cut-off point.

Divisional cost of capital

The same kind of problem with WACC can arise in a corporation with more than one line of business.

Pure play approach

How to come up with the appropriate discount rate if you cannot use the WACC? In cases like these, other investments outside the firm that are in the same risk class as the one under consideration have to be examined, and the market-required return on these investments has to be used as a discount rate. You may, for example, consider entering a new line of business, the appropriate cost of capital can be developed by looking at the market-required returns on companies already in that business.

Pure play approach = The use of a WACC that is unique to a particular project, based on companies in similar lines of business.

The subjective approach

With the subjective approach, the firm’s WACC may change through time as economic conditions change. A firm with a WACC of 14%, for example, can place its projects into different categories. A category with high risk, moderate risk, and low risk for example. Refer to the table on page 381 and Figure 13.2 on page 382 for an example.

What are flotation costs?

Flotation costs (f_A) = As soon as a firm accepts a new project, it may be required to issue, or float, new bonds and shares. Sometimes it is suggested that the firm’s WACC should be adjusted upwards to reflect flotation costs. This is not the best approach, as the required return does not depend on the source of the funds, but the risk of the investment. How to include flotation costs in project analysis?

Example: A firm has a cost of equity of 20% and is 100% equity; WACC and cost of equity thus are the same. This particular company is going to expand existing operations by €100 million. The expansion will be funded by selling new equity. The firm estimates that the flotation costs will run to 10% of the amount issued. With flotation costs considered, what is the cost of the expansion?

100 million = (1 – 0.1) * amount raised

Amount raised = 100 million / 0.9 = €111.11 million

The true cost of expansion thus is €111.11 million

General expression for calculating flotation costs, also with debt included (the example assumed an equity-only firm):

f_A= (E / V) x f_E+ (D / V) x f_D

The true cost when flotation cost is included = expansion cost / (1 – f_A)

How does raising capital work? - Chapter 14

Key Notations

• EPS: Earnings per share

• IPO: Initial public offering

• SEO: Seasoned equity offering

What can capital be supplied by?

1. Private equity firms: venture equity and non-venture equity markets.

2. Venture capital

• • Wealthy families, provide start-up capital

  • Private partnerships and corporations

  • Large corporations, venture capital subsidiaries

  • Individual investors

Private equity firm

Venture capital (VC) is financing new ventures, often with high risk.

Stages of financing

1. Seed money

2. Start-up

3. Later stage capital

4. Growth capital

5. Replacement capital

6. Buyout financing

What are public issues of securities?

• Pathfinder prospectus; presents the proposed offering.

• Pre-underwriting conferences; amount of money and type of security.

• Full prospectus; financial and business information.

• Public offering and sale

• Market stabilization

There are two types of public issue

• General cash offer: to general public on a cash basis.

• Right issue: first offered to existing shareholders. The initial public offering (IPO) is the first time that a company makes its equity issue available to the public. Seasoned equity offering (SEO) is a new issue of securities. The company has in this case issued securities to the public before.

Underwriting

Intermediaries between company and public are underwriters. Their tasks are:

• Formulate issue method

• Pricing the securities

• Selling the securities

To share the risk of not selling all the securities underwriters form a group, a syndicate. Underwriters get compensation for selling the securities. This is the gross spread.

Gross spread = offering price – underwriter’s buying price.

Types of underwriting

• Firm commitment underwriting: sell entire issue to the underwriters; the underwriter has full financial responsibility.

• Best effort underwriting: underwriter sells as much as possible, without financial responsibility.

• Dutch auction underwriting: Investors can bid for shares, this determines the offer price. Uniform price auction means that all successful bidders pay the same price.

Green shoe provision, the underwriters have the option to purchase additional shares from the issues at the offering price.

Lock-up agreement: after an IPO insiders must wait before they can sell equity.

In the quiet period, communication with the public must be limited.

Under-pricing

An IPO is mostly offered below his true market price. Firms with few to no sales in the previous year have a bigger chance of under-pricing than others. The issuer’s existing shareholders will have an opportunity loss when the shares are sold for less than they are worth. So under-pricing is a cost to the issuing firm.

Often if firms announce that new equity issues are coming, the share value goes down. That’s because of:

1. Managerial information

2. Debt usage

3. Issue costs

Costs of issuing securities

Flotation costs:

• Gross spread: paid to the underwriting syndicate

• Other direct expenses: legal fees and taxes

• Indirect expenses: costs of management time

• Abnormal returns: Price drop of existing shares

• Under-pricing: equity sold below the true value

• Green shoe option: underwriters can buy additional shares

Rights

Offer a rights issue to existing shareholders. The shareholders can buy with the rights a number of new shares at a specified price within a specified time. For each share of equity they own, the shareholders have been given one right.

Financial management decisions:

• What is the subscription price? (= Price for a share of equity that the existing shareholders are allowed to pay)

• How many rights needed to purchase a share?

Number of new shares: funds to be raised / subscription price.

Number of rights needed to buy a share of equity: ‘Old’ shares / ‘new’ shares.

• Effect rights offering on existing share price.

Value of a right: old price – new price.

It’s clever to have a standby underwriting to purchase the unsubscribed portion of the issue. Pay the underwriter a standby fee.

Dilution: loss in existing shareholders’ value. For example:

• Dilution of proportionate ownership.

If a company issues new shares of equity to the public, if the existing owners don’t buy them they own a smaller percentage of the firm.

• Dilution of market value

• Dilution of book value and earnings per share

Long-term financing

• Term loans, direct business loans of one to five years.

• Private placements, provided by investors with a longer maturity.

Difference between direct private financing and public issues of debt

• No costs of stock exchange registration

• More restrictive covenants

• Easier to renegotiate

• Insurance companies and pension funds vs. banks

• Lower costs of distributing bonds in the private market

Bank loan

• Line of credit: the bank authorizes a maximum loan amount.

• Loan commitment: pre-specified loan amount at a pre-specified interest rate. Loan commitment has two types: revolver and non-revolving.

How does financial leverage and capital structure policy work? - Chapter 15

Key Notations:

• D: Market value of debt

• E: Market value of equity

• EBIT: Earnings before interest and taxes

• EPS: Earnings per share.

• R_A: Return on assets

• R_D: Return on debt

• R_E: Return on equity

• ROE: Return on equity

• T_C: Corporate tax rate

• V_L: Market value of a levered firm

• V_U: Market value of an unlevered firm

• WACC: Weighted average cost of capital

In previous chapters, the capital structure was given. In chapter 1, debt-equity ratios and capital structure decisions were already discussed. Capital structure decisions can have important implications for the value of the firm and its cost of capital. The optimal capital structure for a firm is very context-dependent.

What is capital structure?

Recap; The balance sheet. On the left side you see current assets and fixed assets and on the right side you see current liabilities, debt and preferred stock and shareholder’s equity. The right side is also called the financial structure of the company, as it shows how everything in the company is paid for. The debt and shareholder’s equity are the capital structure. A firm has to discover how to maximize the value of a share of equity. When the WACC is minimized the value of the firm is maximized, and the capital structure of the firm is optimal.

What is financial leverage?

Financial leverage refers to the extent to which a firm relies on debt. The more debt financing used, the more financial leverage employed. Financial leverage can dramatically alter the pay-offs to shareholders in the firm.

An All-Equity firm is considering issuing debt. An All-Equity firm a company who only has equity and zero debt, also called an unlevered firm.

Suppose you have €8.000.000 in assets and €8.000.000 in equity. Now, you want to divide this €8.000.000 50/50, meaning you get €4.000.000 in debt and €4.000.000 in equity. We assume the share price is not going to change. In the first situation (All-Equity) you had 400.000 shares outstanding. Now, assuming the share prices remain the same, you have 200.000 shares outstanding, as half of the amount of equity goes to debt. With €4.000.000 debt and €4.000.000 equity, Return on Investment (ROE) and Earnings per Share (EPS) are higher, as total equity and number of shares have fallen, See Table 15.4 on page 339. This table shows what happens to EBIT, Net Income, ROE and EPS after the €8.000.000 is divided 50/50 in debt/equity.

Figure 15.1 on page 431 shows levels of EBI (Earnings Before Interest, no Taxes) on the horizontal axis and levels of EPS on the vertical axis for a firm with debt and an all-equity firm (no debt). What you see is that at a certain level (EPS of €2 and EBI of €800), it doesn’t matter whether the firm as debt or no debt. Below this break-even point there are disadvantages to holding debt, and above this point there are advantages to holding debt. So for each firm, and with many capital structures, it is possible to sketch whether or not it is favourable to hold debt based on EBI and EPS.

Corporate borrowing and homemade leverage

Some conclusions based on the previous section;

The effect of financial leverage depends on a company’s EBIT
>> High EBIT means that leverage is more beneficial

Leverage increases the returns to shareholders, ROE and EPS

EPS and ROE are sensitive to changes in EBIT, meaning shareholders are exposed to more risk with debt

Capital structure is a very important consideration

Shareholders can borrow and lend money to adjust the amount of financial leverage. This is called homemade leverage = The use of personal borrowing to change the overall amount of financial leverage to which the individual is exposed.

Firms can benefit from interest paid on debt, because it’s tax deductible. The tax savings, also called interest tax shield, is the interest payment * the corporate tax rate.

What is capital structure and what is the cost of equity capital?

Modigliani-Miller model = Two nobel-prize winners came up with two propositions on whether or not there exists an optimal capital structure. The key of their theory is that the investment decision of a firm is separate from its financing decision: First, which products and services to invest in and then, what mix of financing sources to finance the investment.

Assumptions:

• Homogeneous expectations

• Homogeneous business risk classes

• Perpetual cash flows >> Firm value = Cash Flow / R_WACC

• Perfect capital markets

  • Perfect competition circumstances

  • Firms and investors can borrow/lend at the same rate

  • Equal access to all relevant information and to all financial markets

  • No transaction costs

  • No taxes

There are two propositions in the MM model (without corporate taxes)

1. The firm’s value is not affected by leverage V_L = V_E
   Where V_L is the value of the firm and V_E is

2. The return to stockholders is R_E = R_A + (R_A – R_D) * (D/E), where
   R_E is the return on (levered) equity (cost of equity)

• R_A is the return on the firm’s assets

• R_D is the firm’s cost of debt

D/E is the firm’s debt-to-equity ratio, which increases the risk and r_e
With WACC and thus R_D remaining constant, there is no optimal capital structure, it is irrelevant.

What are the two propositions in the MM model (with corporate taxes)?

1. The firm’s value increases with leverage V_L = V_E + T_C * D, where D is the value of debt and T_C * D is the corporate tax shield, which is the reduction in income taxes that results from taking an allowable deduction from taxable income (interest on debt for example). So with more debt, there is a higher tax shield and higher net income (cash flows), so higher firm value.

2. Some of the increase in equity risk and return is offset by interest tax shield.
   R_E = R_A + (D/E) × (1-T_C) × (R_A - R_D).

See Figure 15.4 on page 440. With increasing debt, the value of the firm increases, which is prove for MM Proposition 1.
See Figure 15.5 on page 441. With an increasing D/E ratio, cost of equity R_e rises, the cost of debt R_D remains constant and overall, the WACC thus, slowly decreases

Overall conclusion: Optimal Capital Structure to use as much debt as possible: 100%

What is bankruptcy?

If increasing debt levels leads to increasing firms values, then why do firms not attempt to go for maximum debt (100% as in the MM models)? Here, the bankruptcy risk comes in. The higher the debt, namely, the higher the chances to go bankrupt, as you may not be able to pay debt and other obligations.

At bankruptcy, value of equity = 0.

The costs of bankruptcy:

• Direct costs = Legal and administrative expenses.

• Indirect costs = Financial distress, money spend on resources to avoid bankruptcy and customers walking away because they don’t trust the firm.

• Agency costs = A result of conflicts of interest. Shareholders can use costly selfish strategies: Incentive to take large risks, incentive towards underinvestment, milking the property.

What is the optimal capital structure?

Bankruptcy costs and their effects on the optimal capital structure were not included in the MM models. Bankruptcy costs, however, are very important and affect the optimal capital structure of a firm. A firm borrows up to the point where the tax benefit from an extra unit of currency in debt is exactly equal to the cost that comes from the increased probability of financial distress, this is described in the static theory of capital structure.

Refer to Figure 15.6 on page 448. It looks a lot like Figure 15.4 on page 440, but now bankruptcy costs are included. What you see is that the actual value of the firm increases to a maximum, and then decreases and is no linear relation. The maximum firm value is the optimal point and the optimal amount of debt.

Conclusion: The gains from the tax shield on debt is offset by financial distress costs. An optimal capital structure exists that just balances the additional gain from leverage against the added financial distress costs.

See Figure 15.7 on page 448. Here, you see that the WACC falls initially, because of the tax advantage of debt. Beyond the optimal point (optimal amount of debt, maximal firm value), WACC rises because of financial distress costs.

Summary

• Case 1
  This was what was proposed by MM Proposition I. With no taxes or bankruptcy costs, the value of the firm and its WACC are not affected by capital structures. The purple horizontal line.

• Case 2
  This is what was proposed by MM Proposition II. With taxes and no bankruptcy costs, the value of the firm increases and the WACC of capital decreases as the amount of debt goes up

• Case 3
  This is what was proposed by the Static Theory. With corporate taxes and bankruptcy costs, the value of the firm reaches a maximum, the point that represents the optimal amount of debt. At the same time, WACC is minimized at that point

What is the extended pie model?

Critics of the M&M Propositions say that it fails to take into account real-world issues. The extended pie model states that cash flows do not only consist of the payments to shareholders and payments to creditors, but include payments to the government (G), bankruptcy costs (B) and payments to any other claimant of the cash flows of the firm. G decreases as debt rises, because of the tax shield. B rises as debt rises.

CF = payments to shareholder + payments to creditors + payments to government (tax) + payments to bankruptcy courts and lawyers + other claimants to the cash flow.

>> Figure 15.9 on page 360 shows what happens with lower- and higher financial leverage.

Marketed claims = By shareholders and bondholders; can be bought and sold in financial markets

Non-marketed claims = Government and potential litigants in lawsuits.

Normally, the value of the firm, V_T, is reflected by the marketed claims’ value (V_M). The extended pie model proposes that V_T is the sum of V_M and all other claims, V_N.

V_T = E + D + G + B + …

V_T = V_M + V_N

Essence of the model: V_T is unaltered by capital structure. Only V_M can be altered by capital structure, but changes in V_M (higher or lower leverage) lead to changes in V_N. Higher leverage means that tax claims decrease and bankruptcy claims increase. In total, V_T does not change.

What is signalling?

This chapter looks at the relationship between a company's profitability and it debt level. Logically, a firm with low anticipated profits will take on a low level of debt, a successful firm can take on a higher level of dept. Rational investors therefore view debt as a signal of firm value. This however also creates an opportunity for a financial manager to fool the investors. This "fooling" is however only profitable on the short term, once the public learns that the company is not valuable the rate will drop, the firm's dept level is now above the optimal level.

However, even if managers attempt to fool investors, the more valuable firms will still want to issue more debt than the less valuable firms. This is because, while all firms will increase debt levels somewhat to fool investors, the costs of extra dept prevents the less valuable firms issuing more debt than the more valuable firms issue. Announcements of debt can therefore still be seen as a positive sign for the firm.

What is the pecking-order hypothesis?

The pecking order hypothesis = There is no optimal capital structure, there is no appropriate mix. Namely, firms have a preferred order of raising capital. The way firms behave if they need financing, they are first going to use retained earnings as this is the cheapest. If there are no retained earnings, first firms start with debt financing, as that is less costly and there is less loss of control. Too much debt, however, can put the firm into bankruptcy so a final option would be using equity.

Three implications of the pecking order hypothesis;

• Profitable firms will borrow less, because they have more retained earnings.

• Less profitable companies will need more external funding.

• As a last resort, firms will sell equity to fund investment opportunities.

How does the bankruptcy process work?

The consequence of using debt is the possibility of financial distress, which can be defined in several ways;

• Business failure, by a loss of creditors

• Legal bankruptcy, Bankruptcy is a legal proceeding for liquidating or reorganizing a business.

• Technical insolvency, firm is unable to meet financial obligations.

• Accounting insolvency, negative net worth. The total book liabilities are higher than the book value of the total assets.

What are issues around dividends and payouts? - Chapter 16

Key notations

• D = dividends

• P = share price

• r = interest/discount rate

What are cash dividends and dividend payments?

Dividend = A payment made out of a firm’s earnings to its owners, in the form of either cash or stock.

Distribution = A payment made by a firm to its owners from sources other than current or accumulated retained earnings.

Cash dividends

The most common type of dividend is a cash dividend. The basic types of cash dividend are regular cash dividends; extra dividends; special dividends; liquidating dividends. Commonly, public companies pay regular cash dividends usually paid four times a year.

Dividend payment

The procedure for dividend payment:

1. Declaration date = Date on which the board of directors passes a resolution to pay a dividend

2. Ex-dividend date = The date of two business days before the date of record

3. Date of record = The date by which a holder must be on record to be designated to receive a dividend

4. Day of payment = The date on which the dividend is paid

What is dividend policy?

Dividend policy = The time pattern of dividend payout. Relevant dividend policy questions can be; should the firm pay out a large percentage of its earnings now or a small percentage?

Does dividend policy matter?

1. Current Policy: Dividends are set equal to Cash Flow
   Currently, dividends at each date are set equal to the cash flow of €10.000 and there are 100 shares outstanding. The dividend per share equals 10.000/100 = €100. Assuming a required return of 10%, the share price today (P₀) is:
   P₀ = [D1/(1+R)] + [D2/(1+R²)] = (100/1.10) + (100/1.10²) = €173.55
   The firm as a whole thus is worth 173.55 * 100 = €17.335

2. Alternative policy: Initial dividend is greater than the Cash Flow
   There is decided to pay €110 per share on Date 1, so the total dividend equals 110 * 10.000 = €11.000. The cash flow, however, is €10.000 (see Current Policy), so we must get €1000 extra. >> We issue €1000 worth of equity at Date 1. The new shareholders, now, desire enough cash flow available at Date 2, otherwise they don’t invest. They want to earn the required 10% of return on their €1000 investment.
   1000 * 1.1 = €1100 of the Date 2 cash flow. The old shareholders, now, get 10.000 – 1100 = €8900.
   P₀ = (110/1.1) + (89/1.1²) = €173.55

Conclusion: Dividend Policy is Irrelevant. Both manners come down to P₀ of €173.55

Homemade dividends = The tailored dividend policy created by individual investors who undo corporate dividend policy by reinvesting dividends or selling shares of equity.
New policy is adopted: Dividends of £110 on Date 1 and £89 on Date 2 (See alternative policy above). Bob Investor, actually, prefers dividends per share of £100 at both Date 1 and Date 2. Will he be disappointed? Bob is able to replicate the desired dividend policy by reinvesting the €10 of unneeded funds received on Date 1 (110>100) by buying more shares at a 10% return.

What real-world factors favor a low-dividend payout?

Where the conclusion from the above section was that dividend policy is irrelevant, there are arguments in favor of a low dividend payout.

• Taxes; Dividends are taxed as an individual’s income

• Flotation costs; If flotation costs would be included, the share price shall decrease if new equity is sold

• Dividend restrictions; In some cases, a corporation may face restrictions on its ability to pay dividends. Take the example of bond indentures for example, where a common feature is a covenant prohibiting dividend payments above some level

What real-world factors favor a high-dividend payout?

Where the conclusion from the above section was that dividend policy is irrelevant, and there were arguments in favor of a low dividend payout, there are also arguments in favor of a high dividend payout.

• Desire for current income; Many individuals desire current income and thus high dividend payouts

• Tax and other benefits from high dividends

What is the information content of dividends?

Three different positions on dividends:

1. Homemade dividend argument, dividend policy is irrelevant

2. Tax effects and new issue costs >> low dividend policy is best

3. Desire for current income and related factors >> high dividend policy is best

If you want to examine which of the positions is the right one, look at what happens if a company announces dividend changes. This is reflected in the information content effect.

Information content effect = The market’s reaction to change in corporate dividends payout. If a company for example all of a sudden increases its dividends, this means that they have very regular and high cash flows, which will attract investors. So dividends reveal something about a company’s wealth.

In line with the above reasoning, the Clientele effect = The observable fact that equities attract particular groups based on dividend yield and the resulting tax effects.

What are share repurchases: an alternative to cash dividends?

There are other ways of distributing cash than via cash dividends. Share repurchase = The purchase, by a corporation, of its own shares of equity; also known as a buyback. Share repurchases are typically accomplished in one of three ways;

1. Simply purchasing own equity, just as anyone would buy shares of a particular equity. The firm does not reveal itself as a buyer in this case

2. Instituting a tender offer. The firm announces to all of its shareholder that it is willing to buy a fixed number of shares at a specific price

3. Repurchasing shares from specific individual shareholders, a targeted repurchase.

Example: An all-equity firm has an excess cash of €300,000. The firm pays no dividends and its net income for the year just ended is €49,000. The market value balance sheet before paying excess cash is depicted on page 385.
The shares outstanding = 100.000
The market value of equity = €1.000.000
The share price = 1.000.000 / 100.000 = €10
Earning Per Share (EPS) = 49,000 / 100,000 = €0.49
Price-to-Earnings Ratio (PE) = 10 / 0.49 = €20.4

The company, now, is considering two options:

1. Pay €3 per share on extra cash dividend [300.000/100.000 = 3]
   If commissions, taxes and other imperfections are ignored, the shareholders should not care which option is chosen.
   If the firm pays 100.000 * 3 = €300.000 in cash, the new balance sheet after paying out excess cash is depicted on page 386
   The shares outstanding = 100.000
   The market value of equity = €700.000
   The share price = 700.000 / 100.000 = €7
   Earning Per Share (EPS) = 49,000 / 100,000 = €0.49
   Price-to-Earnings Ratio (PE) = 7 / 0.49 = €14.3
   >> The shareholder’s wealth with 100 shares: (100 * 7) + (100 * 3) = €1000

2. Share repurchase of 30.000 shares
   If the firm purchases 30.000 shares at a value of 30.000 * 10 = €300.000, there are 70.000 left outstanding and the balance sheet looks the same as the balance sheet after paying out excess cash.
   The shares outstanding = 70.000
   The market value of equity = €700.000
   The share price = 700.000 / 70.000 = €10
   Earning Per Share (EPS) = 49,000 / 70,000 = €0.70
   Price-to-Earnings Ratio (PE) = 10 / 0.70 = €14.3
   >> The shareholder’s wealth with 100 shares: 100 * 10 = €1000

Conclusions: If there are no imperfections, a cash dividend and a share repurchase are essentially the same thing. Investors will be indifferent about what a firm eventually does.

What is the relationship between dividend and payout policies?

Dividend cuts are frequently viewed as bad news by market participants, therefore companies will only cut dividends if there is no other option. Therefore you can conclude that, dividend growth delays earnings growth and dividend growth will normally be much smoother than earnings growth.

Five observations about dividend:

1. Aggregate dividend an share repurchases are massive
2. A relatively small number of large, mature firms hold most dividends
3. Managers will not quickly cut the dividends.
4. Raising dividends will only be done slowly and incrementally as earnings grow.
5. Share prices react tot unanticipated changes in dividends.

What are stock dividends and stock splits?

Stock dividends

Stock dividend = A payment made by a firm to its owners in the form of equity, diluting the value of each share outstanding. A stock dividend is commonly expressed as a percentage. A 20% stock dividend means that a shareholder receives one share for every five currently owned.

Stock splits

Stock split = An increase in a firm’s shares outstanding without any change in owners’ equity. For example, a three for one split > Each share of stock is split into three new shares

Reverse split = A stock split in which a firm’s number of shares outstanding is reduced

Again, nothing happens with the wealth of investors as a result of stock dividends and stock splits.

Example: All-equity firm with a total market value of €660.000 and 10.000 shares. With a 10% stock dividend, the total number of shares outstanding rises to 11.000 shares, and the worth of the shares drops from €66 to €60. A shareholder who had 100 shares worth €66 each now has 110 shares worth €60 each. It both comes down to €6600.

Example: Consider a two-for-one stock split and refer back to the example above. You have 20.000 shares instead of 10.000 (2 for 1 split), so each share now is worth 660.000 / 20.000 = €33. The number of shares thus doubles and the price per share halves. Someone with 100 shares worth €66 now has 200 shares worth €33. There is no difference.

What is short-term financial planning and management? - Chapter 17

Key Notations

• ACP: Average collection period

• C: Cash balance

• C*: Optimal or target cash balance

• CC: Carrying costs per unit

• EAR: Effective annual rate of return

• EOQ: Economic order quantity

• F: The fixed cost of making a securities trade to replenish cash

• L: Lower cash balance limit

• NPV: Net present value

• P: Price per unit

• PV: Present value

• Q: Quantity sold per period or quantity of inventory ordered per period

• R: The opportunity cost of holding cash

• R: Monthly required return

• T: Total amount of new cash needed for transaction purposes over the relevant planning period

• T: Total sales per period

• U*: Upper cash balance limit

• V: Variable cost per unit

• σ² Variance of the net cash flow per period

What are reasons for holding cash?

There are three motives for liquidity;

1. Speculative motive = The need to hold cash to take advantage of additional investment opportunities, such as bargain purchases

2. Precautionary motive = The need to hold cash as a safety net to act as a financial reserve

3. Transaction motive = The need to hold cash to satisfy normal disbursement and collection activities associated with a firm’s ongoing operations

Holding cash has its benefits and costs. The liquidity is necessary for transaction needs, but there are opportunity costs. Search for a good cash balance, benefits versus costs.

Liquidity management: a firm should have the right quantity of liquid assets.

Cash management: collecting and disbursing cash.

What does float mean?

Float = The difference between book cash (cash balance as reported in financial statements) and bank cash (balance shown on bank accounts), representing the net effect of cheques in the process of clearing, the moving through the banking system.

Disbursement float decreases the book balance, but not the bank balance. Cheques written by a firm are a good example. If a firm buys something worth €5000 by writing a cheque, the book cash decreases by €5000, whereas the bank cash remains at its old level until the cheque is presented to the bank of the supplier.

Collection float increases book balance. Cheques received by the firm are a good example.

Net float = total collection floats + total disbursement floats.

Float management = Speed up collections, slow down disbursements

Total collection or disbursement times can be broken down into three parts: mailing time, processing delay and availability delay:

• Mailing time = The part of the collection and disbursement process during which cheques are trapped in the postal system

• Processing delay = The time it takes the receiver of a cheque to process the payment and deposit it in a bank for collection

• Availability delay = Refers to the time require to clear a cheque through the banking system

Measuring float

Average daily float = total float / total days, very often the number 30 is used for a month.

If you have an Item A with an amount of €5.000.000 and 9 days of processing and availability delay, and an Item B with an amount of €3.000.000 and 5 days of processing and availability delay, your average daily float equals;

[(5000000 * 9) + (3000000 * 5)] / 30 = €2.000.000 average daily float.

Average daily receipts = total receipts / total days

In the above case, total receipts are 5000000 + 3000000 = €8.000.000;

8000000 / 30 = €266.666,67

Weighted average delay = (% of Item 1 in total) * number days in delay + (% of Item 2 in total) * number of days in delay + etc.

Of the total of €8.000.000 receipts, €5.000.000 (= 5/8 of the total) is delayed for 9 days. The other 3/8 is delayed for 5 days.
(5/8) * 9 + (3/8) * 5 = 7.50 days

Average daily float = average daily receipts * weighted average delay

Average daily float = 266666.67 * 7.5 = €2.000.000

How do you invest idle cash?

• Seasonal or Cyclical Activities: Firms with predictable cash flow patterns. Surplus cash flows during part of the year and deficit cash flows for the rest of the year.

• Planned or Possible Expenditures: Firms may issue bonds and shares to provide cash for a large expenditure (before the cash is needed), investing the proceeds in long-term marketable securities to finance plan construction programmes, dividend payments, etc.

What is target cash balance?

Target cash balance = A firm’s desired cash level as determined by the trade-off between carrying costs (holding too much cash) and shortage costs (holding too little cash, also called adjustment costs).

Opportunity costs mean the costs of holding excess cash; like money you could have earned if you would have invested the excess cash. Trading costs, then, get higher when securities must be sold to establish a cash balance. The optimal point is the intersection between opportunity costs and trading costs. What you see here is that total costs of holding cash are minimal at this intersection point. The issue now is to determine an optimal cash balance policy that minimizes these costs (trading and opportunity) through a trade off.

The Baumol-Allais-Tobin (BAT) Model = How to Estimate a Target Cash Balance?
Example: Golden Socks began week 0 with a cash balance of C = €1.2 million, outflows exceed inflows by €600,000 per week. Its cash balance will drop to zero at the end of week 2; its average cash balance will be C/2 = €1.2 million / 2 = €600,000 over the 2 week period. At the end of week 2, Golden Socks must replace its cash either by selling marketable securities or by borrowing. This all is depicted in Slide 42 of the Lecture Slides to be found on Nestor. To solve Golden Socks’ problem, we need to know the following;

• F = The fixed cost of selling securities to replenish cash

• T = The total amount of new cash needed for transaction purposes over the relevant planning period—say, one year.

• R = The opportunity cost of holding cash; this is the interest rate on marketable securities.

According to the BAT model:
* The total opportunity costs of cash balances, in monetary terms, must be equal to the average cash balance multiplied by the interest rate: Opportunity Cost (€) = (C/2)×R
* The trading costs must be calculated by calculating the number of times that the firm must sell marketable securities in a year. We already know the total amount of cash disbursements during the year (600.000 * 52 weeks = €31.200.000). If the initial cash balance is set at €1.2 million, Golden Socks will sell €1.2 million of marketable securities every 2 weeks. Trading costs = (31.200.000/1.200.000) * F = 26F. More generally: Trading costs = (T/C) * R

Total costs, now, = [(C/2) * R] + [(T/C) * R]
Now we can very easily calculate the optimal amount of cash. We already said the optimal point is the point where opportunity costs equal trading costs. So;
C* is at the point where [(C/2) * R] = [(T/C) * R], or rearranged:

• C* = √ ((2T * F) / R)

The Miller-Orr Model = Designed to deal with cash inflows and outflows that fluctuate randomly from day to day

The following variables are included:

• Upper limit, U*, to the amount of cash

• Lower limit, L, to the amount of cash

• Target cash balance, C*

A firm allows its cash to fluctuate between the upper- and lower limits. As long as C* is in between U* and L, nothing happens. As soon as the cash balance reaches the upper limit, the firm moves U* - C* cash out of the account into marketable securities. This action moves the cash balance down to C* again. As soon as C* reaches the lower limit, the firm sells C* - L worth securities and deposits this cash in the account.

Using the model

Management first defines the lower limit L, which defines a safety stock which depends on how much risk of a cash shortfall the firm is willing to tolerate. Similar to the BAT model, the optimal cash balance depends on opportunity costs and trading costs. Given L is set by the firm, F is the fixed cost per transaction of buying and selling marketable securities, and R is the interest rate per period on marketable securities, Miller and Orr propose the following for U* and C*;

C* = L + (3/4 * F * σ² / R)^1/3

U* = 3 * C* - 2 * L

Average cash balance = (4* C* - L) / 3

How to get to these equations is extremely technical and complex and won’t be discussed in detail. The only thing you should be able to do is calculating U*, C* and the average cash balance given L, F, R and the standard deviation.

What is the relationship between credit and receivables?

Firms stimulate sales by offering credit. Firms that offer credit allow their customers to get goods first and pay later. There are costs involved in offering credit. There is a risk involved, for example, of not getting back your money. Credit policy decision compares the benefits of increased sales and the costs of granting a credit.

Components of credit policy:

1. Terms of sale (cash or credit conditions)

2. Credit analysis (determine probability that customers won’t pay)

3. Collection policy (collecting cash)

On page 421, the trade receivables period is depicted with the help of a timeline, that shows cash flows associated with granting credit.

Trade receivables = average daily sales * ACP

ACP = Average Collection Period

What are the terms of sale?

Terms of sale are made up of three distinct elements:

1. The period for which credit is granted (credit period)

2. The cash discount and the discount period

3. The type of credit instrument

Terms of sale are usually quite similar within a given industry, but differ substantially across industries.

Example: With a 2/10, Net 30, payment in the first 10 days gets the buyer a discount of 2%. After this period, the buyer has 20 days to pay the amount due, without any discount. The buyer will pay faster. Key question: Does the cash discount provide a significant incentive for early payment? This question will be answered later.

In this simple example, the net credit period is 30 days. The cash discount period is 10 days.

Invoice = A bill for goods or services provided by the seller to the purchaser. The invoice date is the beginning of the credit period.

Length of credit period depends on the buyer’s inventory period and operating cycle.

Other factors that influence the credit period;

• Perishability and collateral value

• Consumer demand

• Cost, profitability and standardization

• Credit risk

• Size of the account

• Competition

• Customer type

Cash discount = A discount given to induce prompt payment. It speeds up the collection of receivables. An example:
Suppose, the order is for €1000 and the discount is given by the 2/10, Net 30
The buyer can pay €980 in 10 days or wait another 20 days and pay €1000. In other words; the buyer is borrowing €980 for 20 days and paying €20 interest on the ‘loan’.
Interest rate = 20/980 = 2.0408% This is, however, the rate for a 20 day period. In a year, there are 365 / 20 such periods = 18.25. The annual rate is therefore given by: EAR = 1.020408^18.25 – 1 = 44.6%

What is proposed credit policy analysis?

What are the factors that influence the decision to grant a credit? Granting a credit only makes sense if the NPV from doing so is positive.

In evaluating credit policy, there are five basic factors to consider:

• Revenue effects; revenue collections will be delayed, but because buying on credit is favorable to consumers, revenues may rise

• Cost effects; where the revenues of the firms are delayed, the costs of sales will be incurred immediately

• Cost of debt; if the firm grants a credit, it must arrange to finance the resulting receivables. As a result, short-term borrowing increases

• The probability of non-payment; some percentage of consumers will never pay for the products they received

• The cash discount

How to evaluate the proposed credit policy

Pear Computers is evaluating a request from some major customers to change its current policy to net one month (30 days). The following has to be defined in order to analyze this proposal ;

P = price per unit

v = variable cost per unit

Q = current quantity sold per month

Q’ = quantity sold under the new policy

R = monthly required return

Price equals €49, variable costs equal €20, the old quantity sold was 100 pieces and the new would be 110. Required return is 2%. In steps:

• Cash flow with old policy = (price –variable cost) x current quantity = (49 – 20) * 100 = €2900

• Cash flow new policy = (price – variable cost) x quantity new policy = (49 – 20) * 110 = €3190

• Incremental cash flow = (price – variable cost) x (new Q – old Q) = (49 – 20) * (110 – 100) = €290

• Present value = [(P - v) (Q’ - Q)] / R = [(49 – 20) * (110 – 100)] / 0.02 = €14.500
  note: Cash flows were treated as a perpetuity, as the same benefit will be realized every month for ever under this specific policy

• Cost of switching = PQ + v (Q’- Q)

• NPV of switching = - [PQ+ v (Q’- Q)] + [(P-v)(Q’- Q)] / R = [- Costs of switching] + [incremental cash flow] / R = [49 * 100 + 20 * (110 – 100)] + [(49 – 20) * (110 – 100)] / 0.02 = €9400

>> The switch to a new policy would be very profitable

The above example assumed an increase in sales of 10 units, but this is only an estimate. It may be useful to calculate the amount of extra units that is needed to break even.

Break-even: Q’- Q = PQ / [(P-v) / (R-v)] = units. For pear;
Q’ – Q = (49 * 100) / [(49 – 20) / (0.02 – 20)

Q’ – Q = 3.43 units.

What is optimal credit policy?

The difference between granting credit and not granting credit has been discussed in previous paragraphs and is quite straightforward. The optimal amount of credit has not been discussed yet. The optimal amount of credit is determined by the point at which the incremental cash flows from increased sales are exactly equal to the incremental costs of carrying the increase in investment in trade receivables.

Credit cost curve = A graphical representation of the sum of the carrying costs and the opportunity costs of a credit policy.

Components of the graph:

Carrying costs = Come in three forms: the required return on receivables; the losses from bad debts; the costs of managing credit and credit collections (costs associated with running the credit department).
Opportunity cost = The cost associated with the extra potential profit from credit sales that are lost because credit is refused. As soon as credit policy is relaxed (less strict), opportunity costs go down.

>> The optimal amount of credit (the optimal investment in receivables) is at the intersection point between carrying costs and opportunity costs. Total costs are at minimum at this point.

It should be noted that, generally speaking, costs and benefits from extending credit differ per firm and industry. A firm with much excess capacity, low variable operating costs and a loyal base of customers is more likely to extend credit.

What is credit analysis?

When should credit be granted? This is a rather complicated decision and requires some thorough thinking.

1. One-time sales; the simplest case. A customer wishes to buy one unit at price P on credit. If credit is refused, the customer will not buy anything. If credit is granted, in one month the customer will either pay or not pay. Probability of not paying (defaulting) equals π (pi). Since this is a one-time sale, pi is the percentage of new customers that buy once that will not pay. R is the return on receivables, v is variable costs.
   NPV of granting credit = -v + ( 1 – π) x P / (1 + R)

If the firm refuses to grant credit, the incremental cash flow equals 0 (the customer will not buy anything in that case). If the firm grants credit, it spends v this month and expects to collect (1 – π) next month.
The break-even probability can be calculated by solving for NPV = 0
-v + ( 1 – π) x P / (1 + R) = 0; the outcome is the chance of return a firm tolerates.

2. Repeat business; the one-time sale example should be extended. A new customer that does not default the first time will remain a customer forever and never default. If a firm grants credit, it spends v this month. Next month, the firm gets either nothing (default) or P (customer pays). In case the firm gets P, it will get the amount P – v forever.
   Present value = value of a new customer.

PV = (P – v) / R

the NPV of granting credit:

NPV = - v + (1 – π) * (P – v) / R

What is a collection policy

Collection policy = Monitoring receivables to spot trouble, obtaining payments on past-due accounts.

To keep track of payments, most firms monitor outstanding accounts. First of all, firms keep track of their average collection period (ACP) through time. Second, firms make an ageing schedule, of which an example is shown on page 432.

Ageing schedule = A compilation of trade receivables by the age of each account. If the firm in the example has a credit period of 60 days, 25% of its customers are late with paying.

Collecting overdue payments

A firm usually goes through the following sequence of procedures for customers whose payments are overdue:

• Delinquency letter about the past-due status of the account

• Phone call to the customer

• Collection agency

• Legal action

What is inventory management?

The main goal of inventory management is to minimize the costs. There are three types of inventory: raw material, work in progress and finished goods.

Inventory costs:

• Carrying costs = Direct opportunity costs from holding inventory. Examples are storage and tracking costs, insurance and taxes, losses due to obsolescence, deterioration or theft, opportunity cost of capital.

• Shortage costs = When you have an inadequate inventory. This brings restocking costs and costs related to safety reserves.

What are different techniques that can be used?

ABC approach

ABC approach = Simple approach to inventory management. Basic idea; divide inventory into three groups. The underlying rationale is that a small portion of inventory in terms of quantity might represent a large portion in terms of inventory value.

The Economic Order Quantity (EOQ) Model

EOQ model = This is the best known approach for explicitly establishing an Optimal Inventory Level, which is beneficial for the firm since holding inventory costs money.
Main idea: Inventory-carrying costs rise and restocking costs decrease as inventory levels increase. The optimal size of Inventory Order is reached at point Q* where total costs of holding inventory are at a minimum and where Carrying costs and Restocking costs cut each other.
Carrying Costs = Average Inventory + Carrying Costs per Unit
Carrying Costs = (Q/2) × CC
Restocking Costs = Fixed Cost per Order × No. of Orders
Restocking Costs = F × (T/Q)
Total Costs = (Q/2) × CC + F ×(T/Q)
The optimal size of inventory now can be found by looking for the minimum value of Total Costs, or by setting Restocking costs equal to Carrying costs:
(Q/2) × CC = F ×(T/Q), or rearranged:
Q* = Economic order quantity (Q*) = The restocking quantity that minimizes the total inventory costs

Extensions to the EOQ model

Thus far, we assumed that the company will let its inventory run down to zero and then reorder. In reality, this is not practical. Two extensions:

1. Safety stocks; Minimum level of inventory a firm keeps on hand.

2. Reorder points; To allow for a delivery time, firms place order before inventories reach a critical level.

Managing derived-demand inventories

Some inventories highly depend on the number of output planned, which is based on consumer demand or marketing programmes. A good example is the car manufacturing industry. There are two methods for demand-dependent inventories.

Materials requirements planning = A set of procedures used to determine inventory levels for demand-dependent inventory types such as work in progress and raw materials

Just-in-time inventory (JIT) = A system for managing demand-dependent inventories that minimizes inventory holdings

How to manage international corporate finance? - Chapter 18

Key Notations

• F: Forward exchange rate

• FC: Foreign country

• : Inflation rate

• HC: Home country

• IFE: International Fisher effect

• IRP: Interest rate parity

• NPV: Net present value

• P: Price

• PPP: Purchasing power parity

• R: Risk-free rate

• S: Exchange rate

• UFR: Unbiased forward rate

• UIP: Uncovered interest parity

What role does globalization play?

1. American depository receipt: makes it possible to trade equity in the united states, by representing shares of a foreign equity,

2. Cross-rate: the exchange rate between two currencies quoted in a third currency.

3. Eurobond: a way to raise capital for international companies and governments.

4. Eurocurrency: the money is deposited in a financial centre outside the country.

5. Foreign bonds: issued in a single country.

6. Gilts; securities from the British and Irish government.

7. London interbank offered rate; rate for overnight loans.

8. Swaps: exchange two securities or currencies. Interest rate or currency swaps.

How does the foreign exchange market work?

Participants: importers, exporters, portfolio managers, foreign exchange brokers, traders, speculators. Exchange rate: price of one country’s currency in terms of another currency. Cross-rate: the exchange rate for a foreign currency in terms of another foreign currency.

Triangle arbitrage opportunity = profit by exchanging in steps with the cross-rate.

Spot trade: trade currencies based on the exchange rate today, the spot exchange rate.

Forward trade: exchange currency in the future, with the forward exchange rate.

What is purchasing power parity?

Keeping purchasing power constant, a product costs the same in other currencies. That’s the absolute PPP. 1 pound or 1 euro will buy you the same number of drinks, but that’s only applicable to traded and uniform goods.

If the price isn’t equal, there’s a possibility to make profits. Relative PPP: How change in the exchange rate over time will happen, the expected exchange rate. E (St) = .

Covered interest arbitrage

Because of locking in the forward exchange rate, change in the exchange rate doesn’t matter.

1. Convert

2. Agree to forward exchange rate

3. Invest

4. Convert back

5. Profit

What is interest rate parity (IRP)?

F_t = Forward exchange rate for settlement at time t

R_HC= Home country nominal risk-free interest rate

R_FC= Foreign country nominal risk-free interest rate

IRP: Interest rate parity = the condition starting that the interest rate differential between two countries is equal to the percentage difference between the forward exchange rate and the spot exchange rate. Shortly, F₁/S₀ = (1+R_FC)/(1+R_HC)

IRP approximation: F_t = S₀ x [1 + (R_FC - R_HC)]^t

UFR: Unbiased forward rate, this is the condition stating that the current forward rate is an unbiased predictor of the future spot exchange rate.

How does international capital budgeting work?

In deciding whether to take an investment there are to basis approaches.

Method 1: Home currency approach, convert before estimating the NPV. For doing this the future exchange rates have to be estimated to convert the future cash flows from the one currency to the other.

E(S_t) = S₀ x [1 + (R_EURO - R_DOLLAR)]^t

Method 2: Foreign currency approach, convert after estimating the NPV.

R_EURO - R_DOLLAR = h_EURO - h_DOLLAR

What is the exchange rate risk?

Short-run exposure. Your profit will depend on the future exchange rate. Reduce or eliminate fluctuations by locking in an exchange rate.

Long-run exposure; unanticipated changes in economic conditions, for example higher wages. Reduce or eliminate by borrowing in foreign country.

Translation exposure: problems for the accountants;

1. Appropriate exchange rate to use for translating each balance sheet account

2. How should balance sheet accounting gains and losses from foreign currency translation be handled?

Managing exchange rate risk, know and control your positions in a foreign currency.

What is political risk?

Changes in value can arise because of political actions. This can be because of changes in tax laws, but also of an internal war or corruption.

• Use of local financing

• Structuring the operation in such a way that it requires significant parent company involvement to function

What role does Islamic finance play?

One big difference between Islamic corporate finance and "Western" corporate finance is that in Islamic countries it is not done to charge interests of any kind on financial securities; making money from money is forbidden. This creates some challenges. Ways to solve this are for example to share profits or to lease.

How to understand behavioral finance? - Chapter 19

Key Notes

In this chapter we try to understand and explain how financial decisions are influenced by errors. Cognitive errors are errors in reasoning. There are three main categories of cognitive errors:

1. Biases

2. Framing effects

3. Heuristics

What are biases?

Making systematic errors in judgment. There are three relevant biases:

• Overconfidence. Believing that your abilities are better than they are.

• For example, believing that you can forecast the future.

• Over-optimism. Having an optimistic view of the outcomes. Underestimating the probability of a bad outcome. With capital budgeting, an over-optimist will for example overestimate cash flows and underestimate probability of failure.

• Confirmation bias. Searching for information and opinions that confirm what you believe. Try to prove yourself right. This can be a problem if for example managers ignore negative information about potential investments.

What are framing effects?

Framing dependence is making a different decision if the question is asked in an other way. The answer you give depends on how the question is framed.

Loss aversion = focusing on gains and losses instead of overall wealth

• Break-even effect: something will happen that will allow them to break even and escape without a loss. Deny the losses and keep trying to fix them.

• Debt avoidance because debt financing increases the likelihood of losses.

House money = taking more risk with money you have won (casino), it’s less upsetting to lose this money instead of lose the money that you brought / lose from your investment gains

• Self-attribution = When something good happens for reasons beyond your control, taking credit for it.

• Disposition effect = sell winners and hold losers. Avoid the loss, hopes of winning in the future.

Mental accounting = having a personal relationship with your investments, so its harder to sell them.

Other:

• Myopic loss aversion = focusing on the avoidance of short-term losses

• Regret aversion = avoiding to make a decision because of the fear that the decision is less than optimal

• Endowment effect = considering something that you own worth more than when you wouldn’t own it.

• Money illusion = confused between nominal buying power and real buying power.

What are heuristics?

Making decisions based on shortcuts or rules of thumb. Not always a good call, because all the situations are different.

• Affect heuristic = the reliance on instinct.

• Representativeness heuristic = make stereotypes or limited samples representative of a larger group. Decisions based on the opinion about the whole group instead of on the particular thing.

• Clustering illusion = thinking that clustered random events aren’t really random. For example flipping a coin, if you get 10 times heads in a row, it still is a random event, which you can’t influence.

• Gambler’s fallacy = assuming that things that occur in the long run, will be corrected in the short run. An event that didn’t happen for a while, has a higher probability of happening now. (Roulette).

• Hot-hand illusion = predicts continuation in the short run (basketball). When a player scored several points, the chance of him scoring more points is higher than before.

Other heuristic errors and biases:

1. Law of small numbers

2. Recency bias

3. Anchoring and adjustment

4. Aversion to ambiguity

5. False consensus

6. Availability bias

What is market efficiency?

Markets are efficient because of some smart and well-financed investors. They buy and sell to exploit mispricing. This is called arbitrage. Arbitrage is risky and costly, so there are only a few arbitrageurs.

Limits to arbitrage (barriers):

1. Firm-specific risk: imperfect and/or costly

2. Noise trader risk: a trader whose trades are not based on information or meaningful financial analysis / sentiment-based risk

3. Implementation costs: costs of correcting a mispricing.

Bubble = market prices soar far in excess

Crash = market prices collapse

What is financial risk management? - Chapter 20

Key Notes

Since the early 1970s, prices for all kinds of goods and services have become increasingly volatile. This volatility can cause serious damages, and firms are taking steps to shield themselves from price volatility.

Hedging = Reducing a firm’s exposure to price or rate fluctuations, also called immunization.

Corporate risk management involves buying and selling derivative securities = A financial asset that represents a claim to another financial asset. Options, for example.

Three important areas with increase of volatility:

• Interest rate volatility

• Exchange rate volatility

• Commodity price volatility

How do you manage financial risk?

The price and rate volatility are very high these days. The nature of the firm’s operations and financing decide if this is a cause for concern for the firm.

To analyze a firm’s exposure to financial risks, risk profile can be made. This shows how the changes in prices or rates that affect the value of the firm. A risk profile includes the following aspects:

• ΔV = changes in value, vertical.

• ΔP = changes in price, horizontal.

The steeper the slope, the more important it is to reduce that exposure. Locking a quantity and price in the future can reduce the risk exposure.

Hedging short-run and long-term exposure

Short-run exposure comes from unforeseen events or shocks result in temporary changes in prices. This is also called transitory changes. Three costs increase suddenly and the firm cannot pass them on to its customers immediately.

Transactions exposure = Short-run financial risk arising from the need to buy or sell at uncertain prices or rates in the near future.

Long-term exposure comes from permanent changes, also called economic exposure.
Economic exposure = Long-term financial risk arising from permanent changes in prices or other economic fundamentals. For example, a new technology is discovered where less oil is needed (change in economic fundamental). Prices for oil have to fall permanently, because there is less demand.

By managing financial risks, the firm can accomplish two important things

• Firm insulates itself from difficult price fluctuations.

• Firm gives itself a little breathing space.

How does hedging with forward contracts work?

Forward contract = A legally binding agreement between two parties calling for the sale of an asset or product in the future at a certain price agreed on today. The date that the sale is done is the settlement date.

Forward contracts are often used to hedge exchange rate risk.

Payoff profile = A plot showing the gains and losses that will occur on a contract as the result of unexpected price changes.
Examples;

• Oil prices increase

  • Buyer benefits by having a lower-than-market price

  • Seller loses because she is obligated to sell at a lower-than-market price

• Oil prices decrease

  • Buyer loses because she ends up paying a higher-than-market price

  • Seller benefits because she ends up getting a higher-than-market price

How does hedging with futures contracts work?

Future contract = A future contract is simply a forward contract with the feature that gains and losses are realized each day rather than only on the settlement date.

Types of contracts;

• Commodity Futures; on goods like wheat, rice

• Financial Futures; on equity for example

Cross-hedging = Using a contract from a closely related asset for hedging another asset

How does hedging with swap contracts work?

Swap contract = An agreement by two parties to exchange, or swap, specified cash flows at specified intervals in the future.

Three basic categories:

• Currency swap; Agreement of two parties to exchange a specific amount of one currency for a specific amount of another. This eliminates the exposure to exchange rate changes. The exchange will be made a couple of times in the future.

• Interest rate swap; The exchange of a floating interest rate for a fixed one. The parties agree on paying each other’s loan.

• Commodity swap; An agreement of exchanging a certain quantity of commodity at fixed times in the future.

A swap dealer is someone who guides company’s in the process of entering a swap. A firm contacts the swap dealer. He takes the other side of the agreement and tries to find another party.

How does hedging with option contracts work?

Option contracts = An agreement that gives the owner the right, but not the obligation, to buy or sell a specific asset at a specific price for a set period of time. You as a buyer get the opportunity to buy or sell something at a specified price at a point in the future.

Terminology:

Call option = An option that gives the owner the right, but not the obligation, to buy an asset at a fixed price during a particular period

Put option = An option that gives the owner the right, but not the obligation, to sell an asset

Three different price elements:
Exercise/Strike Price = The price at which the asset can be purchased (call) or sold (put).
Premium = The cost, price or value of the option itself.
The underlying or actual spot price of the asset in the market.

What are options? - Chapter 21

Key Notations:

• C: Call price

• N (d): Probability that a standardized, normally distributed, random variable will be less than or equal to d.

• P: Put price

• PV (E): Present value of exercise price

• R_f: Risk-free rate of return

• ^S: Equity or share price

• ^t: Time (in years) to expiration date

• σ²: Variance (per year) of the continuous share price return

What are some of the basic options?

Chapter 15 already gave a brief introduction to options, here some important definitions around options:

• Exercising the option = The act of buying or selling the asset via the option contract.

• Strike or exercise price = The fixed price in the option contract at which the holder can buy or sell the underlying asset

• Expiration date = The last day on which an option may be exercised, or the maturity date of the option.

• American option = An option that can be exercised before the expiration date.

• European option = An option that can only be exercised on the expiration date.

• Call option = An option that gives the owner the right, but not the obligation, to buy an asset at a fixed price during a particular period

• Put option = An option that gives the owner the right, but not the obligation, to sell an asset

Option pay-offs

Assume a purchase of a call option on asset X with a strike price of 58.50 per unit and a premium of 0.50 for one unit of X. The strike price can be seen as a vertical line, as it is fixed. At all spot rates below the strike prices, the buyer of the option chooses not to exercise its call option, because the purchase will be cheaper on the open market [“Out of the Money”]. In this case, the buyer will only lose the premium of 50 cents he paid. At point 58.50, the option will be exercised and the profit starts increasing [“At the Money”]. At point 59, you find the break-even price and above that point, only profits are possible. So at any point higher than 58.50, the buyer of the option exercises the option because he will make a profit by purchasing at strike price and selling at market price [“In the Money”].
Profit = Spot Rate – (Strike Price + Premium)

Note that this example is from the perspective of the buyer of the option. For the seller of the option, it works the other way around: the profit for the buyer is a loss for the seller
>> Zero-sum game; one wins, one loses.

What is put-call parity?

Protective put = The purchase of equity and a put option on the equity to limit the downside risk associated with the equity.

Suppose, you buy a share worth €110 and a put option with a strike price of €105. The put option has a life of one year, and the premium is €5. Total investment = 110 + 5 = €115. You are going to hold your investment for one year and then sell out. The rationale behind this is that if the company happens to have share prices below €105, you can exercise your put option and sell your equity for €105. See Table 21.1 on page 480 for the possible outcomes here.

A protective put strategy is a combination of a call option (with the same strike price as a put option) and a risk-free investment. Put-call parity (PCP) condition:

Price of Underlying Equity + Price of Put = Price of Call + Present Value of Strike Price.

In symbols; S + P = PV (E) + C

What is option valuation?

S₀ = Share price today.

S₁ = Share price at expiration.

C₀ = Value of the call option today.

C₁ = Value call option on the expiration date.

E = Exercise price on the option.

Recap from the discussion in section 16.1:

Option out of the money:

C₁=0 if S₁ – E < 0

Option in the money:

C₁= S₁ – E if S₁ – E > 0

Time premium = Investors are willing to pay an extra amount if there is a possibility that the share price will rise. In determining the value of a call option, we need an upper and a lower bound. Upper bound = share price. Lower bound = share price – exercise price

Value of an option depends on five factors:

• Current value of the underlying asset

• Exercise price on the option

• Time to expiration on the option

• Risk-free rate

• Variance of return on the underlying asset

Value of the option = share price – exercise price.

What is an option pricing model?

Present value of the exercise price on the option, calculated at the risk-free rate;

• PV = E / (1 + R_f)

• S₀ = C₀ + (E/1+R_f)

• C₀ = S₀ – (E/1+R_f)

The value of the call option = share price – present value exercise price.

Total value/share price = risk-free asset value + call value

Combining the call option and a risk-free investment to duplicate the pay-off from holding equity:

• Equity value – risk-free investment = an amount short.

• Determine how many call options needed: ΔS / ΔC

What is the Black-Scholes Model?

The Black Scholes Model is very complex and technical, so therefore the focus will be on the main result and how to use it;

C = SN(d₁) – E_e^-RtN(d₂)

with ;

d₁ = [ln(S / E) + (R + σ² / 2)t] / √σ²t

d₂ = d₁ - √σ²t

Five parameters:

• S = Current share price

• E = Exercise price of call

• R = Annual risk-free rate of return, continuously compounded

• σ² = Variance of the continuous share price return

• t = Time to expiration date

N (d) = probability that a standardized, normally distributed, random variable will be less than or equal to d.

Step 1: calculate d1 and d2

Step 2: calculate N (d1) and N (d2) Table 21.4

Step 3: calculate C ; Option underpriced of overpriced?

Put option: Put-call parity (PCP), rearrange to solve the put price: P = Ee ^-R2 + C - S.

What are Employee share options (ESO)?

Different from regular share options: 10-year life, cannot be sold, ‘vesting’ period.

The advantages of employee share options:

• Get employees to focus on corporate goals.

• No immediate cost to the corporation.

Value executive share options determined by:

• Share price (S) equals the exercise price (E)

• Risk-free rate

• Time interval, t

• Variance

What are the values of debt and equity?

Case I: The debt is risk free:

Equity worth = Face value – (Present value – Risk-free part)

Case II: The debt is risky:

• ΔS / ΔC = number of options that exactly replicates the value of the assets of the firm.

• S (lowest) / (1+ risk-free rate) = PV

• "V_u = # options x C_o - PV" . Solve " C_o "

• The equity is thus worth C_o

• The debt is worth V_u - C_o

• Interest rate on the debt = (face value / debt) – 1 = %

What are options and capital budgeting?

Real options = An option that involves real assets as opposed to financial assets such as shares of equity.

Investment timing decision: all projects compete with themselves in time. Compare the NPV of taking the project now with the NPV of taking it later.

• NPV = - costs + cash flow / discount rate

• NPV= NPV future / n x discount rate

Option to wait = ΔNPV = extra value created.

Option can never have a negative value, when that happens the option value is zero.

Managerial options; opportunities to modify a project

Contingency planning, look at some of the possible futures that could come about, and what actions we might take if they do.

• Option to expand

• Option to abandon

• Option to suspend or contract operations

• Options in capital budgeting

• Strategic options -> options for future, related business moves

What are mergers and acquisitions? - Chapter 22

Key Notations:

• EPS: earnings per share

• NPV: Net present value

• V: value of the firm

What forms of takeover are there?

1. Merger, when one company takes over the assets and liabilities of another company. The acquiring firm keeps its name and identity. Sometimes an entire new firm is created, this is called a consolidation. An advantage of a merger is that it’s legally simple. The disadvantage is that it must be approved by the shareholders of the firms, getting the necessary votes can be difficult.

2. Acquisition of shares, purchasing the firm’s voting shares. The firm offers in public to buy shares, this is called a tender offer. An advantage is that no vote is required and no shareholder meetings. The disadvantage is that you can’t have a complete absorption of a firm.

3. Acquisition of Assets, buying the assets of another firm. As an advantage, a minority shareholders can’t hold out. The disadvantage is that the legal process can be costly.

There are different types of acquisition. The horizontal acquisition, the bidder chooses a firm in the same industry. When the firms are in the same production process, we speak of vertical acquisition. And when the firms don’t have any relation to each other, then it’s called a conglomerate acquisition.

• Proxy contests. Replace the existing management to gain control of the firm. Get the shareholders to use their proxy votes and vote for new directors.

• Going private. A small group of investors buys the equity shares of a public firm, this is often called leveraged buyouts.

Some mergers are between companies in different countries, this makes the taxation of the mergers and acquisitions very complex. The accounting and tax rules are often very different in other countries.

What sort of benefits can one expect from acquisitions?

If the value of the combined firm is greater than the value of the sum of the separate firms, than the acquisition is beneficial. The difference between those values is the incremental net gain (ΔV). The value of the company is thus ΔV + Vb = Vb* = the value of Firm B to Firm A.

The incremental cash flow (ΔCF) is the difference in cash flow of the combined company and the sum of the two companies. So the cash flow benefits can arise from:

• Revenue enhancement: Marketing gains, strategic benefits and market power.

• Cost reductions: Greater operating efficiency by economies of scale, economies of vertical integration and complementary resources.

• Lower taxes: tax losses, unused debt capacity, surplus funds and asset write-ups.

• Reductions in capital needs

Rules for evaluating the potential benefits:

• Use the market values

• Only estimate incremental cash flows

• The discount rate has to be correct

• Watch the transaction costs

Sometimes the management is inefficient, so changing the management can increase the value. An acquisition can provide an appearance of growth in earnings per share. This shows that the firm is doing better than it is in reality.

People think that diversification is a benefit of a merger, but in fact it doesn’t always create value. Diversification can reduce unsystematic risk, but we need to reduce the systematic risk to increase the value of the assets. So reducing the unsystematic risk doesn’t affect the value of the firm.

What is the cost of a merger?

First calculated the net incremental gain (ΔV), then the total value of Firm B to firm A (Vb*). If we know the costs of the acquisition, we can calculate the NPV:

NPV = Vb* - Cost to Firm A of acquisition. There are two options to pay for a merger, cash acquisition and equity acquisition.

With equity acquisition you have to calculate how many shares you have to give up.

• Number of shares = costs / share price.

• Shares outstanding = shares before merger + new shares.

• Value of merged firm = Vab = Va + Vb + ΔV.

• Per-share value = Vab / shares outstanding.

• True cost of the acquisition = shares to firm B x per-share value.

• NPV = Vb* - cost

A firm has to choose between financing the acquisition with cash or with shares of equity. Factors to think about when making that choice: Sharing gains, taxes and control.

Defensive tactics (to resist unfriendly attempts).

• Corporate charter: the conditions for a takeover. Sometimes firms adjust the corporate charters to make the takeover more difficult.

• Repurchase and standstill agreements: the firm buys its own equity from some individual investors.

• Poison pills and share rights plans: Distributing equity rights to existing shareholders. The flip-in provision means that when there’s an unfriendly takeover attempt, the holders can receive equity in the firm, which is worth twice the exercise price. This increases the costs of taking over the firm.

• Going private and leveraged buyouts: The shares aren’t public anymore, so a takeover via tender offer can’t happen.

What are the shareholders' benefits?

Let’s find out how mergers and acquisitions can benefit shareholders. The target firm shareholders get paid anyway, that’s clear.

Shareholders from the bidding firm don’t win or lose very much, that’s because of:

• It’s not sure if the expected gains can be completely achieved.

• The target firms are usually much smaller than the bidding firms.

• Management doesn’t act in the best interest of the shareholders. Often the management wants to increase the size of the firm and then the value per share decreases.

• The NPV of acquiring can be zero because of the competitive market.

• Share price already reflects the anticipated gains.

Divestiture, selling business assets, operations, divisions and/or segments to a third party.

• Equity carve-out. A new completely separate company is created and the only shareholder is the parent company. Then there’s an initial public offering to sell a part of the parent’s equity to the public.

• Spin-off. Distribute shares to existing parent company shareholders.

• Split-up. To split a company into two or more new companies.