Lecture notes Finance and Risk Management for IB

Contains lecture notes based on the lectures on 2014-2015.

Lecture one

“Chapter 1, 2 and 3” > Fundamentals of Corporate Finance

Finance = The art and science of managing wealth;

• Making decisions about what assets to buy and when
  Take into account: Time and Uncertainty

Financial Management = Those activities that create or preserve the economic value of the assets of an individual, small business, or corporation.

The areas focused on in Finance are; Corporate finance (focus), investments, financial institutions and markets and international finance.

What is corporate finance?
Investment = What long-term investments will you make?
Timing: cash outflow today can create cash inflow in the future
Financing = Where will you get long-term financing for long-term projects (investments)?
Timing: cash inflow today and cash outflow in the future to meet obligations
Liquidity = How to manage everyday activities
Timing: Balance of cash inflows and outflows in the short term.
> Uncertainty for all cases = Risk involved. Key question; What is a sufficient return? Riskier investments mostly mean a higher return.

Responsibilities of the financial manager are investment decisions, financing decisions, short-term financial planning, oversee accounting and audit function in firm and ensuring the financial welfare of the firm.
Refer to the organizational chart in Slide 7 of the Lecture Slides to be found on Nestor; On top there is the Chief Financial Officer, with a Treasurer and a Controller under him, splitting up the Financial Management Decisions, which are;

• Capital budgeting; Planning and managing long-term investments. Take Apple taking over Beatz for example. All done to increase the economic value and wealth of the firm

• Capital structure; The mixture of a long-term debt and equity maintained by a firm. How much to borrow is a question to ask, but also what are the least expensive sources of funds for the firm?

• Working capital management; The management of a firm’s short-term assets and liabilities. How much cash and inventory should be kept? And should we sell on credit?

Corporate structure

• Sole proprietorship = Eenmanszaak for the Dutch.
  Advantages;

  • Simplest and easiest form of business

  • Least amount of legal documentation

  • Least regulated

  • Owner keeps all profits

Disadvantages;

• • Personal tax rate on profits

  • Obligations of the business are the sole responsibility of the owner, and personal assets may be necessary to pay obligations (personal and business assets are commingled)

  • Business entity limited to life of owner

  • Can have limited access to outside funding for the business

• Partnership = VOF for the Dutch
  Advantages;

  • Agreements between partners may be easily formed

  • Involves more individuals as owners and therefore usually more expertise

  • Larger amount of capital usually available to the business (compared to proprietorship)

Disadvantages;

• • Assets of general partners are combined with assets of the business

  • Profits treated as personal income for tax purposes

  • Difficult to transfer ownership

• Corporate Structure = Business form existing as a separate legal entity from its owners
  Advantages;

  • Unlimited life

  • Easy transfer of ownership

  • Limited liability

  • Easy raising capital

Disadvantages;

• Double taxation (corporate and personal income)

• Cost of set-up and report filing

The money cycle = The movement of money from lenders (investors) to borrowers (corporations). For a depiction of the money cycle, see Slide 18 of the Lecture Slides to be found on Nestor. The role of the Financial Manager is to manage the money cycle. Making sure the money obtained from investors is used for the firm’s operations.

The financial statements approach for corporate decisions
The balance sheet provides a point-in-time snapshot of the firm’s assets, liabilities, and owners’ equity. On the asset side of the balance you see the long-term assets like the plant, property and equipment, which leads us to Corporate decision 1; The capital budgeting decisions. How to invest your capital and in what to invest your capital? On the liability side of the balance sheet you see long-term liabilities and owner’s equity, which leads us to Corporate decision 2; Financing decisions. How to raise capital to buy assets? When subtracting current liabilities from the current assets, you get net working capital, which leads us to Corporate decision 3; Net working capital management. How much short-term cash flow does a company need to pay its bills?

Earnings Before Interest and Taxes (EBIT) = Revenues – Operating expenses

Depreciation is no cash flow, but an expense. Depreciation expenses provide tax savings by reducing the taxable income.

Managerial goals
A corporation is a big set of contracts.
Agency relationship = You are the owner (you own shares) but do not operate the firm on a daily basis.  There can be conflicts of interest between owners and managers

• Financial goals; to maximize the shareholders’ wealth

• Managerial goals; may be different form the shareholders’ goals

Conflicts of interest may create agency problems.
Corporate governance = The system to reduce the agency problem.

The shareholders can devise contracts that align the incentives of the managers with the goals of the shareholders;

• Designing managerial compensation plans,

• The threat of being fired,

• The threat of takeover

Financial Markets
Money market = Financial assets that will mature within one year
Financial market = Financial assets that will mature over a year

Primary market = Corporations raise external funds through financial assets, such as stock and bonds. From investor to corporation
Secondary market = What will happen if investors want to sell their securities? The sale of “used” securities from one investor to another. From investor to investor

Lecture two

“Chapter 3, 4 and 5” > Financial ratios, time value of money

Contents of this lecture

• Ratio analysis

• Du Pont identity

• Time value of money: Compounding and Discounting Single Cash Flows

• Time Value of Money: Compounding and Discounting Multiple Cash Flows

Ratio analysis
Financial ratios = Ways of comparing and investigating the relationships between different pieces of financial information. Via financial ratios you can understand the financial state of a firm by comparing the ratios of the firm with those of its competitors.
> Financial ratios can reflect different characteristics of a company, which can be liquidity ratios, financial leverage ratios, turnover ratios, profitability ratios or market value ratios.

Liquidity or short-term solvency ratios
Generally speaking, the higher the ratio, the better the health of the company.

Current ratio = current assets / current liabilities

Quick ratio = (current assets – inventory) / current liabilities
> You subtract inventory, because inventory might take a long time to leave the company, making that it is no cash for a long time and thus making the outcome less reliable.

Cash ratio = cash and cash equivalents / current liabilities

Financial Leverage or Long-Term Solvency Ratios
Generally speaking, the higher the ratio, the better you are capable of meeting long term obligations.

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

Debt-equity ratio = total debt / total equity

Equity multiplier = total assets / total equity

Times interest earned ratio = EBIT / interest

Cash coverage ratio = (EBIT + depreciation) / interest

Asset Management or Turnover Ratios

Inventory turnover = COGS / inventory
> Higher inventory turnover is better, because it means more sales/COGS per unit inventory

Days’ sales in inventory = 365 days / inventory turnover
> How long on average the inventory is in your company

Receivable turnover = sales / trade receivables

Days’ sales in receivables = 365 days / receivables turnover
> How long on average it takes before people pay their debts to you as a company

Total asset turnover = sales / total assets

Profitability Ratios
These ratios are in line with what is said in the first lecture; they show how well the company succeeds in maximising benefits and value for its shareholders. The higher these ratios, the better.

Profit margin = net income / sales

Return on assets = net income / total assets

Return on equity = net income / total equity

Market Value Ratios
The higher these ratios, the better.

EPS = net income / shares outstanding
> EPS stands for Earnings Per Share.

PE ratio = price per share / earnings per share
> The higher, the more shareholders are willing to pay for a share

Market-to-book-ratio = market value per share / book value per share

The Du Pont Identity
The return on equity is the value created for shareholders. ROE is affected by operating efficiency, asset use efficiency (how well are you managing the assets of your company) and financial leverage. Changing the ROE formula (net income / total equity)
ROE = profit margin x total asset turnover x equity multiplier

Time value of money
€1 today versus €1 after one year…
… Receiving €1 today is worth more than €1 in the future, due to growing value opportunities over time. If you can get money now, you better take it now than in the future.
Opportunity cost of receiving €1 in the future is the interest we could have earned if we had received the €1 sooner.

Future value calculations = Translate €1 TODAY into its equivalent in the FUTURE (compounding-investing).
Present value calculations = Translate €1 in the FUTURE into its equivalent TODAY (discounting-borrowing).

Some parameters in calculating future/present value

• Interest rate (Rate, r)

• Time that money remains invested (n, NPER)

• Amount that is invested today, present value (PV)

• Future value of the investment in n years (FVn)

• Periodic equal payments or deposits (A:Annuity) or (PMT)

Future value
Compounding = The process of accumulating interest on an investment over time to earn more interest.

Interest on interest = Interest earned on the reinvestment of previous interest payments.

Example
You deposit €100 in an account earning annual 10%, how much would you have in the account after 2 years? Three ways:

1. Year 0; Invest €100. Year 1; €100 * 1.1 = €110. Year 2; €110 * 1.1 = €121

2. Year 0; Invest €100. Year 1; €100 * 1.1 = €110. Year 2; €100 * 1.1 * 1.1 = €121

3. Year 0; Invest €100. Year 1; €100 * 1.1¹ = €110. Year 2; €100 * 1.1² = €121

In symbols > Year 0 you invest V0 at r%, in year 1 you earn V1 = V0*(1+r), in year 2 you earn V2 = V0*(1+r)². Et cetera. Even more generally ; FV = PV * (1 + r)ⁿ
> You can also look an interest factor up in a given table [Appendix Table A.1 in the book] using the interest percentage and the period of time. You multiply your cash amount by the looked up factor.

Example
If you deposit €100 in an account earning annual 6% with quarterly compounding, how much would you have in the account after 5 years?

FV = PV (1 + (r / m) ) ^{m x n}
Where m = # of compounding periods in a year, 4 in this case.
r/m = 6%/4 = 1.5%. m x n = 20
Solution > FV = 100 (1.015)²⁰ or FV = 100 * 1.3469 = €134.69

Example
Due to quarterly compounding (see previous example), the actual annual rate is not 6% any more. Therefore, we calculate the Effective Annual Rate (EAR), which is a standardized rate and a comparison of several alternative investments given different stated interest rates and compounding intervals.

m = Frequency of compounding (m=2 semiannual, m=4 quarterly, m=12 monthly)
EAR = ( 1 + ( annual rate / m ))^m – 1
EAR = ( 1 + ( 0.06 / 4 ))⁴ – 1 = 0.0614 = 6,14%

Present value
Present value = The current value of future cash flows discounted at the appropriate discount rate.

Discount = Calculate the present value of some future amount.

Example
You are saving and your goal is to have €1000 in two years. If you can earn 10% on you money, how much do you have to put up today?
Calculating present value is exactly the opposite of calculating future value. Instead of calculating Year 2, you calculate Year 0. Three ways:

1. Year 2; Receive €1000. Year 1; €1000 / 1.1 = €909.09. Year 0; €909.09 / 1.1 = €826.45

2. Year 2; Receive €1000. Year 1; €1000 / 1.1 = €909.09. Year 0; €1000 / 1.1 / 1.1 = €823.45

3. Year 2; Receive €1000. Year 1; €1000 / 1.1¹ = €909.09. Year 0; €1000 / 1.1² = €826.45

In symbols > Year 2 you receive V2 at r%, in year 1 you earn V1 = V2/(1+r), in year 2 you earn V2 = V2/(1+r)². Et cetera. Even more generally ; PV = FV / (1 + r)ⁿ
> You can also look an interest factor up in a given table [Appendix Table A.2 in the book] using the interest percentage and the period of time. You multiply your cash amount by the looked up factor.

Periodically ; PV = FV / ( 1 + r / m ) ^{m x n}

Example
If you sold land for €11,933 that you bought 5 years ago for €5,000, what is your annual rate of return? Two ways:

1. PV = FV / ( 1 + r ) ⁿ
   5000 = 11933 / ( 1 + r ) ⁵
   (5000/11933) = 1 / ( 1 + r ) ⁵
   0.419 = 1 / ( 1 + r ) ⁵
   1 / 0.419 = ( 1 + r ) ⁵
   (2.3866)^1/5 = ( 1 + r )
   r = 0.19

2. FV = PV (1 + r)ⁿ
   11,933 = 5,000 * (1+r)⁵
   (11,933 / 5,000) = (1+r)⁵
   2.3866 = (1+r)⁵
   (2.3866)^1/5 = (1+r)
   r = 0.19

How to use Tables for Interest Factors? > At the row for year 5, move horizontally across interest rates to reach the PVIF of 0.419.

Example
Suppose you placed €100 in an account that pays 9.6% interest, compounded monthly. How long will it take for your account to grow to €500?

PV = FV / ( 1 + r / m ) ^{m x n}
r/m = 0.096/12 = 0.008 | m x n = 12 x n = N
100 = 500 / (1+ .008)^N
5 = (1.008)^N > You can use the tables from here
ln 5 = ln (1.008)^N
ln 5 = N ln (1.008)
1.60944 = .007968 N, making N = 202 months

Annuities
Annuity = A sequence of equal cash flows, occurring at the end of each period.

Example
If you invest €1,000 each year at 8%, how much would you have after 3 years?
Investing, here, starts in year 1 (See Slide 43 of the Lecture Slides to be found on Nestor).
FV = PMT * (( 1 + r )ⁿ – 1 ) / r
FV = 1000 * (( 1.08 )³ – 1 ) / 0.08 = €3246

How to use Tables for Interest Factors? > Look up the factor that comes out of the combination of the interest rate (8%) and the holding periods (3) in the table of Appendix A.4. Multiply the investment by the factor.

Example
What is the PV of €1,000 at the end of each of the next 3 years, if the opportunity cost is 8%?
Investing, here, starts at year 1 (See Slide 46 of the Lecture Slides to be found on Nestor)

PV = PMT * [( 1 – ( 1 / ( 1 + r )ⁿ ))) / r]
PV = PMT * [ (1 / r) – (1/r(1+r)ⁿ) ]
PV = 1000 * [ (1/0.08) – 1 / ( 0.08 ( 1 + 0.08 )³ ] = 2.577
> 1000 x 2.577 = €2577

Perpetuities
Perpetuity = Receiving a fixed payment every period (month, year, etc.) forever. Or other stated; an annuity that goes on forever.
PV = PMT / r

Uneven cash flows; See Slides 53&54 of the Lecture Slides to be found on Nestor. Each single year another amount of money is added. Here, you should discount each cash flow separately.

Lecture three

“Chapter 6 and 7” > Bond and equity valuation

Bonds carry less risks than shares. This will become more clear later on in the lecture.

Valuation of bonds and stocks
The value of equity equals the present value of future cash flows. We can estimate the future cash flows with the help of Size (how much) and Timing (when).
We discount cash flows at an appropriate rate;

• Rate should match risk

• An expected rate of return (yield to maturity) for bonds

• Required (or expected) rate of return for common stocks

Bonds
Maturity = The specified date on which the principal amount of a bond is paid
Yield to Maturity (YTM) = The rate required in the market on a bond.
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.
See Slide 8 of the Lecture Slides to be found on Nestor for an example of a bond.

Example: We issue a bond with 10 years to maturity with annual coupons of $80 (=fixed). Similar bonds have a YTM of 8%. What would this bond sell for?
What this bond would sell for can be calculated using the present value of the face value + the present value of annuities (coupon payments).
PV =  Σ80 / 1.08^t + 1000 / 1.08¹⁰ = $1000, As the coupon rate equals the YTM

The present value of the annuities can be found by dividing the coupon by the PVIFA, which can be found in Appendix A. the present value of the face value can be found by dividing the face value by the PVIF, which can be found in Appendix A.

Example: Find the value of a 14% coupon bond with annual payments, $1000 par value and 15 years to maturity if the YTM is 12%.
PV = Σ140 / 1.12^t + 1000 / 1.12¹⁵ = $1136.54, As the coupon rate > YTM, meaning that buying similar bonds would offer you less return. This bond is selling at premium.

Example: Find the value of a 14% coupon bond with annual payments, $1000 par value and 15 years to maturity if the YTM is 16%.
PV = Σ140 / 1.16^t + 1000 / 1.16¹⁵ = $888.49, As the coupon rate < YTM, meaning that buying similar bonds would offer you more return. This bond is selling at discount.

Interest rate risk
Long-term bonds carry higher risk of decreasing in value than short-term bonds. This is illustrated in the graph in Slide 21 of the Lecture Slides to be found on Nestor.

Example: The same 14% par value bond, now with semi-annual payments and 15 years to maturity. The YTM is 14%. For how much does it sell?
PV = Σ70 / 1.07^t + 1000 / 1.07³⁰ = $1000

Example: Finding the YTM. Suppose you want a 6-year 8% coupon bond and the price is $955,14 for a bond with a face value of $1000. What is the yield on this bond?
955.14 = 80 * [(1-1 / (1+r)⁶] + 1000 / (1+r)⁶
In this case you have to come up with YTM yourself and plug it into the formula until you have a proxy. You know that the bond is selling at discount so the YTM has to be higher than 8%.

Stocks and stock valuation
The major financing vehicle is the equity financing.
Ownership;

• Claim to residual profits

  • Dividends are cash claims

• Claim to residual assets in case of bankruptcy

• Voting rights

  • Participation in the management

  • Elect board of directors, which selects the team to operate the company.

The value of stock equals the PV of expected future cash flows and cash flows in this case a dividends and the future selling price. The discount rate depends on the risk involved.

Differences between bonds and shares;

So why bonds carry less risk must be clear by now.

Dividend pricing models

• Single or some specified period

• Zero growth

• Constant growth

• Non-constant growth

Example: You expect to get $5.50 paid dividend at the end of the year. The stock price is expected to be $120 at that time.
P0 = Div1 / (1+r)¹ + Price1 / (1+r)¹ >> Single-period formula
r = D1/P0 + [(P1-P0) / P0] Where D1/P0 is the dividend yield and [(P1-P0) / P0] is the capital yield.
P0 = [Div1 / (1+r)¹] + [(Div2 + Price2) / (1+r)²] >> Multiple-period formula

Example: Multi-period formula at zero growth
P0 = [Div1 / (1+r)¹] + [Div2 / (1+r)²] + [Div3 / (1+r)³] … + [Divn / (1+r)ⁿ]
Future cash flows are constant, so the PV of zero growth stock is calculated the same as the PV of a perpetuity.

Example: Multi-period formula at constant growth
Dividends always grow at constant rate g
D1 = D0 * (1+g)
D2 = D0 * (1+g)²
D3 = D0 * (1+g)³
It equals the present value of a growing perpetuity
The value of a share of equity P
P0 = [D0 * (1+g) / R – g]

Dividends will be $4 per share. Investors require 16% return on similar companies. The dividends increase by 6% every year. What is the equity’s value today and in 4 years?
Today; P0 = 4 / (0.16-0.06) = $40
In 4 years; D4 = D1 * (1+g)³ = 4 * 1.063 = $4.764.
P4 = D4 * (1+g)/(R-g) = 4.764 * 1.06 / (0.16-0.06) = $50.50

Example: Multi-period formula for non-constant growth
Dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter. A common stock paid a $2 dividend. The dividend is expected to grow at 8% for 3 years and then will grow at 4% in perpetuity (infinity). What is the stock worth if the discount rate is 12%?
The constant growth phase beginning in year 4, can be valued as a growing perpetuity at time 3. The price of stock in year 3;
P3 = (2*1.08³*1.04)/0.12-0.04 = $32,75
Today, the stock is worth;
P0 = (2.16/1.12) + (2.33/1.12²) + ((2.52+32.75)/1.12³) = $28.89

Lecture four

“Chapter 12, 8 and 9” > Risk and Return; Capital Budgeting

Risk and return
Characteristics of individual securities

• Expected return

• Variance and standard deviation

• Covariance and correlation

Expected return
E(R) = ΣRi * Pi
Where; E(R) = Expected Return of an asset, i = observations (state of the economy), n = total frequency, R = return, P = probability
Example: See Tables in Slide 7 and 8 of the Lecture Slides to be found on Nestor.
E(R)_stock = 1/3 * (-7%) + 1/3 * (12%) + 1/3 * (28%) = 11%
E(R)_bond = 1/3 * (17%) + 1/3 * (7%) + 1/3 * (-3%) = 7%
Expected return of a Stock is higher than expected return of a Bond.

We can calculate projected or expected risk premium as the difference between expected return on a risky investment and the certain return on a risk-free investment.
Risk premium = expected return – risk free rate = R_i – R_f
Example: Suppose the risk-free investments are offering 4%. What is the projected risk premium on the Stock Fund? > Risk premium = 11 – 4 = 7%

Risk = Uncertainty in the distribution of possible outcomes. It is the variation of actual returns form our expected return.

Variance and standard deviation
σ² = Σ[(R_i – E(R))² * P_i], the standard deviation σ is the square root of the variance.
The higher standard deviation and variance, the riskier the investment.
See the Tables in Slides 16-18 of the Lecture Slides to be found on Nestor for calculations of the squared deviations > Rate of Return – Expected return squared.
Variance stock = 1/3 * 3.24% + 1/3 * 0.01% + 1/3 * 2.89% = 0.0205
Standard deviation stock = 14.3%
Variance bond = 1/3 * 1% + 1/3 * 0% + 1/3 * 1% = 0.0067
Standard deviation bond = 8.2%

Note that stocks have a higher expected return than bonds, and higher risk.

Return and Risk for Portfolios

• Creating a portfolio by having these two securities (bonds and stocks) together provided different return and risk characteristics

• Example: A portfolio that is 50% invested in bonds and 50% invested in stocks.

The expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio.
E(R)_p = Σ wi * E(R_i), where wi = value of investment I / total value of portfolio
or E(R)_p = w_b * E(R)_b + w_s * E(R)_s

Example: See Table in Slide of the Lecture Slides to be found on Nestor

50%×( 7 %) +50%×(11 %) = 9%

See Table in Slide 26 of the Lecture Slides to be found on Nestor
The variance of the portfolio (calculated the same way as the variance for stocks and bonds) is lower than both variances, mainly because of a negative correlation between the two securities, which is the advantage of diversification. Creating a portfolio offers a decrease in risk. An equally weighted portfolio (50% in stocks and 50% in bonds) has less risk than stocks or bonds held in isolation.

See Table in Slide 27 of the Lecture Slides to be found on Nestor. The more equities in the portfolio, the less risk.

Diversification = Spreading an investment across a number of assets will eliminate some, but not all, of the risk.

Two types of risk;

• Systematic risk = A risk that influences a large number of assets, also called market risk. Cannot be diversified. For example; if a whole market goes bankrupt, all companies in the market face losses, not just one.

• Unsystematic risk = A risk that affects at most a small number of assets. Also, unique of asset-specific risk. For example; when a supplier of a computer company goes bankrupt, the return of the computer company goes down. This is only one company affected. Or if the CEO of a company unexpectedly dies. You can eliminate this type of risk via diversification.

Capital asset pricing model and beta; The measure of risk in a well-diversified portfolio

How do we measure market risk which is non-diversifiable? > Capital Asset Pricing Model

Relationship between Risk and Expected Return (CAPM)

Expected return on the market ; E(R_m) = Rf + Market Risk Premium

Expected return on an individual security ; E(Ri) = Rf + βi * (E(Rm)-Rf), where (E(Rm)-Rf) is the market risk premium

The best measure of the risk of a security in a large portfolio is the beta (β) of the security. Beta measures the responsiveness of a security to movements in the market portfolio.

β = Cov(Ri,Rm) / σ² (Rm)
Clearly, your estimate of beta will depend upon your choice of a proxy for the market portfolio. Once individual stock betas are determined, the portfolio beta is easily calculated as the weighted average: βp = Σwi * βi

This formula is called the Capital Asset Pricing Model (CAPM) >>
E(Ri) = Rf + βi * (E(Rm)-Rf)
Expected rate of return on a security = Risk free rate + Beta of the security * Market risk premium. Assume βi = 0, then the expected return is Rf.

Now suppose: We have a portfolio made up of Asset A and a Risk Free Asset. We can calculate some different possible portfolio expected returns and betas by varying the percentages invested in these 2 assets. For this, Refer to Slide 39 of the Lecture Slides to be found on Nestor. Changing the percentage of Asset A in the portfolio changes the expected rate of return and the beta of the portfolio.
See Slide 40 of the Lecture Slides to be found on Nestor. What you see is a graphical, linear depiction of the Table provided in Slide 39. With an increasing beta, the expected return of the portfolio also increases. The line you see is the Security Market Line (SML), and in equilibrium, the reward-to-risk ratio must be the same for all the assets in the market. Now refer to Slide 42 of the Lecture Slides to be found on Nestor. If all assets shown in this graph would be in equilibrium, they would all plot the same straight line (SML). Here, only A and B are on the straight line, meaning that Asset C’s expected return is too high and Asset D’s expected return is too low.

Capital Budgeting: Net Present Value and Other Investment Criteria

Capital budgeting = The process of planning for purchases of long-term assets
There are some alternative models that have predetermined accept or reject criteria.
Models take into account;

• Timing > Various points in time: economic life (n)

• Amount of cash flows

  • Costs: cash outflow or investment outlay, which occurs generally at time 0 (today)

  • Benefits: cash inflows

Several ways to calculate;

Payback period

The amount of time required for an investment to generate cash flows sufficient to recover its initial cost. Payback Period = number of years to recover initial costs.

Time Period 0 1 2 3

Project 1 - 25 15 8 10 in euros

Project 2 - 5 2.5 2.5 2.5 in euros

Accept > Payback Period is less than benchmark

Reject > Payback Period is greater than benchmark

Project 1 ; 15 + 8 = 23; 23 < 25. € 25 – € 23 = € 2 will be recovered in the third year

[2 years + (€ 2/€ 10)=2.2 years] So payback period is 2.2 years

Project 2 ; 2.5 + 2.5 = €5, Payback period is 2 years

Payback period advantages;

• Easy to understand

• Adjusts for uncertainty of later cash flows

• Biased towards liquidity

Payback period disadvantages;

• Ignores the time value of money

• Requires an arbitrary cut-off point

• Ignores cash flows beyond the cut-of date

• Biased against long-term projects, such as R&D and new projects

Discounted payback period

The length of time required for an investment’s discounted cash flows to equal its initial cost.
Time period 0 1 2 3

Project 2 -5 2.5 2.5 2.5 in euros

PV year 1: 2,50/(1+0.12) = €2.23
PV year 2: 2.50/(1+0.12)² = €1.99
Total PV = 2.23+1.99 = €4.23

The rest of the initial outlay = 5−4.23 = €0.77

Now we know that the payback period is not 2 years for Project 2 with the discounted payback, so we have to calculate the PV of year 3.
PV year 3: 2.50/(1+0.12)³ = €1.78 >> The payback period must be more than 2 years!

[2 years +(€ 0.77/€ 1.78)]= 2.43 years

Other methods:

1. Net Present Value (NPV)
   NPV = Total PV of annual net cash flows – cost

NPV = - CF0 + [CF1/(1+r)¹] + [CF2/(1+r)²] + … + [CFn/(1+r)ⁿ], where CF = annual cash flows, CF0 = initial cost, r = discount rate, n = economic life
With the NPV you can clearly see the benefit of the project (sum of PV annual cash flows) versus the costs of the project (initial investment)

1. 1. Accept the project if NPV > 0

   2. If projects are independent, accept both projects

   3. If projects are mutually exclusive, Choose the highest NPV.

   4. Accepting positive NPV projects benefits shareholders because it will increase the value of firm.

2. Profitability Index (PI)
   Very similar to NPV. Instead of subtracting the initial outlay from the PV of inflows, the PI is the ratio of initial outlay to the PV of inflows
   PI = Σ [CFt / (1+r)^t] / CF0

   1. Accept if PI > 1

   2. Select alternative with highest PI

3. Internal Rate of Return (IRR)
   IRR is the discount rate that makes NPV zero
   $0 = - CF0 + [CF1/(1+r)¹] + [CF2/(1+r)²] + … + [CFn/(1+r)ⁿ]

You have to find r instead of NPV in this case.

1. Accept if IRR > hurdle rate

2. Hurdle rate = Weighted average cost of capital, the minimum acceptable rate of return that should be earned on a project

3. Select alternative with highest IRR

4. Trial-error method: Choose various required rates until total present value of cash flows equals the İnitial outlay.

IRR is the maximum rate of return that the firm would expect to have from the project.

Up to this rate the firm can get a positive NPV (IRR > hurdle rate). After this rate, NPV is negative (IRR < hurdle rate).
Crossover point = the discount rate that produces the same NPV for the two projects. You can calculate the crossover point yourself >> See Slide 67 for an example.

Which model is the best?
The best model would be the NPV

• It reflects stated objective of the firm (to maximize its economic value)

• Investment with NPV > 0 will increase the firm value

• Increasing in shareholder wealth

Advantages of IRR

• Easy to understand and communicate

  • Doesn’t use r

  • Provide an answer as rate of return

Disadvantages of IRR

• IRR may not exist or there may be multiple IRR

• Scale problem

  • Would you rather make 100% or 50% on your investments?

  • What if the 100% return is on a €1 investment while the 50% is on a €1000 investment?

Incremental cash flows

The incremental cash flows for project evaluation consist of any and all changes in the firm’s future cash flows that are a direct consequence of taking the project. They show the difference between a firm’s future cash flows with a project and those without the project.

The stand-alone principle = The evaluation of a project may be based on the project’s incremental cash flows.

5 types of incremental cash flows;

• Cash flows

• Sunk costs = A cost that has already been incurred and cannot be removed and therefore should not be considered in an investment decision.

• Opportunity costs = The most valuable alternative that is given up if a particular investment is undertaken.

• Side effects = The cash flows of a new project that come at the expense of a firm’s existing projects.

• Allocated costs

Operating cash flow = Net Income + Depreciation – Increase (+ Decrease) in Net Working Capital

Lecture five

“Chapter 13 and 15” > Cost of Capital and Capital Structure Policy

Contents

• Cost of Capital

• Capital Structure

Cost of Capital
There are three broad sources of financing available or raising capital;
Debt, Common Stock (equity) and Preferred Stock (hybrid equity)
Difference common and preference: >> Preferred Stockholders have certain privileges concerning dividends. However, they have no voting rights.

Each of the three sources has its own rate of return required by investors to provide funds to the firm. Component sources of;

• Debt financing, R_d are commercial banks, nonbank lenders, suppliers and bond holders

• Equity financing, R_e, are common stockholders and retained earnings

• Hybrid equity financing, R_ps, are preferred stockholders

Weighted Average Cost of Capital (WACC) = The minimum acceptable rate of return that the firm should earn on its investments of average risk, in order to be profitable
WACC = Σ Weight _{component i} * Cost _{component i}
It is the discount rate for computing the Net Present Value (NPV) of the company, but also for individual projects. So you may conclude that if IRR > WACC you should accept the project/investment. If you want to determine WACC you should estimate the relative weights and the costs of debt, preferred stock and common stock of a firm (the component sources of capital).

1. Debt Component
   The cost of debt R_d is the rate that firms have to pay when they borrow money from banks, finance companies and other lenders and for bonds it is the Yield To Maturity on a firm’s outstanding bonds.
   Interest expenses are tax-deductible >> After-tax cost of debt = R_d * (1-T_c), where T_c is the corporate tax rate.

2. Preferred Stock Component
   Preferred stockholders receive a constant dividend with no maturity point. The cost of preferred stock R_ps can be calculated as follows; R_ps = D_p / Net price, where D_p is the annual dividend and the Net price are the Net proceeds per share of preferred stock.

3. Equity Component
   The cost of equity R_e is the rate of return that investors are demanding or expecting to make on money invested in a company’s common stock. The cost of equity can be estimated by using either the SML approach (See Chapter 12 of the Book) >>
   E(R_e) = R_f + β * [ E(R_m) – R_f ] or the Dividend Growth Model (See Chapter 7 of the Book) >> R_e = (D₁/P₀) + g
   Note that however you may think retained earnings have no cost (as they are earnings), they actually do have. They have an opportunity cost for the shareholders not being able to invest the money themselves.
   For newly issued common stock, the price must be adjusted for flotation costs, which are costs paid when a company makes a new issue of either stocks or bonds. They include the costs of printing the certificates.
   R_E = [D₀ * (1+g)] / [P₀ * (1-F)] + g , where F = flotation costs in a percentage.

The following equation can be used to combine all the weights and components costs into a single average cost that can be used as the firm’s discount rate or hurdle rate
WACC = [(E/V) * R_e] + [(PS/V) * R_ps] + [(D/V) * R_D] * (1 – T_C)
Example: See Slide of the Lecture Slides to be found on Nestor.
You see for each capital component the weight and the after-tax cost.
Solution; WACC = (0.38 * 5.32%) + (0.14 * 10.53%) + (0.48 * 11.36%) = 8.94%

Finance is a zero-sum game; One wins, one loses.

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. See also Slides 13 and 14 of the Lecture Slides to be found on Nestor.

The effects of financial leverage on returns and earnings per share
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.

Debt (leverage) generates higher returns to stockholders. See Slide 16 of the Lecture Slides to be found on Nestor. 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.
>> Note that: The higher the variability in EPS, the higher the risk.

Refer to Slide 17 of the Lecture Slides to be found on Nestor. Above the breakeven point you see the advantage of including debt and below you have a disadvantage of debt. So if you are at point 400;1 you better not include any debt, as it gives a disadvantage then. At the intersection, 0;0 you don’t lose and don’t gain. From the point 800;2 you should include debt in your capital structure.

Key question: Can firm value be maximized by choosing a particular mix of debt and equity? So; Is there and optimal mix of debt and equity (optimal capital structure)?

The firm market value equals the present value of the expected future cash flows.

PV = CF_n / (1+r)ⁿ >> The higher the discount rate, the lower the present value and vice versa

If we can reduce the WACC, the firm value can be increased (Recap: WACC is the discount rate for computing the Net Present Value (NPV) of the company, but also for individual projects). The Optimal Capital Structure is the one that minimizes the firm’s cost of capital and maximizes firm value.

Different theories for optimal capital structure

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
Refer to Slide 22 of the Lecture Slides to be found on Nestor >> With WACC and thus R_D remaining constant, there is no optimal capital structure, it is irrelevant.

There are 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 Slide 26 of the Lecture Slides to be found on Nestor. With increasing debt, the value of the firm increases, which is prove for MM Proposition 1.
See Slide 27 of the Lecture Slides to be found on Nestor. 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%

The static theory of capital structure = 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.

Bankruptcy costs;

• Direct; Legal and administrative expenses (distribution of assets to shareholders)

• Indirect; Costs of avoiding bankruptcy filing incurred by a financially distressed firm

• Financial distress costs; The direct and indirect costs associated with going bankrupt or experiencing financial distress

This was all missing in the MM model.

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.

See Slide 33 of the Lecture Slides to be found on Nestor. Here, you see a similar model as in Slides 26/27 but now the 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 Slide 34 of the Lecture Slides to be found on Nestor. 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 (See Slide 35 of the Lecture Slides to be found on Nestor):

• Case 1
  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
  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
  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
   

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.

Lecture six

“Chapter 16 and 17” > Dividend Policy; Working Capital Management; Financial Planning

Contents

• Dividends and dividends policy

• Short-term financial planning and management

Dividends and dividends policy
Key terminology
Dividends = A payment made out of a firm’s earnings to its owners, in the form of either cash or stock. >> Dividends are not compulsory; they can do it if they think it is beneficial for the company.
Distribution = A payment made by a firm to its owners from sources other than current or accumulated retained earnings.
Regular cash dividend = A cash payment made by a firm to its owners in the normal course of business, usually paid four times a year.

Different types of dividends;

• Regular cash dividends

• Stock dividends >> You give your shareholders stocks instead of cash in order to increase NPV for example

• Stock splits >> Done when stock prices are very high for example. Splitting stocks lowers the share price. Suppose, a share sells for €500. Buying 10 shares would cost someone €5000. The firm can tell their shareholders and future shareholders; each share of €500 is now equal to 5 shares of each €100

Dividends are distributions from net income (retained earnings) to the shareholders. Dividends are important, because dividends affect the firm’s capital structure and assets (cash) and because they can change stock price when the firm unexpectedly changes its dividend policy.

Many companies pay a regular cash dividend and public companies often pay quarterly. Sometimes firms will throw in an extra cash dividend. Often companies will declare stock dividends so no cash leaves the firm and the firm increases the number of shares outstanding.

The standard method of cash dividend payment
Declaration Date (means that the board of directors declares that a dividend will be paid) >> Ex-Dividend Date (if you buy on this date or days after this date you have no right on the first next dividend payment, if you do before this date you do) >> Date of Record (how many investors and who are going to receive dividends on the declaration date?) >> Date of Payment (actual money is sent). See Slide 6 of the Lecture Slides to be found on Nestor for an example and clarification of the standard method.

Price behaviour around ex-dividend date
The share price falls by the amount of the dividend on the ex-dividend date (which occurs at point 0 in Slide 9 of the Lecture Slides to be found on Nestor). If the dividend is €1 per share and the share price is €10 before the ex-dividend date, on the ex-dividend date and after the ex-dividend date the share price equals €9.

Does dividend policy matter?
Dividend policy = The time pattern of the dividend pay-out. It is not determined by the value/height of the dividend.

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

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

Homemade dividends = Replication of the Dividend Policy by an individual investor.
New policy is adopted: Dividends of £110 on Date 1 and £89 on Date 2 (See alternative policy). 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 you now get is illustrated in the Table in Slide 17 of the Lecture Slides to be found on Nestor.

Real world factors affecting dividend payouts

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

• Flotation costs >> Issuing new shares costs money (administration costs)

• Dividend restrictions

• Desire for current income

• Tax exempt investors

Information content of dividends = 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.
The clientele effect = The observable fact that equities attract particular groups based on dividend yield and the resulting tax effects.

An alternative to cash dividends
Share repurchases = The purchase, by a corporation, of its own shares of equity. Also called a buyback. See Slide 23 of the Lecture Slides to be found on Nestor for the frequency of repurchases over time.
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 at the end of the year is represented in Slide 24 of the Lecture Slides to be found on Nestor.
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
   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 is represented in Slide 25 of the Lecture Slides to be found on Nestor
   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 in Slide 25
   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. Real world considerations, however, on Dividends versus Repurchases;

• Taxes are lower for repurchases

• Higher flexibility of repurchases

• Dividends send positive signals of the company’s fundamentals to the market (See information content of dividends)

• Dividends require no monitoring, they are verifiable. Issuing a repurchase can be done in two ways; Announcing it in the news for example or Not announcing it and buying as an ‘investor’

• Repurchases and over/undervaluation of shares

See the Table in Slide 31 of the Lecture Slides to be found on Nestor for pros and cons of paying dividends.

Stock dividends and stock splits
Stock dividend = A payment made by a firm to its owners in the form of equity, diluting the value of each share outstanding.
Stock split = An increase in a firm’s shares outstanding without any change in owners’ equity.
Trading range = The price range between the highest and lowest prices at which an equity is traded.
Reverse split = A stock split in which a firm’s number of shares outstanding is reduced.

Short term financial planning and management
Cash management and liquidity management are not the same!
Liquidity management = The optimal quantity of liquid assets a firm should have on hand. The best possible is to pay your obligations as late as possible and to collect your accounts receivable as fast as possible.
Cash management = The optimization of mechanisms for collecting or disbursing cash.

Reasons for holding cash

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

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

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

Investing 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.
See Slide 37 of the Lecture Slides to be found on Nestor.

Determining the target cash balance
Target cash balance = A firm’s desired cash level as determined by the trade-off between carrying costs and shortage costs.
Adjustment costs = The costs associated with holding too little cash. Also, shortage costs.

See Slide 39 of the Lecture Slides to be found on Nestor
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. 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:
Formula 1 (see appendix)

Cash discounts
Cash discount = A discount given to induce prompt payment. It speeds up the collection of receivables. An 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, see liquidity management.

Key question: Does the cash discount provide a significant incentive for early payment?
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%

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 as holding inventory costs money.
Main idea: Inventory-carrying costs rise and restocking costs decrease as inventory levels increase. See Slide 55 of the Lecture Slides to be found on Nestor for a graphical depiction of the model. 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:
Formula 2 (see appendix)

Lecture seven

“Chapter 20 and 21” > Risk Management and Options

Risk management generally focuses on managing external factors that cause volatility in a firm’s cash flows. So firms desire a constant level of cash flows, no peaks and

Key terminology
Hedging = Reducing a firm’s exposure to price or rate fluctuations. Also called immunization.
Derivative security = A financial asset that represents a claim to another financial asset.

See Slides 6, 7 and 8 of the Lecture Slides to be found on Nestor. Here, you see quite low volatility (Slide 6), very high volatility (Slide 7) and moderate volatility (Slide 8). You can put all of these into perspective. In Slide 6, price levels are depicted. It is quite logic that price levels don’t go up and down on a daily basis. In Slide 7, government bond yields are depicted, and these yields change on a daily basis. In Slide 8, oil prices are shown. Oil prices can fluctuate, due to changes in supply and demand or other forces, but they don’t fluctuate that often.

A tool for identifying and measuring a firm’s exposure to financial risk;
The risk profile = A plot showing how the value of the firm is affected by changes in prices or rates. See Slide 10 of the Lecture Slides to be found on Nestor. You see a risk profile for a seller, a Wheat Grower in the example >> Increases in prices increase the firm value. In Slide 11 of the Lecture Slides to be found on Nestor, you see a risk profile of a buyer, a Food Processor using wheat. >> An increase in price decreases the firm value.

Types of exposure
Transactions exposure = Short-run financial risk arising from the need to buy or sell at uncertain prices or rates in the near future.
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.

Hedging with forward contracts
Back to the risk profile of wheat buyers and sellers: If these two firms get together, much of the risk can be eliminated: The grower (seller) and the processor (buyer) can simply agree that, at set dates in the future, the grower will deliver a certain quantity of wheat, and the processor will pay a set price. A forward contract = A legally binding agreement between two parties calling for the sale of an asset or product in the future at a price agreed today.

In the long run, a business is either viable or it will fail. No amount of hedging can change this. However, by hedging over the near term, the firm can accomplish 2 important things:
1. The firm protects itself from transitory price fluctuations with negative effects.
2. The firm buys itself time to adapt to fundamental changes in market conditions.

The basics;
Settlement date = One party must deliver the goods to the other on a certain date in the future.
Forward price = The other party pays the previously agreed forward price and takes the goods.
>> Note that, the buyer of the contract has the obligation to take delivery and pay for the goods and the seller has the obligation to make the delivery and accept the payment.

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 obligaed 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

See Slides 18, 19 and 20 of the Lecture Slides to be found on Nestor for a graphical depiction of the above described.
From the buyer’s perspective: Increasing prices means your value increases, because you can pay a lower-than-market price.

Hedging Currency Risk with Forward Contracts: An example for Importers
A Dutch company will pay $1 million for imports from the US in 3 months >> So the firm faces risk if the exchange rate changes:

• It will pay more € if the US dollar appreciates

• It will pay less € if the US dollar depreciates

How can you cover the risk? Buy US$ with a forward contract today to fix the exchange rate.
So you sign a forward agreement to buy US$ at a 1.56US$/€ exchange rate.
The value of €1.000.000 in US$ = 1000000/1.56 = €641.026, This is what the firm will be paying using a forward contract regardless of the exchange rate at that point in time (in 3 months). The benefit of the forward contract is a profit for the firm, namely:
If the $ turns out to gain value and the exchange rate is 1.30 US$/€ at maturity and you would not have signed a contract, you would have to pay 1000000/1.3 = €769.231 instead of €641.026 with the contract. The disadvantage is the loss you could make. If the US$ loses value versus the € and the exchange rate is 1.70 US$/€, you would have to pay only 1000000/1.70 = €588.235

Hedging Currency Risk with Forward Contracts: An example for Exporters
A Dutch company will RECEIVE $1 million for exports from the US in 3 months. How can you cover the risk? Sign a forward contract to sell US$ at 1.56 US$/€ exchange rate. This is what the firm will be receiving by using forward contract regardless of the exchange rate at that point in time (in 3 months). The disadvantage of the forward contract is a profit for the firm, namely: If the $ turns out to gain value and the exchange rate is 1.30 US$/€ at maturity and you would not have signed a contract, you would have received 1000000/1.3 = €769.231 instead of €641.026 with the contract. The benefit is the loss you could make. If the US$ loses value versus the € and the exchange rate is 1.70 US$/€, you would receive 1000000/1.70 = €588.235

Hedging with futures contracts
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

Swap contract = An agreement by two parties to exchange, or swap, specified cash flows at specified intervals in the future.

Types of contracts;

• Currency swaps

• Interest rate swaps

• Commodity swaps

See Slide 26 of the Lecture Slides to be found on Nestor for an example of an Interest Rate Swap.

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.

• Call option = An option that gives the owner the right, but not the obligation, to buy an asset

• 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.

Call options
Example for the Buyer of the Option: 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. See Slide 34 of the Lecture Slides to be found on Nestor. The strike price is depicted by 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)

Example for the Writer of the Option: 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. See Slide 38 of the Lecture Slides to be found on Nestor.

The strike price is depicted by 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 writer will gain the 50 cents the buyer paid for the option. At point 58.50, the option will be exercised and the profit starts decreasing [“At the Money”]. At point 59, you find the break-even price and after that point, only losses 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”] and the writer of the option faces losses.

Conclusions: This is a zero-sum game. The one wins, the other loses.

Put options
Example for the Buyer of the Option: Assume a purchase of a put option on asset X with a strike price of 58.50 per unit and a premium of 0.50 for one unit of X. See Slide 40 of the Lecture Slides to be found on Nestor. The strike price is depicted by a vertical line, as it is fixed. At all spot rates above the strike price, the buyer chooses not to exercise because the buyer will be able to sell with a higher price on the open market, so he only loses his premium [“Out of the Market”]. After the point 58.5 [“At the Money”], the buyer will make a profit by purchasing at market price and selling at strike price, so the option, here, is exercised [“In the Market”].
Buyer makes profit if Strike Price > Spot Price
Profit = Strike Price - (Spot Rate + Premium)

Example for the Seller of the Option: Assume a purchase of a put option on asset X with a strike price of 58.50 per unit and a premium of 0.50 for one unit of X. See Slide 40 of the Lecture Slides to be found on Nestor. The strike price is depicted by a vertical line, as it is fixed. At all spot rates above the strike price, the buyer chooses not to exercise because the buyer will be able to sell with a higher price on the open market, so he only loses his premium [“Out of the Market”]. The writer, here, makes a profit equal to the premium. After the point 58.5 [“At the Money”], the buyer will make a profit by purchasing at market price and selling at strike price, so the option, here, is exercised [“In the Market”]. The writer, now, faces a loss.

Intrinsic value of call options
An investor bought a call option for equity A with an exercise price of $80 and maturity of 2 months. The premium she paid was $2. Currently, equity A can be bought in the market for $85. What is the intrinsic value of the premium of the call option the investor bought? >> As the option is in-the-money, the intrinsic value is given by $85 - $80 = $5.

Intrinsic value of put options
An investor bought a put option for equity B with an exercise price of $80 and maturity of 2 months. The premium she paid was $2. Currently, equity B underlying market value is $90. What is the intrinsic value of the premium of the put option the investor bought? >> Currently, the investor can sell the asset for $90 in the market, which is $10 more that the exercise price of the put. As no investor would rationally choose to sell for less than the market value, the option is worthless today. Note that the value is not -10 in here, as there are no negative values for options. The value, thus, is zero.

Valuing options
The value of an option can be regarded as the PV of the expected payout when the option expires. Popular option pricing model = Black Scholes Option Pricing Model (BS-OPM). Six variables that impact the price of an option;

• The price of the underlying stock

• The option’s strike price

• The length of time left until expiration

• The expected stock price volatility

• The risk free rate of interest

• The underlying stock’s dividend yield

See Slide 45 of the Lecture Slides to be found on Nestor. Here, you see what happens to the value of call- and put options if one of these six variables changes.