# Capital budgeting and the capital asset pricing model

Capital budgeting and the capital asset pricing model “Less is more. ” – Mies can der Rohe, Architect

Cost of Capital Applications • The company cost of capital is the correct discount rate for projects that have the same risk as the company’s existing business but not for those projects that are safer or riskier than the company’s average. • The company cost of capital equals the company cost of equity for companies that are financed with 100% equity (i. e. companies without any debt). • CAPM is only one model to estimate company cost of equity to arrive at the cost of capital. Other models (like APT) can be employed to do similar analysis.

Using the CAPM to Estimate the Equity Cost of Capital Four steps: Step 1 Measure the risk-free rate rf Step 2 Estimate the expected market risk premium rm - rf Step 3 Estimate beta b Note: Estimation errors tend to cancel out when you estimate betas for portfolios. Step 4 Calculate r = rf + b (rm - rf )

Step 1 Measure the risk-free rate rf • Use for risk free project. – Use the T-bill rate? – Use the T-bond rate? – Use average future T-bill rate expected during life of the project? Expected average T-bill rate = T-bond yield - premium of bonds over bills* * Use historical (or forecasted) premium of bonds with maturity close to expected project life.

Step 2 Estimating the Expected Market Risk Premium • Arithmetic versus Geometric mean return: Suppose stock rises 33% and then falls 25% Arithmetic mean return = (33 - 25)/2 = 4% Geometric mean return = (compound return) 1. 33 x. 75 - 1 = 0% Note: If returns are lognormally distributed, geometric mean = arithmetic mean - variance/2

Step 2 - continued For cost of capital estimation use the arithmetic mean l Suppose stock price is £ 100 and it could rise to £ 133 or fall to £ 75 with equal probability: Expected payoff = (. 5 x 133) + (. 5 x 75) = £ 104 Expected return = 104/100 - 1 = 4% PV = Expected payoff/1. 04 = 104/1. 04 = £ 100 l If we look at this stock over many years, its arithmetic mean return should be 4%, but its geometric mean return is 0%. l Investors would not invest in a project that offered an expected return of 0%.

Step 2 - continued Use a large number of years to estimate the expected risk premium l. The l standard error of the mean is s / N Even with a large number of years the standard error of the mean is high l Example: In the UK standard deviation of market return is about 20%. Therefore with 64 years (N = 64) standard error = 20/ 64 = 20/8 = 2. 5%

Step 3 - Estimating Beta. Example: Microsoft's beta Microsoft return % 30 25 20 Beta = 1. 2 15 10 -5 -15 -20 Mkt return %

Note on the Stability of betas RISK CLASS % IN SAME CLASS 5 YEARS LATER % WITHIN ONE CLASS 5 YEARS LATER 10 (High betas) 35 69 9 18 54 8 16 45 7 13 41 6 14 39 5 14 42 4 13 40 3 16 45 2 21 61 1 (Low betas) 40 62 Source: Sharpe and Cooper (1972)

Step 4 Estimating equity cost of capital with CAPM BOSTON EDISON Estimated equity beta =. 49 Cost of (equity) capital = interest rate + beta x expected market risk premium = interest rate +. 49 x 8. 6 = interest rate + 4. 2% MICROSOFT Estimated equity beta = 1. 20 Cost of (equity) capital = interest rate + 1. 20 x 8. 6 = interest rate + 10. 3%

Capital Structure and the Company Cost of Capital • Stockholders are exposed to: - Business Risk - Financial Risk • Financial risk does not affect the expected return on a firms assets, but it does increase the risk to common stockholders and hence also the return they demand.

Company Cost of Capital • Use Company Cost of Capital (not the expected return on common stock which is just company cost of equity) in capital budgeting decisions. The company cost of capital can be found: 1. Using the firm’s asset beta, (not the beta of common stock). or 2. Using a weighted average of the returns investors expect from securities issued by the firm.

The firm’s asset Beta • The firm’s asset beta is equal to the beta of a portfolio made up of all the securities a firm has issued. Asset Beta = (D/(D+E) Debt Beta) + ( E/(D+E) Equity Beta) • Once you have calculated the asset Beta you can use CAPM to calculate the company cost of capital = rf + basset (r m - r f )

Company cost of capital is average of cost of equity & cost of debt WEIGHTED AVERAGE COST OF CAPITAL (WACC) = EQUITY DEBT + EQUITY COST OF x EQUITY + DEBT + EQUITY x COST OF DEBT NOTE: Taxes are ignored here - we will consider taxes in later chapters.

Avoiding fudge factors example - part 1 Don't add fudge factor to discount rate to cover things that could go wrong. Adjust cash flow forecasts instead. Cash flow in millions Project A B Most likely 1. 0 Probable range. 8 - 1. 2 If r =. 10, PVA = 1. 0/(1+. 1) =. 909 or $909, 000 PVB should be less - but how much less? Note: We assume disaster doesn't change beta Chance of disaster? (cash flow =0) No Yes

Avoiding fudge factors example - part 2 Unbiased forecast = probability-weighted average outcome Suppose for project B probability of disaster is. 2 Then B's unbiased forecast could be: (. 2 x 0) + (. 8 x 1) =. 8

Avoiding fudge factors example - part 3 B's present value is. 8 PV = =. 727 or $727, 000 1. 1 You could get right answer with a 37. 5% discount rate (fudge factor): 1. 0 PV = =. 727 1. 375 But: * you don't know right fudge factor until you can adjust forecast * once you adjust forecast you don't need fudge factor

Cost of capital and project lives Using the same cost of capital for each year's cash flow assumes risk increases steadily with time. Therefore do NOT use a higher cost of capital simply because a project has a long life.

Risk, DCF and CEQ

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