Lesson 7: Cost of Capital

Question 1

Estimating CAPM’s parameters

Answer 1

1. Use the rate on U.S Treasuries as the risk-free interest rate
2. common proxy for the market portfolio is the S&P 500
3. Calculating the risk premium:
   + Way 1: historical approach: average the excess of the market return over the risk-free rate over a historical period (arithmetic average)
   +Way 2: fundamental approach: make some assumption for dividend growth with:
   RMkt = Div1 / (Po) + g (Po: value of the market, g: growth rate of div, Div1: div in the coming year)
4. Ri = rf + αi + βi(RMkt - rf) + εi

Question 2

Reasons why market risk premium has declined over time

Answer 2

1. More investors in the market -> the risk is shared = a larger group
2. Mutual funds and ETFs (exchange traded funds) have decreased the cost of diversification
3. The market has become less volatile

Question 3

Calculate return of the bond

Answer 3

rd = (1-p)y + p(y-L) = y - pL
p: annual probability of default
L : proportion of debt that is lost when a default occurs
y: annual effective interest rate on the bond

Question 4

cost of capital if a project is financed with equity and debt

Answer 4

unlevered cost of capital or asset cost of capital (ru)

Question 5

Calculate unlevered cost of capital (ru)

Answer 5

ru = E/(E+D) * rE + D/(E+D) *rD

Question 6

Calculate unlevered beta

Answer 6

βu = E/(E+D) * βE + D/(E+D) *βD

Question 7

Company’s enterprise value

Answer 7

= equity + debt - cash

Question 8

Net debt

Answer 8

= Debt - Cash