Exercise 8.8 - CAPM
a. Expected return from Johnson & Johnson
Treasury bill rate = 6% expected return on the market = 9%
Beta Johnson & Johnson = 0.75
r (jj) = 0.06 + 0.75 * (0.09 – 0.06) = 0.0825 -> 8.25%
b. Highest expected return -> use the company with the highest beta ->
14.94%
c. Lowest expected return -> use the company with the lowest beta -> 6.48%
d. If the interest rate decreases (the risk-free rate) from 6% to 2% -> r (uss)
= 0.02 + 2.98 * (0.09 – 0.02) = 0.2286 -> 22.86% so the risk-free rate
lowers and contributes less, but the market risk premium increases more.
(because the beta is > 1 and reacts stronger than 1 to 1 on a change in
the market risk premium).
e. Coca-Cola has a beta of 0.46, which is < 1 and when the interest rate
decreases from 6% to 2%, Coca-Cola’s expected return will decrease as
well.
Exercise 8.12 – APT
3-factor APT model, risk-free rate = 7%
1st factor; change in GNP = 5% 2nd factor; change in energy prices = -1%
3rd factor; change in long-term interest rates = 2%
a. Stock whose return is uncorrelated with all 3 factors;
r = 0.07 + 0 * 0.05 + 0 * -0.01 + 0 * 0.02 = 0.07 -> 7%
b. Stock with average exposure to each factor -> b = 1
r = 0.07 + 1 * 0.05 + 1 * -0.01 + 1 * 0.02 = 0.13 -> 13%
c. Stock with high exposure to the energy factor (b = 2) and 0 exposure to
the other factors
r = 0.07 + 0 * 0.05 + 2 * -0.01 + 0 * 0.02 = 0.05 -> 5%
d. B1 and b3 = 1, b2 = -1.5
r = 0.07 + 1 * 0.05 + -1.5 * -0.01 + 1 * 0.02 = 0.155 -> 15.5%
Exercise 9.2
a. False
b. True
Fudge factor: allows to take into account uncertainty, with long-lived
projects the fudge factor applied to the discount rate would compound
over time -> undervaluing the project. The present value will be more
heavily discounted.
Exercise 9.4
Total market value of the common stock of the company = 6 million
Total value of debt = 4 million Beta of the stock = 1.5
Expected market risk premium = 6% risk-free rate = 4%
a. Required return on the company’s stock = r = 0.04 + 1.5 * 0.06 = 0.13 ->
13%
, b. Company cost of capital rA = rD * D/V + rE * E/V = 0.04 * 4/10 + 0.13 * 6/10
= 0.094 -> 9.4%
c. The discount rate for an expansion of the company’s present business is
the company cost of capital (uitleg in slides tutorial)
d. r = 0.04 + 1.2 * 0.06 = 0.112 -> 11.2% (unleveraged = no debt)
Exercise 9.5
Company cost of capital; rA = rE * E/V + rD * D/V
Equity = number of shares * price per share = 500,000
Debt = 300,000 Value = 500,000 + 300,000 = 800,000
RD = 0.08 rE = 0.15 rA = 0.12375 -> 12.38%
Exercise 9.7
Risk-free debt 40% risk-free rate = 10% market risk premium =
8%
Beta = 0.5 Company cost of capital = ?
Expected rate of return = 0.1 + 0.5 * 0.08 = 0.14 -> 14%
Company cost of capital = 0.1 * 0.4 + 0.14 * 0.6 = 0.124 -> 12.4%
Exercise 9.13
50% debt, 50% equity debt beta 0.15 equity beta = 1.25
asset beta = ?
ΒA = 0.5 * 0.15 + 0.5 * 1.25 = 0.7
Exercise 16.4
All-equity financed firm, with 10,000 shares of $100 per share
Options; low-debt; 200,000 high-debt; 400,000 interest
rate of 10%
a. Debt: 200,000
Equity: 1,000,000 – 200,000 = 800,000
D/E = 200,,000 = 25%
b. Earning per share = net income / shares
Net income = earning before interest and tax – interest = 110,000 – 0.1 *
200,000 = 90,000
Shares; 8,000
Earnings per share = 90,,000 = $11.25
c. Net income = 110,000 – 0.1 * 400,000 = 70,000
Shares; 6,000
Earnings per share = 70,,000 = $11.67
Exercise 16.5
Only common stock (no debt) with 25 mln shares of $10
a. Expected return from Johnson & Johnson
Treasury bill rate = 6% expected return on the market = 9%
Beta Johnson & Johnson = 0.75
r (jj) = 0.06 + 0.75 * (0.09 – 0.06) = 0.0825 -> 8.25%
b. Highest expected return -> use the company with the highest beta ->
14.94%
c. Lowest expected return -> use the company with the lowest beta -> 6.48%
d. If the interest rate decreases (the risk-free rate) from 6% to 2% -> r (uss)
= 0.02 + 2.98 * (0.09 – 0.02) = 0.2286 -> 22.86% so the risk-free rate
lowers and contributes less, but the market risk premium increases more.
(because the beta is > 1 and reacts stronger than 1 to 1 on a change in
the market risk premium).
e. Coca-Cola has a beta of 0.46, which is < 1 and when the interest rate
decreases from 6% to 2%, Coca-Cola’s expected return will decrease as
well.
Exercise 8.12 – APT
3-factor APT model, risk-free rate = 7%
1st factor; change in GNP = 5% 2nd factor; change in energy prices = -1%
3rd factor; change in long-term interest rates = 2%
a. Stock whose return is uncorrelated with all 3 factors;
r = 0.07 + 0 * 0.05 + 0 * -0.01 + 0 * 0.02 = 0.07 -> 7%
b. Stock with average exposure to each factor -> b = 1
r = 0.07 + 1 * 0.05 + 1 * -0.01 + 1 * 0.02 = 0.13 -> 13%
c. Stock with high exposure to the energy factor (b = 2) and 0 exposure to
the other factors
r = 0.07 + 0 * 0.05 + 2 * -0.01 + 0 * 0.02 = 0.05 -> 5%
d. B1 and b3 = 1, b2 = -1.5
r = 0.07 + 1 * 0.05 + -1.5 * -0.01 + 1 * 0.02 = 0.155 -> 15.5%
Exercise 9.2
a. False
b. True
Fudge factor: allows to take into account uncertainty, with long-lived
projects the fudge factor applied to the discount rate would compound
over time -> undervaluing the project. The present value will be more
heavily discounted.
Exercise 9.4
Total market value of the common stock of the company = 6 million
Total value of debt = 4 million Beta of the stock = 1.5
Expected market risk premium = 6% risk-free rate = 4%
a. Required return on the company’s stock = r = 0.04 + 1.5 * 0.06 = 0.13 ->
13%
, b. Company cost of capital rA = rD * D/V + rE * E/V = 0.04 * 4/10 + 0.13 * 6/10
= 0.094 -> 9.4%
c. The discount rate for an expansion of the company’s present business is
the company cost of capital (uitleg in slides tutorial)
d. r = 0.04 + 1.2 * 0.06 = 0.112 -> 11.2% (unleveraged = no debt)
Exercise 9.5
Company cost of capital; rA = rE * E/V + rD * D/V
Equity = number of shares * price per share = 500,000
Debt = 300,000 Value = 500,000 + 300,000 = 800,000
RD = 0.08 rE = 0.15 rA = 0.12375 -> 12.38%
Exercise 9.7
Risk-free debt 40% risk-free rate = 10% market risk premium =
8%
Beta = 0.5 Company cost of capital = ?
Expected rate of return = 0.1 + 0.5 * 0.08 = 0.14 -> 14%
Company cost of capital = 0.1 * 0.4 + 0.14 * 0.6 = 0.124 -> 12.4%
Exercise 9.13
50% debt, 50% equity debt beta 0.15 equity beta = 1.25
asset beta = ?
ΒA = 0.5 * 0.15 + 0.5 * 1.25 = 0.7
Exercise 16.4
All-equity financed firm, with 10,000 shares of $100 per share
Options; low-debt; 200,000 high-debt; 400,000 interest
rate of 10%
a. Debt: 200,000
Equity: 1,000,000 – 200,000 = 800,000
D/E = 200,,000 = 25%
b. Earning per share = net income / shares
Net income = earning before interest and tax – interest = 110,000 – 0.1 *
200,000 = 90,000
Shares; 8,000
Earnings per share = 90,,000 = $11.25
c. Net income = 110,000 – 0.1 * 400,000 = 70,000
Shares; 6,000
Earnings per share = 70,,000 = $11.67
Exercise 16.5
Only common stock (no debt) with 25 mln shares of $10
