FIN515 Week 4 Homework
9-1 Future Value of a Company
Assume Evco, Inc., has a current price of $50 and will pay a $2 dividend in one year, and its
equity cost of capital is 15%. What price must you expect it to sell for right after paying the
dividend in one year in order to justify its current price?
Answer:
Find price of stock in 1 year.
Current Price = $50, Dividend = $2, Cost of Equity Capital = 15%
X = Price the stock will sell right after paying the dividend:
50 = (2+ X) /(1+0.15)
X = 55.50
Therefore, price the stock will sell right after paying the one year dividend is $55.5
9-4 Dividend Yield and Cost of Equity Capital
Krell Industries has a share price of $22 today. If Krell is expected to pay a dividend of $0.88
this year, and its stock price is expected to grow to $23.54 at the end of the year, what is
Krell’s dividend yield and equity cost of capital?
Answer:
Dividend Yield = Dividend / Share price = 0.88/22 = 4%
Capital Gain Rate = (End of year stock price – Share price today) / Share price today =
(23.54 – 22) / 22 = 7%
Total expected return (Equity cost of capital) = 4% + 7% = 11%
9-5 No Growth Company
NoGrowth Corporation currently pays a dividend of $2 per year, and it will continue to pay
this dividend forever. What is the price per share if its equity cost of capital is 15% per year?
Answer:
Assume: dividends are paid at the end of the year
Stock pays a total of $2.00 in dividends per year.
Valuing this dividend as a perpetuity: P = $2.00 / 0.15 = $13.33
9-6 Value of Operations of Constant Growth
Summit Systems will pay a dividend of $1.50 this year. If you expect Summit’s dividend to
grow by 6% per year, what is its price per share if its equity cost of capital is 11%?
Answer:
Price per share = 1.50 / (11% – 6%) = $30
9-7 Expected Growth Rate of Constant Growth Company
Dorpac Corporation has a dividend yield of 1.5%. Dorpac’s equity cost of capital is 8%, and
its dividends are expected to grow at a constant rate.
a. What is the expected growth rate of Dorpac’s dividends?
b. What is the expected growth rate of Dorpac’s share price?
Answer:
a) Expected growth rate of Dorpac’s dividends = Equity Cost of capital – Dividend yield =
8% - 1.5% = 6.5%
b) Share price is also expected to grow at rate g = 6.5% since dividend has constant growth
rate
9-12 Non Constant Dividend
Procter & Gamble will pay an annual dividend of $0.65 one year from now. Analysts expect
this dividend to grow at 12% per year thereafter until the fifth year. After then, growth will
level off at 2% per year. According to the dividend-discount model, what is the value of a
share of Procter & Gamble stock if the firm’s equity cost of capital is 8%?
Answer:
PV of first 5 dividends = 0.65 / (0.08-0.12) * ((1-(1.12/1.08)^5) = $3.24
Rest of Payments (value at date 5) = 0.65*(1.12)^4*1.02 / 0.06 = $17.39
Discount value at date 5 for rest of payments to present = $17.39 /(1.08)^5 = $11.83
Value of P&G today is: $3.24 + $11.83 = $15.07
9-19 Enterprise Value
Heavy Metal Corporation is expected to generate the following free cash flows over the next
five years:
Years
1
2
3
4
5
FCF ($
53
68
78
75
82
millions)
After then, the free cash flows are expected to grow at the industry average of 4% per year.
Using the discounted free cash flow model and a weighted average cost of capital of 14%:
a. Estimate the enterprise value of Heavy Metal.
b. If Heavy Metal has no excess cash, debt of $300 million, and 40 million shares
outstanding, estimate its share price.
Answer:
a)
Terminal Value = 82 / (14% – 4%) = $820
Enterprise Value of Heavy Metal = 53 / 1.14 + 68/1.14^2 + 78 / 1.14^3 + (75 + 820) /
1.14^4 =$681
b) Share price of Heavy Metal =(Enterprise value + cash – Debt) / Shares outstanding=
(681 + 0 – 300)/40 = $9.53
12-1 Equity Cost of Capital
Suppose Pepsico’s stock has a beta of 0.57. If the risk-free rate is 3% and the expected
return of the market portfolio is 8%, what is Pepsico’s equity cost of capital?
Answer:
Equity Cost of Capital: risk free rate + Pepsico stock beta * (return on market – risk free
rate) = 3% + 0.57 * (8%-5%) = 5.85%
12-3 Higher Equity Cost of Capital
Aluminum maker Alcoa has a beta of about 2.0, whereas Hormel Foods has a beta of 0.45.
If the expected excess return of the marker portfolio is 5%, which of these firms has a
higher equity cost of capital, and how much higher is it?
Answer:
Alcoa has a higher equity cost of capital (due to higher beta).
Alcoa’s cost of equity is 5% * (2-0.45) = 7.75% higher
12-26 Equity Cost of Capital, Debt Cost of Capital and WACC
Unida Systems has 40 million shares outstanding trading for $10 per share. In addition,
Unida has $100 million in outstanding debt. Suppose Unida’s equity cost of capital is 15%,
its debt cost of capital is 8%, and the corporate tax rate is 40%.
a. What is Unida’s unlevered cost of capital?
b. What is Unida’s after-tax debt cost of capital?
c. What is Unida’s weighted average cost of capital?
Answer:
a) Unlevered cost of capital:
Equity = 40 million shares * 10 per share = 400 million
Debt = $100 million
Unlevered cost of capital = % equity * cost of equity + % debt * cost of debt =
400/500 * 15% + 100/500 * 8% = 13.6%
b) After tax debt cost of capital = Debt cost of capital * (1- tax rate) = 8% * (1-0.4) =
4.8%
c) Weighted Average cost of capital = % equity * cost of equity + % debt * cost of
debt * (1- tax rate) = 400/500 * 15% + 100/500 * 4.8% = 12.96%
Butcher Timber Company hired your consulting firm to help them estimate the cost of
common equity. The yield on the firm's bonds is 9.00%, and your firm's economists believe
that the cost of common can be estimated using a risk premium of 6.00% over a firm's own
cost of debt. What is an estimate of the firm's cost of common from retained earnings?
Answer:
Cost of common from retained earnings = yield on the firm's bonds + risk premium
= 9% + 6% = 15%