Posted: December 5th, 2015

Solving Finance Formulas for Capital Budget, Risk/Return & WACC

Risk Return & Opportunity Costs:

Top hedge fund manager Diana Sauros believes that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $44. The stock will pay a dividend at year-end of $2.00. Assume that risk-free Treasury securities currently offer an interest rate of 1.9%.

Average rates of return on Treasury bills, government bonds, and common stocks, 1900–2013 (figures in percent per year) are as follows.

Portfolio Average Annual

Rate of Return Average Premium (Extra return

versus Treasury bills)

Treasury bills 3.9

Treasury bonds 5.2 1.3

Common stocks 11.5 7.6

What is the discount rate if the interest rate is 2.0%? (Enter your answer as a percent rounded to 2 decimal places.)

Discount rate

%

What price should she be willing to pay for the stock today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Stock price $

for $56.

a. What is the total rate of return on the stock? (Enter your answer as a whole percent.)

Rate of return

%

b. What are the dividend yield and percentage capital gain? (Enter your answers as a whole percent.)

Dividend yield

%

Capital gains yield

%

c.

Now suppose the year-end stock price after the dividend is paid is $48. What are the dividend yield and percentage capital gain in this case? (Negative amounts should be indicated by a minus sign. Enter your answers as a whole percent.)

Dividend yield

%

Capital gains yield

%

You purchase 100 shares of stock for $25 a share. The stock pays a $1 per share dividend at year-end.

a.

What is the rate of return on your investment if the end-of-year stock price is (i) $24; (ii) $25; (iii) $28? (Leave no cells blank – be certain to enter “0” wherever required. Enter your answers as a whole percent.)

Stock price Rate of return

$24

%

$25

%

$28

%

b.

What is your real (inflation-adjusted) rate of return if the inflation rate is 2%? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Stock price Real rate of return

$24

%

$25

%

$28

%

Consider the following scenario analysis:

Rate of Return

Scenario Probability Stocks Bonds

Recession .30 -6 % 15 %

Normal economy .60 18 8

Boom .10 26 5

a.

Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?

Yes

No

b.

Calculate the expected rate of return and standard deviation for each investment. (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place.)

Expected Rate

of Return Standard

Deviation

Stocks

%

%

Bonds

%

%

Risk, Return & Capital Budgeting:

Investors expect the market rate of return this year to be 15%. A stock with a beta of 1.4 has an expected rate of return of 20%. If the market return this year turns out to be 10%, what is the rate of return on the stock? (Do not round intermediate calculations. Enter your answer as a percent rounded to 1 decimal place.)

Stock return

%

You are considering acquiring a firm that you believe can generate expected cash flows of $30,000 a year forever. However, you recognize that those cash flows are uncertain.

a.

Suppose you believe that the beta of the firm is 2.4. How much is the firm worth if the risk-free rate is 5% and the expected rate of return on the market portfolio is 7%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Value of the firm $

b.

By how much will you overvalue the firm if its beta is actually 2.6? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Overvaluation $

The risk-free rate is 5% and the expected rate of return on the market portfolio is 10%.

a.

Calculate the required rate of return on a security with a beta of 1.98. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Required return

%

A share of stock with a beta of .82 now sells for $57. Investors expect the stock to pay a year-end dividend of $2. The T-bill rate is 5%, and the market risk premium is 8%. If the stock is perceived to be fairly priced today, what must be investors’ expectation of the price of the stock at the end of the year? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

Stock price $

We Do Bankruptcies is a law firm that specializes in providing advice to firms in financial distress. It prospers in recessions when other firms are struggling. Consequently, its beta is negative, -.2.

a.

If the interest rate on Treasury bills is 6% and the expected return on the market portfolio is 16%, what is the expected return on the shares of the law firm according to the CAPM? (Enter your answer as a whole percent.)

Expected return

%

b.

Suppose you invested 80% of your wealth in the market portfolio and the remainder of your wealth in the shares in the law firm. What would be the beta of your portfolio? (Round your answer to 2 decimal places.)

Portfolio beta

WACC:

In 2013 Caterpillar Inc. had about 647 million shares outstanding. Their book value was $38 per share, and the market price was $83.00 per share. The company’s balance sheet shows that the company had $26.7 billion of long-term debt, which was currently selling near par value.

a.

What was Caterpillar’s book debt-to-value ratio? (Enter your answer as a decimal rounded to 2 decimal places. Do not round intermediate calculations.)

Book value

b.

What was its market debt-to-value ratio? (Enter your answer as a decimal rounded to 2 decimal places. Do not round intermediate calculations.)

Market value

Olympic Sports has two issues of debt outstanding. One is a 9% coupon bond with a face value of $29 million, a maturity of 10 years, and a yield to maturity of 10%. The coupons are paid annually. The other bond issue has a maturity of 15 years, with coupons also paid annually, and a coupon rate of 10%. The face value of the issue is $34 million, and the issue sells for 96% of par value. The firm’s tax rate is 20%.

a.

What is the before-tax cost of debt for Olympic? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Before-tax cost of debt

%

b.

What is Olympic’s after-tax cost of debt? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

After-tax cost of debt

%

Pangbourne Whitchurch has preferred stock outstanding. The stock pays a dividend of $3 per share, and sells for $30. What is the percentage cost of the preferred stock? (Enter your answer as a whole percent.)

Cost of preferred stock

%

Reliable Electric is a regulated public utility, and it is expected to provide steady dividend growth of 5% per year for the indefinite future. Its last dividend was $3 per share; the stock sold for $35 per share just after the dividend was paid. What is the company’s cost of equity? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Cost of equity

Reactive Industries has the following capital structure. Its corporate tax rate is 40%.

Security Market Value Required Rate

of Return

Debt $30 million 4%

Preferred stock 30 million 6

Common stock 60 million 10

What is its WACC? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

WACC

%

%

Icarus Airlines is proposing to go public, and you have been given the task of estimating the value of its equity. Management plans to maintain debt at 32% of the company’s present value, and you believe that at this capital structure the company’s debtholders will demand a return of 6% and stockholders will require 13%. The company is forecasting that next year’s operating cash flow (depreciation plus profit after tax at 40%) will be $70 million and that investment expenditures will be $32 million. Thereafter, operating cash flows and investment expenditures are forecast to grow in perpetuity by 4% a year.

a. What is the total value of Icarus? (Do not round intermediate calculations. Enter your answer in millions rounded to the nearest whole dollar amount.)

Total value $

million

b.

What is the value of the company’s equity? (Do not round intermediate calculations. Enter your answer in millions rounded to 1 decimal place.)

Company’s equity $

million

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