# What is the firm’s value if cash flows are expected to grow at an annual rate of 12% for the first 2 years, followed by a constant annual rate of 7% from year 3 to infinity?

**P6–1 Interest rate fundamentals: **

The real rate of return Carl Foster, a trainee at an investment banking firm, is trying to get an idea of what real rate of return investors are expecting in today’s marketplace. He has looked up the rate paid on 3-month U.S. Treasury bills and found it to be 5.5%. He has decided to use the rate of change in the Consumer Price Index as a proxy for the inflationary expectations of investors. That annualized rate now stands at 3%. On the basis of the information that Carl has collected, what estimate can he make of the real rate of return?

**P6–10 Bond interest payments before and after taxes **

Charter Corp. has issued 2,500 debentures with a total principal value of $2,500,000. The bonds have a coupon interest rate of 7%.

a. What dollar amount of interest per bond can an investor expect to receive each year from Charter?

b. What is Charter’s total interest expense per year associated with this bond issue?

c. Assuming that Charter is in a 35% corporate tax bracket, what is the company’s net after-tax interest cost associated with this bond issue?

**P6–13 Valuation of assets **

Using the information provided in the following table, find the value of each asset.

Cash flow

Asset End of year Amount Appropriate required return

A 1 $ 5,000 18%

2 5,000

3 5,000

B 1 through $ 300 15%

C 1 $ 0 16%

2 0

3 0

4 0

5 35,000

D 1 through 5 $ 1,500 12%

6 8,500

E 1 $ 2,000 14%

2 3,000

3 5,000

4 7,000

5 4,000

6 1,000

**P6–20 Yield to maturity **

The relationship between a bond’s yield to maturity and coupon interest rate can be used to predict its pricing level. For each of the bonds listed, state whether the price of the bond will be at a premium to par, at par, or at a discount to par.

Bond Coupon interest rate Yield to maturity Price

A 6% 10% _________

B 8 8 _________

C 9 7 _________

D 7 9 _________

E 12 10 _________

**P7–1 Authorized and available shares **

Aspin Corporation’s charter authorizes issuance of 2,000,000 shares of common stock. Currently, 1,400,000 shares are outstanding, and 100,000 shares are being held as treasury stock. The firm wishes to raise $48,000,000 for a plant expansion. Discussions with its investment bankers indicate that the sale of new common stock will net the firm $60 per share.

a. What is the maximum number of new shares of common stock that the firm can sell without receiving further authorization from shareholders?

b. Judging on the basis of the data given and your finding in part a, will the firm be able to raise the needed funds without receiving further authorization?

c. What must the firm do to obtain authorization to issue more than the number of shares found in part a?

**P7–6 Common stock value—Zero growth **

Kelsey Drums, Inc., is a well-established supplier of fine percussion instruments to orchestras all over the United States. The company’s class A common stock has paid a dividend of $5.00 per share per year for the last 15 years. Management expects to continue to pay at that amount for the foreseeable future. Sally Talbot purchased 100 shares of Kelsey class A common 10 years ago at a time when the required rate of return for the stock was 16%. She wants to sell her shares today. The current required rate of return for the stock is 12%. How much capital gain or loss will Sally have on her shares?

**P7–14 Common stock value—All growth models **

You are evaluating the potential purchase of a small business currently generating $42,500 of after-tax cash flow Do =$ 42,500. On the basis of a review of similar-risk investment opportunities, you must earn an 18% rate of return on the proposed purchase. Because you are relatively uncertain about future cash flows, you decide to estimate the firm’s value using several possible assumptions about the growth rate of cash flows.

a. What is the firm’s value if cash flows are expected to grow at an annual rate of 0% from now to infinity?

b. What is the firm’s value if cash flows are expected to grow at a constant annual rate of 7% from now to infinity?

c. What is the firm’s value if cash flows are expected to grow at an annual rate of 12% for the first 2 years, followed by a constant annual rate of 7% from year 3 to infinity?