# payments

Assume that a bond will make payments every six months as shown on the following timeline

(using six-month periods):

**0 1 2 3 20**

$20 $20 $20 20+$1000

a. What is the maturity of the bond (in years)?

b. What is the coupon rate (in percent)?

c. What is the face value?

**4. **Suppose the current zero-coupon yield curve for risk-free bonds is as follows:

**Maturity (years) 1 2 3 4 5**

**YTM **5.00% 5.50% 5.75% 5.95% 6.05%

a. What is the price per $100 face value of a two-year, zero-coupon, risk-free bond?

b. What is the price per $100 face value of a four-year, zero-coupon, risk-free bond?

c. What is the risk-free interest rate for a five-year maturity?

**6. **Suppose a 10-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading for

a price of $1034.74.

a. What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)?

b. If the bond’s yield to maturity changes to 9% APR, what will the bond’s price be?

**7. **Suppose a five-year, $1000 bond with annual coupons has a price of $900 and a yield to maturity

of 6%. What is the bond’s coupon rate?

**11. **Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity,

a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity

on this bond when it was issued was 6%.

a. What was the price of this bond when it was issued?

b. Assuming the yield to maturity remains constant, what is the price of the bond immediately

before it makes its first coupon payment?

c. Assuming the yield to maturity remains constant, what is the price of the bond immediately

after it makes its first coupon payment?

**13. **Consider the following bonds:

**Bond Coupon Rate (annual payments) Maturity (years)**

A 0% 15

B 0% 10

C 4% 15

D 8% 10

a. What is the percentage change in the price of each bond if its yield to maturity falls from 6%

to 5%?

b. Which of the bonds A–D is most sensitive to a 1% drop in interest rates from 6% to 5% and

why? Which bond is least sensitive? Provide an intuitive explanation for your answer.

** **

**Chapter 9**

**3. **Suppose Acap Corporation will pay a dividend of $2.80 per share at the end of this year and $3

per share next year. You expect Acap’s stock price to be $52 in two years. If Acap’s equity cost of

capital is 10%:

a. What price would you be willing to pay for a share of Acap stock today, if you planned to

hold the stock for two years?

b. Suppose instead you plan to hold the stock for one year. What price would you expect to be

able to sell a share of Acap stock for in one year?

c. Given your answer in part (b), what price would you be willing to pay for a share of Acap

stock today, if you planned to hold the stock for one year? How does this compare to your

answer in part (a)?

**5. **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?

**6. **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%?

**12. **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%?

**17. **Maynard Steel plans to pay a dividend of $3 this year. The company has an expected earnings

growth rate of 4% per year and an equity cost of capital of 10%.

a. Assuming Maynard’s dividend payout rate and expected growth rate remains constant, and

Maynard does not issue or repurchase shares, estimate Maynard’s share price.

b. Suppose Maynard decides to pay a dividend of $1 this year and use the remaining $2

per share to repurchase shares. If Maynard’s total payout rate remains constant, estimate

Maynard’s share price.

c. If Maynard maintains the dividend and total payout rate given in part (b), at what rate are

Maynard’s dividends and earnings per share expected to grow?

**21. **Sora Industries has 60 million outstanding shares, $120 million in debt, $40 million in cash,

and the following projected free cash flow for the next four years::

**Year 0 1 2 3 4**

**Earnings and FCF Forecast ($ millions)**

**1 Sales 433.0 468.0 516.0 547.0 574.3**

**2 Growth versus prior year 8.1% 10.3% 6.0% 5.0%**

**3 Cost of Goods Sold (313.6) (345.7) (366.5) (384.8)**

**4 Gross Profit 154.4 170.3 180.5 189.5**

**5 Selling, General and Administrative (93.6) (103.2) (109.4) (114.9)**

**6 Depreciation (7.0) (7.5) (9.0) (9.5)**

**7 EBIT 53.8 59.6 62.1 65.2**

**8 Less: Income Tax at 40% (21.5) (23.8) (24.8) (26.1)**

**9 Plus: Depreciation 7.0 7.5 9.0 9.5**

**10 Less: Capital Expenditures (7.7) (10.0) (9.9) (10.4)**

**11 Less: Increase in NWC (6.3) (8.6) (5.6) (4.9)**

**12 F****ree Cash Flow 25.3 24.6 30.8 33.3**

**24. **You notice that PepsiCo (PEP) has a stock price of $72.62 and EPS of $3.80. Its competitor,

the Coca-Cola Company (KO), has EPS of $1.89. Estimate the value of a share of Coca-Cola

stock using only this data.