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# required interest rates, bonds and yield to maturity

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1.
Assume Venture Healthcare sold bonds that have a 10-year maturity, a 12 percent coupon rate with annual payments, and a \$1,000 par value.
a. Suppose that two years after the bonds were issued, the required interest rate fell to 7 percent. What would be the bonds' value?
b. Suppose that two years after the bonds were issued, the required interest rate rose to 13 percent. What would be the bonds' value?
c. What would be the value of the bonds three years after issue in each scenario above, assuming that interest rates stayed steady at either 7 percent or 13 percent?

2.
Twin Oaks Health Center has a bond issue outstanding with a coupon rate of 7 percent and four remaining until maturity. The par value of the bond is \$1,000, and the bond pays interest annually.
a. Determine the current value of the bond if present market conditions justify a 14 percent required rate of return.
b. Now, suppose Twin Oaks' four-year bond had semiannual coupon payments. What would be its current value? (Assume a 7 percent semiannual required rate of return. However, the actual rate would be slightly less than 7 percent because a semiannual coupon bond is slightly less risky than an annual coupon bond.)
c. Assume that Twin Oaks' bond had a semiannual coupon but 20 years remaining to maturity. What is the current value under these conditions? (Again, assume a 7 percent semiannual required rate of return, although the actual rate would probably be greater than 7 percent because of increased price risk.

3.
Minneapolis Health System has bonds outstanding that have four years remaining to maturity, a coupon interest rate of 9 percent paid annually, and a \$1,000 par value.
a. What is the yield to maturity on the issue if the current market price is \$829?
b. If the current market price is \$1,104?
c. Would you be willing to buy one of these bonds for \$829 if you required a 12 percent rate of return on the issue? Explain your answer.

4.
A person is considering buying the stock of two home health companies that are similar in all respects except the proportion of earnings paid out as dividends. Both companies are expected to earn \$6 per share in the coming year, but Company D (for dividends) is expected to pay out the entire amount as dividends, while Company G (for growth) is expected to pay out only one-third of its earnings, or \$2 per share. The companies are equally risky, and their required rate of return is 15 percent. D's constant growth rate is zero and G's is 8.33 percent. What are the intrinsic values of stocks D and G?

5.
Medical Corporation of America (MCA) has a current stock price of \$36 and its last dividend (D0) was \$2.40. In view of MCA's strong financial position, its required rate of return is 12 percent. If MCA's dividends are expected to grow at a constant rate in the future, what is the firm's expected stock price in five years?

6.
A broker offers to sell you shares of Bay Area Healthcare, which just paid a dividend of \$2 per share. The dividend is expected to grow at a constant rate of 5 percent per year. The stock's required rate of return is 12 percent.
a. What is the expected dollar dividend over the next three years?
b. What is the current value of the stock and the expected stock price at the end of each of the next three years?
c. What is the expected dividend yield and capital gains yield for each of the next three years?
d. What is the expected total return for each of the next three years?
e. How does the expected total return compare with the required rate of return on the stock? Does this make sense? Explain your answer.

7.
Seattle Health Plans currently uses zero-debt financing. Its operating income (EBIT) is 1 million, and it pays taxes at a 40 percent rate. It has \$5 million in assets and, because it is all equity financed, \$5 million in equity. Suppose the firm is considering replacing half of its equity financing with debt financing bearing an interest rate of 8 percent.
a. What impact would the new capital structure have on the firm's net income, total dollar return to investors, and ROE?
b. Redo the analysis, but now assume that the debt financing would cost 15 percent.
c. Return to the initial 8 percent interest rate. Now, assume that EBIT could be as low as \$500,000 (with a probability of 20 percent) or as high as \$1.5 million (with a probability of 20 percent). There remains a 60 percent chance that EBIT would be \$1 million. Redo the analysis for each level of EBIT, and find the expected values for the firm's income, total dollar return to investors, ROE. What lesson about capital structure and risk does this illustration provide?
d. Repeat the analysis required for Part a, but now assume that Seattle Health Plans is a not-for-profit corporation and pays no taxes. Compare the results with those obtained in Part a

8.
Calculate the after-tax cost of debt for the Wallace clinic, a for-profit healthcare provider, assuming that the coupon rate set on its debt is 11 percent and its tax rate is
a. 0 percent
b. 20 percent
c. 40 percent

9.
St. Vincent's Hospital has a target capital structure of 35 percent debt and 65 percent equity. Its cost of equity (fund capital) estimate is 13.5 percent and its cost of tax-exempt debt estimate is 7 percent. What is the hospital's corporate cost of capital?

10.
Richmond Clinic has obtained the following estimates for its costs of debt and equity at various capital structures:

Percent Debt After-Tax Cost of Debt Cost of Equity
0% _ 16%
20 6.6% 17
40 7.8 19
60 10.2 22
80 14. 0 27
What is the firm's optimal capital structure? (Hint: Calculate its corporate cost of capital at each structure. Also, note that data on component costs at alternative capital structures are not reliable in real-world situations.)

#### Solution Summary

The solution determines the required interest rates, bonds and yield to maturity.

\$2.19

## Finance/Accounting multiple choice questions on bonds, interest rates, YTM, Yield to Call etc.

1. One of the basic relationships in interest rate theory is that, other things held constant, for a given change in the required rate of return, the the time to maturity, the the change in price.

a. longer; smaller.
b. shorter; larger.
c. longer; greater.
d. shorter; smaller.
e. Statements c and d are correct.

2. Assume that a 10-year Treasury bond has a 12 percent annual coupon, while a 15-year Treasury bond has an 8 percent annual coupon. The yield curve is flat; all Treasury securities have a 10 percent yield to maturity. Which of the following statements is most correct?

a. The 10-year bond is selling at a discount, while the 15-year bond is selling at a premium.
b. The 10-year bond is selling at a premium, while the 15-year bond is selling at par.
c. If interest rates decline, the price of both bonds will increase, but the 15-year bond will have a larger percentage increase in price.
d. If the yield to maturity on both bonds remains at 10 percent over the next year, the price of the 10-year bond will increase, but the price of the 15-year bond will fall.
e. Statements c and d are correct.

3. Assume that a 15-year, \$1,000 face value bond pays interest of \$37.50 every 3 months. If you require a nominal annual rate of return of 12 percent, with quarterly compounding, how much should you be willing to pay for this bond? (Hint: The PVIFA and PVIF for 3 percent, 60 periods are 27.6748 and 0.1697, respectively.)

a. \$ 821.92 b. \$1,207.57 c. \$ 986.43 d. \$1,120.71 e. \$1,358.24

4. You just purchased a 15-year bond with an 11 percent annual coupon. The bond has a face value of \$1,000 and a current yield of 10 percent. Assuming that the yield to maturity of 9.7072 percent remains constant, what will be the price of the bond one year from now?

a. \$1,000 b. \$1,064 c. \$1,097 d. \$1,100 \$1,150

5. Due to a number of lawsuits related to toxic wastes, a major chemical manufacturer has recently experienced a market reevaluation. The firm has a bond issue outstanding with 15 years to maturity and a coupon rate of 8 percent, with interest paid semiannually. The required nominal rate on this debt has now risen to 16 percent. What is the current value of this bond?

a. \$1,273
b. \$1,000
c. \$7,783
d. \$ 550
e. \$ 450

6. A corporate bond with 12 years to maturity has a 9 percent semiannual coupon and a face value of \$1,000. (That is, the semiannual coupon payments are \$45.) The bond has a nominal yield to maturity of 7 percent. The bond can be called in three years at a call price of \$1,045. What is the bond's nominal yield to call?

a. 4.62%
b. 10.32%
c. 17.22%
d. 5.16%
e. 2.31%

7. A 10-year bond has a face value of \$1,000. The bond has a 7 percent semiannual coupon. The bond is callable in 7 years at a call price of \$1,040. The bond has a nominal yield to call of 6.5 percent. What is the bond's nominal yield to maturity?

a. 3.14%
b. 6.05%
c. 7.62%
d. 6.27%
e. 6.55%

8. Meade Corporation bonds mature in 6 years and have a yield to maturity of 8.5 percent. The par value of the bonds is \$1,000. The bonds have a 10 percent coupon rate and pay interest on a semiannual basis. What are the current yield and capital gains yield on the bonds for this year? (Assume that interest rates do not change over the course of the year).

a. Current yield = 8.50%; capital gains yield = 1.50%
b. Current yield = 9.35%; capital gains yield = 0.65%
c. Current yield = 9.35%; capital gains yield = -0.85%
d. Current yield = 10.00%; capital gains yield = 0.00%
e. Current yield = 10.50%; capital gains yield = -1.50%

9. A 16-year bond with a 10 percent annual coupon has a current yield of 8 percent. What is the bond's yield to maturity (YTM)?

a. 6.9%
b. 7.1%
c. 7.3%
d. 7.5%
e. 7.7%

10. Which of the following statements is most correct?

a. Other things held constant, a callable bond would have a lower required rate of return than a noncallable bond.
b. Other things held constant, a corporation would rather issue noncallable bonds than callable bonds.
c. Reinvestment rate risk is worse from a typical investor's standpoint than interest rate risk.
d. If a 10-year, \$1,000 par, zero coupon bond were issued at a price that gave investors a 10 percent rate of return, and if interest rates then dropped to the point where kd = YTM = 5%, we could be sure that the bond would sell at a premium over its \$1,000 par value.
e. If a 10-year, \$1,000 par, zero coupon bond were issued at a price that gave investors a 10 percent rate of return, and if interest rates then dropped to the point where kd = YTM = 5%, we could be sure that the bond would sell at a discount below its \$1,000 par value.

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