Realized compound yield of the bond

Unit 3 Assignment: Chapter 14 Questions 6,9,10,13,15 and 21 on pages 473 and 474

6. Which security has a higher effective annual interest rate?

a. A 3-month T-bill selling at $97,645 with par value $100,000.

b. A coupon bond selling at par and paying a 10% coupon semiannually.

9. Consider an 8% coupon bond selling for $953.10 with 3 years until maturity making annual coupon payments. The interest rates in the next 3 will be, with certainly, r1 = 8%, r2 = 10%, r3 = 12%. Calculate the yield to maturity and realized compound yield of the bond.

10. Assume you have a 1-year investment horizon and are trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. The first is a zero-coupon bond that pays $1,000 at maturity. The second has an 8% coupon rate and pays the $80 coupon once per year. The third has a 10% coupon rate and pays the $100coupon once per year.

Unit 3: Template for Chapter 14, Question 10

10.

a.

Zero coupon
8% coupon

10% coupon

Current prices

b. Price 1 year from now

Price increase

Coupon income

Pre-tax income

Pre-tax rate of return

Taxes*

After-tax income

After-tax rate of return

c. Price 1 year from now

Price increase

Coupon income

Pre-tax income

Pre-tax rate of return

Taxes**

After-tax income

After-tax rate of return

a. If all three bonds are now priced to yield 8% to maturity, what are their prices?

b. If you expect their yields to maturity to be 8% at the beginning of next year, what will their prices be then? What is your before-tax holding-period return on each bond? If your tax bracket is 30% on ordinary income and 20% on capital gains income, what will your after-tax rate of return be on each?

c. Recalculate your answer to (b) under the assumption that you expect the yields to maturity on each bond to be 7% at the beginning of next year.

13. Fill in the table below for the following zero-coupon bonds, all of which have par values of $1,000.

Price

Maturity(years)

Bond-Equivalent Yield to Maturity

$400

20

-

$500

20

-

$500

10

-

-

10

10%

-

10

8%

$400

-

8%

13. Unit 3: Template for Chapter 14, Question 13

Price

Maturity

(years)

Bond equivalent

YTM

$400.00

20.00

$500.00

20.00

$500.00

10.00

10.00

10.000%

10.00

8.000%

$400.00

8.000%

15. A bond with a coupon rate of 7% makes semiannual coupon payments on January 15 and July 15 of each year. The Wall Street Journal reports the asked price for the bond on January 30 at 100:02. What is the invoice price of the bond? The coupon period has 182 days.

21. A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in 5 years at a call price of $1,100. The bond currently sells at a yield to maturity of 7% (3.5% per half-year).

a. What is the yield to call?

b. What is the yield to call if the call price is only $1,050?

c. What is the yield to call if the call price is $1,100, but the bond can be called in 2 years instead of 5 years?

CFA Problems 2 and 4 on page 476 and 477

2. Bonds of Zello Corporation with a par value of $1,000 sell for $960, mature in 5 years, and have a 7% annual coupon rate paid semiannually.

a. Calculate the:

i. Current yield.

ii. Yield to maturity (to the nearest whole percent, i.e., 3%, 4%, 5%, etc.).

iii. Realized compound yield for an investor with a 3-year holding period and a reinvestment rate of 6% over the period. At the end of 3 years the 7% coupon bonds with 2 years remaining will sell to yield 7%.

b. Cite one major shortcoming for each of the following fixed-income yield measures:

i. Current yield.

ii. Yield to maturity.

iii. Realized compound yield.

4. A convertible bond has the following features:

Coupon

5.25%

Maturity

June 15, 2027

Market price of bond

$77.50

Market price of underlying common stock

$28.00

Annual dividend

$1.20

Conversion ratio

20.83 shares

Calculate the conversion premium for this bond.

Chapter 15 Questions 10 and 12 on pages 500 and 501

10. The term structure for zero-coupon bonds is currently:

Maturity (Years)

YTM (%)

1

4%

2

5

3

6

Next year at this time, you expect it to be:

Maturity (Years)

YTM (%)

1

5%

2

6

3

7

a. What do you expect the rate of return to be over the coming year on a 3-year zero-coupon bond?

b. Under the expectations theory, what yields to maturity does the market expect to observe on 1- and 2-year zeroes at the end of the year? Is the market’s expectation of the return on the 3- year bond grater or less than yours?

CFA Problem 10, on page 505

10. The spot rates of interest for five U.S. Treasury Securities are shown in the following exhibit. Assume all securities pay interest annually.

Spot Rates of Interest

Term to Maturity

Spot Rate of Interest

1 year

13.00%

2

12.00

3

11.00

4

10.00

5

9.00

a. Compute the 2-year implied forward rate for a deferred loan beginning in 3 years.

b. Compute the price of a 5-year annual-pay Treasury security with a coupon rate of 9% by using the information in the exhibit.