Question

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).

a.

Suppose that today you buy a bond with an annual coupon of 9 percent for $1,180. The bond has 17 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected rate of return

%

b1.	Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Bond price

$

b2.	What is the HPY on your investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

HPY

%

Answer 1

a. Rate of return will be that rate that makes the sum of present value of coupon payments and present value of the maturity amount to be equal to $1180.

Annual coupon payments = 9% of $1000 = $90

Thus 1180 = 90*(PVIFA r%, 17) + 10000*(PVIF r%, 17)

Using the trial and error approach we see that at r = 7.14% the present value comes to $1180.

Thus the answer is 7.14%

B1: New YTM = 7.14% - 1 = 6.14%

Thus price = 90*(PVIFA 6.14%, 15) + 1000*(PVIF 6.14%, 15)

= $1,275.41

B2: For HPY 1180 = 90*(PVIFA r%, 2)+1275.25*(PVIF r%, 2)

When we solve the above equation we get r = 11.45%

(Note intermediate answers are shown as rounded to 2 decimal places but for calculation purpose the full answer was used. For instance the full final answer of “a” is 7.1386% and this is rounded off to 7.14%. For B1 all computations have been done using 7.1386%)