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 an annual coupon bond with a coupon rate of 8.1 percent for $855. The bond has 7 years to maturity and a par value of $1,000. What rate of return do you expect to earn on your investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b-1.	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.)
b-2.	What is the HPY on your investment? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a]

YTM is calculated using RATE function in Excel :

nper = 7 (years remaining until maturity with 1 annual coupon payment each year)

pmt = 1000 * 8.1% (annual coupon payment = face value * coupon rate)

pv = -855 (Current price of bond. This is entered with a negative sign because it is a cash outflow to buy the bond today).

fv = 1000 (face value of bond receivable at maturity).

RATE is calculated to be 11.20%. This is the YTM.

b-1]

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 10.2% (YTM of bond after 1% decline)

nper = 6 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 8.1% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

Price of bond is calculated to be $909.21

b-2]

HPY = (sale price + annual coupon payment - purchase price) / purchase price

HPY = ($909.21 + $81 - $855) / $855

HPY = 15.81%