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 6 percent for $1,150. The bond has 20 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000.

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?

b2.	What is the HPY on your investment?

Answer 1

a]

YTM is calculated using RATE function in Excel :

nper = 20 (years remaining until maturity with 1 annual coupon payment each year)

pmt = 1000 * 6% (annual coupon payment = face value * coupon rate)

pv = -1150 (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 4.82%. 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 = 3.82% (YTM of bond)

nper = 18 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 6% (annual coupon payment = face value * coupon rate)

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

PV is calculated to be $1,280.05

b-2]

HPY is calculated using IRR function in Excel :

cash outflow in year 0 = purchase price of bond = $1150

cash inflow in year 1 = annual coupon payment = $60

cash inflow in year 2 = annual coupon payment + selling price = $60 + $1,280.05 = $1,340.05

HPY = 10.59%