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 8.2 percent for $795. The bond has 9 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?

Answer 1

Answer : (a.)Calculation of Expected Rate of Return on Investment ;

Expected rate of Return can be calculated using Rate function :

=RATE(nper,pmt,pv,fv)

nper is the number of years to maturity i.e 9

pmt is the coupon payment i.e 1000 * 8.2% = 82

pv is the current market price i.e 795

fv is the face value i.e 1000

=RATE(9,82,-795,1000)

Therefore expected rate of return is 12.06%

(b.-1) Price of Bond Two years from now if the YTM on your bond has declined by 1 percent :

Price of Bond can be calculated using PV function of Excel

=PV(rate,nper,pmt,fv)

where rate is yield to maturity i.e 12.06% - 1% = 11.06%

nper is the years to maturity i.e 7 (9 - 2)

pmt is the coupon payment i.e 1000 * 8.2% = 82

fv is the face value i.e 1000

=PV(11.06%,7,-82,-1000)

Therfore current price is 865.68

(b-2) Calculation of HPY on investment :

HPY is the interest rate that equals to the price price

therfore HPY can be calculated using rate function

=RATE(nper,pmt,pv,fv)

nper is the number of years of return i.e 2

pmt is the coupon payment i.e 1000 * 8.2% = 82

pv is the purchase price i.e 795

fv is the sale value i.e 865.68

=RATE(2,82,-795,865.68)

Therefore expected rate of return is 14.46%