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The YTM on a bond is the interest rate you earn on your investment if interest rates don't change
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 7 percent for $1,060. The bond has 21 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 and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b) 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.)
c) 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.)
Expert Solution
a) We can calculate the yield to maturity by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = Yield to maturity
Nper = 21 periods
Pmt = Coupon payment = $1,000*7% = $70
PV = $1,060
FV = $1,000
Substituting the values in formula:
= rate(21,70,-1060,1000)
= 6.47%
b) We can calculate the price of bond by using the following formula in excel:-
=-pv(rate,nper,pmt,fv)
Here,
PV = Price of bond
Rate = 6.47%-1% = 5.47%
Nper = 21-2 = 19 periods
Pmt = Coupon payment = $1,000*7% = $70
FV = $1,000
Substituting the values in formula:
= -pv(5.47%,19,70,1000)
= $1,178.07
c) We can calculate the HPY by using the following formula in excel:-
=rate(nper,pmt,-pv,fv)
Here,
Rate = HPY
Nper = 2 periods
Pmt = Coupon payment = $1,000*7% = $70
PV = $1,060
FV = $1,178.07
Substituting the values in formula:
= rate(2,70,-1060,1178.07)
= 11.86%
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