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A 14-year semiannual coupon bond with a YTM of 8.2% sells for par. If you buy...

A 14-year semiannual coupon bond with a YTM of 8.2% sells for par. If you buy the bond today and then sell it next year at a YTM of 7.7%, what is your capital gain on this investment? Enter your answer as a percentage rounded to two decimal places (e.g., 5.64%). (Please show step by step using N, I/Y, PV, PMT and FV on a calculator as well if needed.)

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Homework Answers

Answer #1

Face Value = $1,000

Price of Bond, Current Year = $1,000

If current price of bond is equal to par value, then YTM will be equal to the coupon rate.

Annual Coupon Rate = 8.20%
Semiannual Coupon Rate = 4.10%
Semiannual Coupon = 4.10% * $1,000
Semiannual Coupon = $41

Calculation of next year price of bond:

Time to Maturity = 13 years
Semiannual Period = 26

Annual YTM = 7.70%
Semiannual YTM = 3.85%

Using financial calculator:
N = 26
I = 3.85%
PMT = 41
FV = 1000

PV = -1040.62

Price of Bond, Next Year = $1,040.62

Capital Gain Yield = (Price of Bond, Next Year - Price of Bond, Current Year) / Price of Bond, Current Year
Capital Gain Yield = ($1,040.62 - $1,000) / $1,000
Capital Gain Yield = 4.06%

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