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.)
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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