Question

A bond has a par value of $1,000, a time to maturity of 10 years, and a coupon rate of 8.60% with interest paid annually. If the current market price is $860, what will be the approximate capital gain of this bond over the next year if its yield to maturity remains unchanged? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Par Value = $1,000
Current Price = $860

Annual Coupon Rate = 8.60%
Annual Coupon = 8.60% * $1,000
Annual Coupon = $86

Time to Maturity = 10 years

Let annual YTM be i%

$860 = $86 * PVIFA(i%, 10) + $1,000 * PVIF(i%, 10)

Using financial calculator:
N = 10
PV = -860
PMT = 86
FV = 1000

I/Y = 10.98%

Annual YTM = 10.98%

Price Next Year = $86 * PVIFA(10.98%, 9) + $1,000 * PVIF(10.98%, 9)
Price Next Year = $86 * (1 - (1/1.1098)^9) / 0.1098 + $1,000 / 1.1098
Price Next Year = $868.12

Capital Gain Yield = (Price Next Year - Current Price) / Current Price
Capital Gain Yield = ($868.12 - $860) / $860
Capital Gain Yield = 0.0094
Capital Gain Yield = 0.94%