In: Accounting
What is the annual capital gains yield expected over the next year for a 12 year bond with 6.9% coupon rate paying the coupons every six months and selling at $1,045
Calculation of yield to maturity:
Face Value = $1,000
Current Price = $1,045
Annual Coupon Rate = 6.90%
Semiannual Coupon Rate = 3.45%
Semiannual Coupon = 3.45% * $1,000
Semiannual Coupon = $34.50
Time to Maturity = 12 years
Semiannual Period to Maturity = 24
Let Semiannual YTM be i%
$1,045 = $34.50 * PVIFA(i%, 24) + $1,000 * PVIF(i%, 24)
Using financial calculator:
N = 24
PV = -1045
PMT = 34.50
FV = 1000
I = 3.179%
Semiannual YTM = 3.179%
Calculation of price after 1 year:
Face Value = $1,000
Semiannual Coupon = $34.50
Semiannual YTM = 3.179%
Time to Maturity = 11 years
Semiannual Period to Maturity = 22
Price in 1 year = $34.50 * PVIFA(3.179%, 22) + $1,000 *
PVIF(3.179%, 22)
Price in 1 year = $34.50 * (1 - (1/1.03179)^22) / 0.03179 + $1,000
/ 1.03179^22
Price in 1 year = $1,042.42
Calculation of capital gain yield:
Capital Gain Yield = (Price in 1 year - Current Price) / Current
Price
Capital Gain Yield = ($1,042.42 - $1,045) / $1,045
Capital Gain Yield = -0.0025 or -0.25%