Question

O The mo company currently has one bond issue outstanding. This bond pays a coupon rate of 10% ($100 peryear) and matures in five years, and has a par value of $1,000. If your require a 15% rate of return, What is the capital gains yield of this bond in the first year? (Assuming this is an semi-annual bond 2,986% 3.038% 3.986% 2.038% annat it does

Answer 1

Answer is 3.038%

Face Value = $1,000

Annual Coupon Rate = 10.00%
Semiannual Coupon Rate = 5.00%
Semiannual Coupon = 5.00% * $1,000
Semiannual Coupon = $50

Annual YTM = 15.00%
Semiannual YTM = 7.50%

Calculation of current price:

Time to Maturity = 5 years
Semiannual Period = 10

Current Price = $50 * PVIFA(7.50%, 10) + $1,000 * PVIF(7.50%, 10)
Current Price = $50 * (1 - (1/1.075)^10) / 0.075 + $1,000 / 1.075^10
Current Price = $828.40

Calculation of price in one year:

Time to Maturity = 4 years
Semiannual Period = 8

Price in 1 year = $50 * PVIFA(7.50%, 8) + $1,000 * PVIF(7.50%, 8)
Price in 1 year = $50 * (1 - (1/1.075)^8) / 0.075 + $1,000 / 1.075^8
Price in 1 year = $853.57

Capital Gain Yield = (Price in 1 year - Current Price) / Current Price
Capital Gain Yield = ($853.57 - $828.40) / $828.40
Capital Gain Yield = 0.03038 or 3.038%