Question

A 10-year zero coupon bonds was issued with a yield to maturity of 5% You are an investor with a one-year holding period with an ordinary income tax of 40% and capital gain tax of 20%. Assume in one year the interest rate remains the same. Determine:

1. 1. The current price of the bond
2. 2. The price of the bond at the end of the year
3. 3. The after tax holding period return

Answer 1

a.

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =10

Bond Price =∑ [(0*1000/100)/(1 + 5/100)^k]     +   1000/(1 + 5/100)^10

k=1

Bond Price = 613.91

b.

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =9

Bond Price =∑ [(0*1000/100)/(1 + 5/100)^k]     +   1000/(1 + 5/100)^9

k=1

Bond Price = 644.61

c

capital gain yield = (selling price/purchase price-1)*100=(644.61/613.91-1)*100 = 5%

after tax yield = capital gains yield*(1-capitals gain tax) = 5*(1-0.2) = 4%