A bond: Maturity: 15 years from now, face value: $1000, coupon: $0, bond price:

Question

A bond: Maturity: 15 years from now, face value: $1000, coupon: $0, bond price: $500. A personal income tax is defined as a tax on an income flow. In contrast, a capital gains tax is a tax on the sale or realization of an asset that was purchased as cost lower than the purchased price. For this question, assume that the income tax is 25% and the capital gains tax is 10%.

(a) Suppose you need to sell the bond in 5 years from now, what is the annualized after-tax return on this sale?

(b) Suppose the income tax increased to 0.3, what is the new bond price and the new yield to maturity?

(c) Supose interest rate on the cash flows for cash flows 5 years from now increase and the interest rates on cash flows 10 years from now falls, but in a way that the bond price stays constant. What is the new yield to maturity?

Explanation / Answer

a) YTM is ( 1000 / 500 )^( 1/15 ) - 1 = 4.73%

price of bond after 5 years is 500 * ( 1.0473 )^5 = 629.96

capital gains is 629.96 - 500 = 129.96.

tax is 10% and hence the after tax profit is 0.9 * 129.96 = $116.96

b)

New price and yield to maturity doesnt depend on income tax and hence they remain at 500 and 4.73%

c) if the price of the bond and the time period hasnt changed yield to maturity doesnt change and hence its 4.73%

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