Question

1. You buy a bond with two years to maturity, a face value of $4,000 and an annual coupon payment of $300. Show your calculations (or explain your answer in one sentence if there are no calculations) for each question below

1. After 1 year, you cash in the coupon and sell the bond. If the market interest rate is now 3%, how much can you sell your bond for?
2. Calculate (i) the rate of capital gains, and (ii) your total rate of return on the bond.
3. What is the yield to maturity for the new buyer, who buys from you at the price you found in c.?

Answer 1

a) The price at which bond can be sold is the present value of benefit receive in future.

Present value of $300 which is received after end of year 2 and $4000 .

= $300 / ( 1 + 0.03)¹ + $4000 / ( 1 + 0.03)¹

= $4175

b) Capital gain on sale of bond = ( $4175 - $4000 ) = $175

Rate of capital gain = ($175 / $4000) * 100% = 4.375%

Rate of Return = (Coupon + Capital gain) / Bond price

= ( $300 + $175 ) / $4000

= 11.875%

c) Yield to maturity = [( Face value/ Bond price ) / Time ] - 1

= [( $4000 / $4175 ) / 1 ] - 1 = 4.19 %