At the beginning of the year, you bought a $1,000 par value corporate bond with

Question

At the beginning of the year, you bought a $1,000 par value corporate bond with an annual coupon rate of 13 percent and a maturity date of 16 years. When you bought the bond, it had an expected yield to maturity of 11 percent. Today the bond sells for $1,330. a. What did you pay for the bond? b. If you sold the bond at the end of the year, what would be your one period return on the investment? Assume that you did not receive an interest payment during the holding period. a. The price you paid for the bond is $. b. If you sold the bond today, your one-period return on the investment is %.

Explanation / Answer

a.

Price of bond = Present value of coupon payments + Present value of face value

Annual coupon amount = $1,000 * 13% = $130

Maturity = 16 years

Present value of annuity = Annuity * {1-(1+r)-n}/r

Present value of annuity of coupon payments = $130 * (1 – 1.11-16)/0.11 = $130 * 7.3792 = $959.30

Present value of face value = $1,000 / 1.1116 = $1,000/5.3109 = $188.29

Price of the bond = $959.30 + $188.29 = $1,147.59

b.

Selling price of bond = $1,330

Gain on sale of bond = $1,330 - $1,147.59 = $182.41

One period return = $182.41 / $1,147.59 = 0.1590 = 15.90%

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