Question

(1 point) A 9-year bond with a face value of 1000 dollars is redeemable at par, pays coupons at 5.9 percent per 6 months, and has a yield rate of 7.6 percent convertible semiannually. Suppose the book value immediately after the payment of the 7th coupon is equal to the price of a perpetuity (at the time of the 7th coupon) that will start making annual payments one year after the 7th coupon. If the perpetuity earns interest at 3.9 percent effective, how large is each perpetuity payment?

Answer 1

The bonds sell in the market at prices not only determined by the market rate but also for necessity of funds, bond rate not exactly matching the market rate, credit rating of the bond and the demand and supply of the bond etc. Effective yield rate of 7.6% convertible semi annually means 3.8% for six months. So $29.5 (5.9%/2*1000) on $776.32 (29.5 / 0.038) will give 3.8% for six months. So the bond is selling at $776.32 to give 7.6% effective yield rate. However the book value of the bond will be $1000 as the company has to pay $1000 on maturity. The book value of the bond will be $776.32 in the hands of buyer who revalues the assets on fair market value. So the perpetuity payment of 3.9 percent effective on $776.32 will be $30.28. The perpetuity payment of 3.9% effective on $1000 will be $39. The question is silent on whose book value should be considered - that of the seller of the bond or buyer. A rational assumption is that the book value of the buyer will be taken to determine the price of the perpetuity. So the perpetuity payment of 3.9 percent effective on $776.32 will be $30.28.