Master Craft Control Inc.has bonds that mature in 6 1/2 years with a par value of $1,000.They pay a coupon rate of 9% with semiannual payments.If the required rate of return on these bonds is 11% what is the bond's value?

Question

Quizplus · Accepted Answer

The bond's value can be calculated using the present value of its future cash flows, which include the semiannual interest payments and the principal amount at maturity. The formula for the present value of an annuity (the interest payments) and the present value of a lump sum (the principal repayment) can be used here. Given a 9% annual coupon rate with semiannual payments, the semiannual interest payment is $45 ($1,000 * 9% / 2). There are 13 periods (6.5 years * 2) and a semiannual discount rate of 5.5% (11% / 2). The bond's value is calculated as follows:$$ \text{Present Value of Interest Payments} = \frac{\$45 \times [1 - (1 + 0.055)^{-13}]}{0.055} $$$$ \text{Present Value of Principal} = \frac{\$1,000}{(1 + 0.055)^{13}} $$Adding these two components gives the bond's value, which is approximately $908.83. This calculation involves the present value of an annuity formula for the coupon payments and the present value of a lump sum for the bond's par value at maturity.