Question

Jamestown, Inc., plans to issue $4 million of bonds with a coupon rate of 7 percent, a par value of $1,000, semiannual coupons, and 10 years to maturity. The current market interest rate on these bonds is 6 percent. In one year, the interest rate on the bonds will be either 12 percent or 6 percent with equal probability. Assume investors are risk-neutral. If the bonds are noncallable, what is the price of the bonds today?

Answer 1

Given in the question :-

Face Value of Bond : $ 1,000.

Maturity : 10 years

Coupon Rate : 7 % semiannual coupons

Current Market Interest Rate i.e, Required Rate of Return : 6 %

As the Bonds are non-callable, the Expected Interest Rate on the bonds after one year is not useful.

Semiannual Interest Amount = $ 1,000 * 7%/2 = $35.

Discount Rate = 6% per annum = 3% semiannually

Fair Value of Bond today is calculated as follows :-

Fair Value = Present Value of Interest Payments + Present Value of Redemption Amount

                = Interest * PVIFA_n + Redemption Value * PVIF

were, PVIFA_n = Present Value Interest Factor Annuity

         PVIF = Present Value Interest Factor

Fair Value = $35 * PVIFA(3%,20) + $1,000 * PVIF(3%,20)

                = 35 * 14.8775 + 1,000 * 0.5537

                = 520.7116 + 553.6758

                = $ 1074.3874.

Thus, the Fair Value or Price of the Bond with Semiannual Coupon Rate of 7% for 10 years to maturity is $ 1074.3874.