Question

Valuing Callable Bonds Assets, Inc., plans to issue $5 million of bonds with a coupon rate of 7 percent, a par value of $1,000, semiannual coupons, and 30 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 9 percent or 5 percent with equal probability. Assume investors are risk-neutral.

a. If the bonds are noncallable, what is the price of the bonds today?

b. If the bonds are callable one year from today at $1,080, will their price be greater or less than the price you computed in (a)? Why?

Answer 1

a. Price of the bond = Coupon * [ 1 - ( 1 + periodic yield ) ^-no of periods ] / periodic yield + principal * 1 / ( 1 + periodic yield)^no of periods

Coupon = 1000 * 7% * 0.5 = 35

periodic yield = 6 / 2 = 3%

no of periods = 30*2 = 60

Price of the bond = 35 * [ 1 - 1.03^-60 ] / 0.03 + 1000 * 1/1.03^60

= 35 * 27.68 + 1000 * 0.16973

= 968.64 + 169.73

= $1,138.38

b. If the bond is callable in 1 year at $1080 then the price will be lesser than the price computed in a.

Price of callable bond = price of non callable bond - value of call option.

Hence we have to dedcut the value of call option as issuer has a call option on the bond ie the issuer can redeem the bonds when the market interest rate is lower than the already set with bond.