Question

Assets, Inc., plans to issue $8 million of bonds with a coupon rate of 6 percent, a par value of $1,000, semiannual coupons, and 30 years to maturity. The current market interest rate on these bonds is 10 percent. In one year, the interest rate on the bonds will be either 10 percent or 4 percent with equal probability. Assume investors are risk-neutral.

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

Answer 1

With 10% interest rate in one year:

FV = 1000
Nper = 29 * 2 = 58
PMT = 1000 * 6% / 2 = 30
Rate = 10% / 2 = 5%

Present value of bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(5%,58,-30,-1000)
= $623.61

Value of bond today = ($30 / (1 + 5%)) + ($30 + $623.61) / (1 + 5%)^2
= $28.57 + $592.84
= $621.41

With 4% interest rate in one year:

FV = 1000
Nper = 29 * 2 = 58
PMT = 1000 * 6% / 2 = 30
Rate = 4% / 2 = 2%

Present value of bond can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(2%,58,-30,-1000)
= $1,341.45

Value of bond today = ($30 / (1+5%)) + ($30 + $1,341.45) / (1+5%)^2
= $28.57 + $1,243.95
= $1,272.52

Price of the bond today = ($621.41 * 50%) + ($1,272.52 * 50%)
= $310.71 + $636.26
= $946.97

Price of the bond today = $946.97