Question

Assets, Inc., plans to issue $5 million of bonds with a coupon rate of 8 percent, a par value of $1,000, semiannual coupons, and 30 years to maturity. The current market interest rate on these bonds is 7 percent. In one year, the interest rate on the bonds will be either 12 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. If the bonds are callable one year from today at $1,150, will their price be greater or less than the price you computed in part (a)? Greater Lesser

Answer 1

Ans:

(a). Face Value of Bond = $1000

Coupons Rate = 8% of $1000= $80

Time Period= 30 years

Current market rate = 7%

For Calculation of the price of bond today we have to calculate the present value of future cash flows.

So, Present Value of Bond is = Present value of all Coupons + Present value of maturity amount

= $80 × PVIFA(7%,30)+ $ 1000 × PVIF(7%,30)

= $ 80 × 1/(1+0.07)^1+$ 80 × 1/(1+0.07)^2+$ 80 × 1/(1+0.07)^3+.... ..+$ 80 × 1/(1+0.07)^30 + $1000 × 1/(1+0.07)^30

=$80 × 12.409 + $1000 × 0.131

= $992.72 + $131

= $1123.72

The price of bond today = $1123.72

(b). In one year interest rate on the bond will be either 12% or 4% with equal probability.

Expected Interest rate at year 1= 0.5 × 12% + 0.5 × 4% = 8%

The bond are callable from today at one year = $1150

Then, Price of Bond = Present value of coupons + Present value of callable amount

= $80 × PVIFA(8%,1) + $1150 × PVIF(8%,1)

= $80 × 0.926 + $1150 × 0.926

=$74.08 + $1064.9

= $1138.98

Price of the Bond is greater than the price computed in part (a), because the Call amount is higher than the expected price of bond after one year and expected return for one year also increased.

Notes:

For PVIF = 1/(1+r)^n

PVIFA = 1- (1/(1+r)^n) / r

Here,

r= expected rate of return

n= Number of Years