Question

8. 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 bonds will be either 9 percent or 5 percent with equal probability. Assume inves tors 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?

I'm trying to understand how to do the problem. I'm not just looking for an answer. Please show the formulas used to solve the problem. If you can, please also explain why we are using that formula. Thank you.

Answer 1

Answer 8(a). Face Value of Bond = $1000

Coupons Rate = 7% of $1000= $70

Time Period= 30 years

Current market rate i.e Expected Rate of Return = 6%

As we know that Coupon Amount of $70 is to be paid annually for 30 years, further Bond holders would received $1000 at the end of 30th year.

For Calculating the price of bond today we have to calculate the present value of all future cash flow from said bond.

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

= $70*PVIFA(6%,30)+ $ 1000 * PVIF(6%,30)

= $ 70*1/(1+0.06)^1+$ 70*1/(1+0.06)^2+$ 70*1/(1+0.06)^3+.... ..+$70*1/(1+0.06)^30+

$1000*1/(1+0.06)^30

=$70*13.765+$1000*0.174

= $963.54+$174.11

= $1137.65

The price of bond today= $1,137.65 Ans

Answer 8(b). In one year interest rate on the bond will be either 9% or 5% with equal probability

So,Expected Interest rate at year 1= 0.5*9%+0.5*5%= 7%

If the bond are callable at one year from today @$1080

Then

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

= $70*PVIF(7%,1)+$1080*PVIF(7%,1)

= $70*0.935+$1080*0.935

= $1074.77

Price of the Bond is less than the price computed in part (a), because at the end of year one expected return from said bond has been increases to 7%.

Note.

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

PVIFA= (1- PVIF(r,n))/n

Where r= expected rate of return and n= Number of Year i.e. for 1st=1 , 2nd =2 and 3rd=3