A bond has the following features: * Coupon rate of interest: 8% * Principal: $1

Question

A bond has the following features:

* Coupon rate of interest: 8%
* Principal: $1,000
* Term to maturity: 10 years

a. What will the holder receive when the bond matures?

b. If the current rate of interest on comparable debt is 12percent, what should be the
price of this bond? Would you expect the firm to call this bond?Why?

c. If the bond has a sinking fund that requires the firm to setaside annually with a trustee
sufficient funds to retire the entire issue at maturity, how muchmust the firm remit each
year for 10 years if the funds earn 9 percent annually and there is$10 million outstanding?

Explanation / Answer

Typically, bond agreements require a company to make periodicinterest payments to bondholders throughout the life of the bond,and then repay the principal amount of the bond at the end of thebond's lifespan.

b.  We have N=10yrs, M=Maturity value of bond =1000, Coupon rate = 8%. So INT = 8%xM = 8%*1000 = 80, & Debtrate Kd=12%
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N) Putting values we get Vb=80(PVIFA 12%,10) + 1000(PVIF 12%,10) ie Vb = 80*[1/Kd - 1/{Kd(1+Kd)^N}] +1000*(1/(1+Kd)^N ie Vb = 80*[1/12% - 1/{12%*(1+12%)^10}] +1000*(1/(1+12%)^10) ie Vb = 80*(1/12% - 2.6831) + 1000*0.322 ie Vb = 80*5.650 + 322 ie Vb= 774 So value of Bond is 774 when comparable Debt is12%   Firm is NOT expected to call this bond as Firm is paying acoupon rate of only 8% while if Firm takes debt, it has to pay 12%on debt. Thus Firm is better off with Coupon rate of 8%.
c. SInking fund requiring regular annual contribution issimilar to an annuity of 10 Yrs with Int rate of 9%. FV of annuity=FVA= $10M, Interest rate i = 9%, n= 10 yrs. We need to find annualpayment PMT.
Formula is FVAn = PMT(FVIFAi,n) ie FVAn = PMT*[(1+i)^n - 1]/i
So PMT = FVAn0/{[(1+i)^n - 1]/i} ie PMT = 10,000,000/{[(1+9%)^10 - 1]/9%} ie PMT = 10,000,000/15.193 = $658,200.90 Thus Firm has to put aside $658,200.90 annually for 10 yearsto repay the $10M bonds.

b.  We have N=10yrs, M=Maturity value of bond =1000, Coupon rate = 8%. So INT = 8%xM = 8%*1000 = 80, & Debtrate Kd=12%
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N) Putting values we get Vb=80(PVIFA 12%,10) + 1000(PVIF 12%,10) ie Vb = 80*[1/Kd - 1/{Kd(1+Kd)^N}] +1000*(1/(1+Kd)^N ie Vb = 80*[1/12% - 1/{12%*(1+12%)^10}] +1000*(1/(1+12%)^10) ie Vb = 80*(1/12% - 2.6831) + 1000*0.322 ie Vb = 80*5.650 + 322 ie Vb= 774 So value of Bond is 774 when comparable Debt is12%   Firm is NOT expected to call this bond as Firm is paying acoupon rate of only 8% while if Firm takes debt, it has to pay 12%on debt. Thus Firm is better off with Coupon rate of 8%.
c. SInking fund requiring regular annual contribution issimilar to an annuity of 10 Yrs with Int rate of 9%. FV of annuity=FVA= $10M, Interest rate i = 9%, n= 10 yrs. We need to find annualpayment PMT.
Formula is FVAn = PMT(FVIFAi,n) ie FVAn = PMT*[(1+i)^n - 1]/i
So PMT = FVAn0/{[(1+i)^n - 1]/i} ie PMT = 10,000,000/{[(1+9%)^10 - 1]/9%} ie PMT = 10,000,000/15.193 = $658,200.90 Thus Firm has to put aside $658,200.90 annually for 10 yearsto repay the $10M bonds.

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