Question

Jiminy’s Cricket Farm issued a 16-year, 6 percent semiannual coupon bond 2 years ago. The bond currently sells for 91 percent of its face value. The company’s tax rate is 38 percent. The book value of the debt issue is $40 million. In addition, the company has a second debt issue, a zero coupon bond with 11 years left to maturity; the book value of this issue is $30 million, and the bonds sell for 50 percent of par.

a.	What is the company’s total book value of debt? (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567.)
b.	What is the company’s total market value of debt? (Enter your answer in dollars, not millions of dollars, e.g. 1,234,567.)
c.	What is the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

1. Total Book value of debt= book value of coupon bond+Book value of zero coupon bond
   Book value ca be known from the face value of bons
   =(40*10^6)+(30*10^6)=70,000,000
   
2. Total Market value of debt = market value of coupon bond+ market value of zero coupon bond
   =(91%*40*10^6)+(50%*30*10^6)=51,400,000
   
3. We use rate formulae in excel to find the cost of debt of each bond
   =rate(nper,pmt,pv,fv,type,guess)
   Coupon bond:
   Nper=14*2(since total bond years is 16 and 2 years passed remaining is 14 and coupon payment semiannual)
   Pmt=coupon payment=face value*rate=(40*10^6*6%/2) (semiannual payment)
   Pv=-91%*40*10^6
   Fv=40%*10^6
   Type=0
   Guess=0
   =rate(14*2,(40*10^6*3%),(-91%*40*10^6),40*10^6,0,0)
   =3.51%
   Annual rate =3.51%*2=7.02%
   
   Zero coupon bond:
   Nper=11
   Pmt=coupon payment=face value*rate=(30*10^0)=0
   Pv=-50%*30*10^6
   Fv=30%*10^6
   Type=0
   Guess=0
   =rate(11,0,(-50%*30*10^6),30*10^6,0,0)
   =6.50%
   
   Cost of debt together is weighted average cost =(wt of coupon bond* cost of coupon bond debt)+(wt of zero coupon*cost of zero coupon)
   Wt of coupon=market value of coupon bond/( market value of coupon bond+ market value of zero coupon bond)
   =(91%*40*10^6)/51400000=70.82%
   Wt of zero coupon=market value of zero coupon bond/( market value of coupon bond+ market value of zero coupon bond)
   =(50%*30*10^6)/51400000=29.18%
   cost of debt=(70.82%*7.02%)+(29.18%*6.50%)=6.87%
   After tax cost of debt= cost of debt*(1-tax)
   =6.87%*(1-38%)=4.26%