Charles River Company has just sold a bond issue with 40 warrants attached. The
ID: 2669557 • Letter: C
Question
Charles River Company has just sold a bond issue with 40 warrants attached. The bonds have a 20-year maturity, an annual coupon rate of 12.0 percent, and they sold at their $1,000 par value. The current yield on similar straight bonds is 15.0 percent.(a) What is the implied value of each warrant?
(b) Each warrant can be exchanged for one share at an exercise price of $25. Suppose, current stock price is $18 and is expected to appreciate at an annual rate of 6 percent a year. If investors exercise all warrants at the end of nine years, what will be the firm’s cost of capital for this issue of bonds with warrants?
Explanation / Answer
Maturity =Nper = 20; Coupon = 12%; PMT = 12%*1000 = 120; FV = 1000; YTM=Rate=15% and then solve for PV = PV(rate,nper,pmt) = PV(15%,20,120) = ($812.22) SO Value of Bond VB = 812.22 Total value = Straight-debt value + Warrant value. $1,000 = $812.22 + 40(Warrant value) So Warrant value = (1000-818.22)/40 = $4.54 .......................Ans (a) Current Stock price P0=18, g=6% The stock’s expected price 9 years from now is P9 = P0*(1+g)^9 ie P9 = 18*(1+6%)^9 = $30.41 So The profit from each warrant 9 years from now is therefore ($30.41-$25 exercise price) = $5.41 The total value of the warrants is 40*$5.41 = $216.40 Looking at a time line we can see the investment’s cash flows: t = 0: -1,000 t = 1-8: 70 t = 9: 216.40 + 70 + 1000 = $1,286.40 The IRR of this stream is = IRR(-1000, 70,70........8 times,1286.40) = 8.68% SO Firm's cost of capital for this issue of Bond with warrant is 8.68%