Manjit Mittal, CFO, India Steel Industries Corp., is considering issuance of con

Question

Manjit Mittal, CFO, India Steel Industries Corp., is considering issuance of convertible bonds. The bonds will be of 30-year maturity and will have a coupon rate of 9.75 percent, par value of $1,000, and will be sold at a price of $1,075 (this is Vpackage from the lecture slides). The convertible bonds will have a 6-year call protection and the call price is $1,150. The conversion ratio is 25 on par value basis. The company’s stock is currently selling at $30 a share. The company paid a dividend of $2.00 last year and the dividends are expected to grow at a constant 6.0 percent rate into the foreseeable future. The company’s straight bonds have a 12.5 percent coupon rate. Assume semi-annual coupon payments in your computations.

(a) What is the convertible’s straight bond’s value? What is the implied value of the convertible feature?
(b) What will be the floor value of the bond at the end of year 7? Assume that straight bonds of comparable risk will have yield-to-maturity = 11.5 percent at that time (hint: this suggests what rd is at that time).
(c) Assuming full conversion of bonds into stock at the end of 8½ years. What will be the firm’s actual cost of capital for this issue of convertible bonds?
(d) Did the company gain or lose by issuing bonds with conversion feature, as opposed to issuing straight bonds? What motivated the investors to buy bonds at a lower coupon rate of 9.75% when bonds of comparable risk were offering 12.50%? Explain.

Explanation / Answer

(a) What is the convertible’s straight bond’s value? What is the implied value of the convertible feature? For COnv Bond, we have nper = 30Yrs, FV=$1000, coupon =9.75%. So PMT = 9.75%*$1000=$97.50 Strainght Bond coupon rate is 12.5% Value of Straight Bond V = PMT*(PVIFA i, n) + FV (PVIF i, n) where PMT is of COnv Bond, i = from equivalent Straight Bond, n=duration of Conv bond. So Conv Bond's straight value =V = $97.50*(PVIFA12.5%, 30) + $1,000 (PVIF12.5%, 30) ie V = 97.50*7.7664 + 1000*0.0292 = $786.42 .....Ans (a1) The convertible bond value equals straight bond value plus conversion option value. The $786.42 represents a floor (minimum) below which the convertible value will not fall. This occurs when the conversion option value is essentially worthless SO Implied Value of COnv Feature is 1075-786.42 = $288.58 .....Ans (a2) SO COnv rate = $288.58/25 shares = $11.54 against Mkt price of $30 .....(A) (b) What will be the floor value of the bond at the end of year 7? Assume that straight bonds of comparable risk will have yield-to-maturity = 11.5 At End of Y7, Conv Bond's straight value =V= $97.50*(PVIFA11.5%, 7) + $1,000 (PVIF11.5%, 7) ie V = 97.50*4.6370 + 1000*0.4667 = $918.81 ...................Ans (b) (c) Assuming full conversion of bonds into stock at the end of 8½ years. What will be the firm’s actual cost of capital for this issue of convertible bonds? We have current DIv D0=$2.0, g= 6%, Po=$30 So Ks = D1/P0+g = Do*(1+g)/P0 +g = 2*(1+6%)/30 + 6% =13.07% So P8=P0*(1+g)^8.5 = 30*(1+6%)^8.5 = $49.23 So The profit from each Bond 8 years from now is therefore ($49.23-$30 conv price) = $19.23 The total value of the COnv option is 25*$19.23 = $480.75 Looking at a time line we can see the investment’s cash flows: t = 0: -1,075 t = 1-7: 97.50 t = 8: $480.75+ 97.50 + 1000 =1578.25 The IRR of this stream is = IRR(-1075, 97.50,97.50........7 times,1578.25) = 12.12% So firm’s actual cost of capital for this issue of convertible bonds is 12.12%.....Ans (c) (d) As we see from (A) above, INvestor will get Copany shares at $11.54 against Mkt price of $30. SO it is good for investor.

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