Convertibles A convertible security (usually convertible bonds or convertible pr
ID: 2764169 • Letter: C
Question
Convertibles A convertible security (usually convertible bonds or convertible preferred stock) may be tendered for shares of common stock in the issuing firm. In other words, the bonds or preferred stock may be converted to common stock. Like warrants, convertibles can lead to diluted earnings, because new shares of common stock are issued. However, unlike warrants, convertibles: Do not result in new capital for the firm Result in new capital for the firm Consider the case of Cheung Zap Inc.: Cheung Zap Inc. just issued nine-year convertible bonds at a par value of $1,000. At any time before maturity, investors have the option to exchange their bonds for shares of Cheung's common stock at a conversion price of $51.84. Cheung's convertible bonds pay a 6.48% annual coupon, but if Cheung had issued straight-debt bonds (no conversion), it would have had to pay 10.80% annual interest. Based on the information available, complete the table: Cheung's common stock currently sells for $34. Would an investor want to convert the bonds now? Yes No Suppose analysts expect Cheung to pay a dividend of $5.00 at the end of the year and for the dividend to grow at a constant rate of 6% per year. What is the expected conversion value five years from now? $1,316.55 $2,358.72 $658.28 $877.70Explanation / Answer
1) unlike warrants, convertibles do not result in new capital for the firm
because it is merely an accounting transfer from debt to equity
2)
par value of bond , M = $1000
maturity of bond , n = 9 years
conversion price , c = $51.84
coupon rate of convertible bond , r = 6.48% = 0.0648
Annual coupon value , C = r*M = 0.0648*1000 = 64.8
YTM ( yield to maturity) = 10.8% = 0.108
pure debt value = present value of coupons + present value of maturity amount
Present value of coupons = C*PVIFA( 10.8% , 9 years)
PVIFA( 10.8% , 9 years) = present value interest rate factor of annuity
= [((1+YTM)n - 1)/((1+YTM)n*YTM)] = [((1.108)9 - 1)/((1.108)9*0.108)] = 5.58035572
Present value(PV) of coupons = C*PVIFA( 10.8% , 9 years) = 64.8*5.58035572 = 361.60705
PV of maturity amount = par value/(1+YTM)n = 1000/(1.108)9 = 397.321582
pure debt value = 361.60705 + 397.321582 = $758.928633 or $758.93 ( rounding off to 2 decimal places)
Conversion ratio = par value of bond/conversion price = 1000/51.84 = 19.29012346 or 19 ( rounding off to nearest whole number)
Value of convertible option = par value - pure debt value = 1000-758.928633 = $241.071367 or $241.07
3)
since the conversion price = 51.84 which is much greater than current stock price, investors would not want to convert the bonds right now, since they would be paying much more than the current worth of stocks
4) current stock price , p0 = 34
dividend , d = $5
growth rate of dividend , g = 6% = 0.06
expected conversion value 5 years from now = p0*(1+g)5*Conversion ratio = 34*(1.06)5*19.29012346 = $877.694245 or $877.70 ( after rounding off)