Average: 16 Attempts: 4. Convertibles A convertble security (usually convertible

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Average: 16 Attempts: 4. Convertibles A convertble security (usually convertible bonds or convertble preferred stodk) may be tendered at the option of the holder for shares of common stnck in the issuing firm. In other words, the bonds or preferred stodk may be converted to common stock when warrants are exercised, new shares are issued, or treasury stock the company has previously purchased is provided to the warrant holder. When convertibles are exerdsed: O New capital is provided to the issuer. O Debt is replaced by common stock on the balance sheet. Consider the case of Cheung Zap Inc.: Cadesi g Zap Inc just issued 11-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 prike of $66.24 hung's convertible bonds pay a 8.28% annual coupon, but ifCheung had issued straight-debt bonds (no conversion), it would have had to pay 13.80% annual interest. Based on the information available, complete the table: Value Conversion ratio of Cheung's bond issue: Pure-debt value of this convertible debt issue: value of the convertibie option: cheung's common stock currently sells for $40 per share. Would an investor want to convert the bonds now? Yes O No Suppose analysts expect cheung to pay a dividend of 1.00 per share at the end of the year and for the dividend to grow at constant rate of 5% per year. whats the expected conversion vauthe yun om now? o $3,545.83 O $606.23

Explanation / Answer

1) when convertibles are exercised, Debt is replaced by common stock on balance sheet

2) par value of bond = M = $1000

conversion price , p = $66.24

Conversion ratio = M/p = 1000/66.24 = 15.09661836 or 15.10 ( rounding off to 2 decimal places)

3) coupon rate , c = 8.28% = 0.0828

coupon value , C = c*M = 0.0828*1000 = 82.8

maturity of bond , n = 11 years

yield , YTM = 13.80% = 0.1380

pure debt value of convertible = present value of coupons + present value of maturity amount

Present value of coupons = C*PVIFA( 13.80% , 11 years)

PVIFA( 13.80% , 11 years) = present value interest rate factor of annuity

= [((1+YTM)n - 1)/((1+YTM)n*YTM)] = [((1.1380)11 - 1)/((1.1380)11*0.1380)] = 5.49831804

Present value(PV) of coupons = C*PVIFA( 13.80% , 11 years) = 82.8*5.49831804 = 455.26073339

PV of maturity amount = par value/(1+YTM)n = 1000/(1.1380)11 = 241.23211102

pure debt value = 455.26073339 + 241.23211102 = $696.49284 or $696.49 ( rounding off to 2 decimal places

4) value of the convertible option = price of bond with convertible option - pure debt value = 1000 - 696.49284 = $303.5071556 or $303.51 ( rounding off to 2 decimal places)

5) since the conversion price is 66.24 is > current stock price of $40

investor would not want to conver the bonds now

6) current price of stock , p0 = 40

conversion ratio , c1 = 15.10

growth rate of dividend , g = 6% = 0.06

conversion value 5 years from now = p0*(1+g)5 *c1 = 40*(1.06)5*15.10 = 808.28824 or $808.30 ( rounding off to 2 decimal places)

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