A 10.25%, 14-year convertible bond has a conversion rate of 19 and is selling at a...

A 10.25%, 14-year convertible bond has a conversion rate of 19 and is selling at a quote of 98.40. The common stock is selling at $35 and comparable non-convertible bonds are yielding 13%. The common stock pays an annual dividend of $1.50 per share.

A. Calculate the conversion value of the bond

B. Calculate the conversion premium (if any)

C. Calculate the investment value of the bond

D. Calculate the investment premium (if any)

E. Calculate the payback period

Solutions

Expert Solution

A). Conversion value = market price per share*number of shares per bond

= 35*19 = 665

B). Conversion premium = market price of convertible bond - conversion value

Market price of convertible bond = par value*98.40% = 1,000*98.40% = 984

Conversion premium = 984-665 = 319

Conversion premium (in %) = 319/conversion value = 319/665 = 47.97%

C). Investment value of the bond = price of a similar non-convertible bond

FV (par value) = 1,000; PMT (annual coupon) = annual coupon*par value = 10.25%*1,000 = 102.5; N (number of coupons) = 14; rate = 13%, solve for PV.

Market price of non-convertible bond = 826.68

D). Investment premium = market price of convertible bond - market price on non-convertible bond

= 984-826.68 = 157.32

Investment premium (in %) = 157.32/market price of non-convertible bond = 157.32/826.68 = 19.03%

E). Annual dividend on 19 shares = 19*1.50 = 28.50

Annual interest on convertible bond = 102.5

Favorable income differential = annual interest - annual dividend = 102.5 - 28.50 = 74

Payback period = conversion premium/favorable income differential

= 319/74 = 4.31 years

jeff jeffy answered 1 year ago

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