Question

A certain 5% annual coupon rate convertible bond​ (maturing in 20​ years) is convertible at the​ holder's option into 17 shares of common stock. The bond is currently trading at $790. The stock​(which pays 56¢ a share in annual​ dividends) is currently priced in the market at ​$33.79 a share.

QUESTIONS: HUGE THUMBS UP FOR CORRECT ANSWERS

c. The conversion value of this issue is (blank) $ ? (Round to the nearest​ cent.)

d.. The conversion premium in dollars is (blank) $ ? (Round to the nearest​ cent.)

e. The​ bond's payback period is (blank) years ?  ​(Round to one decimal​ place.)

f.  . If comparably​ rated, nonconvertible bonds sell to yield 7 % .what is the investment value of the​ convertible?

The investment value of the convertible is (blank) $ ? (Round to the nearest​ cent.)

Answer 1

c)
Conversion value = Conversion ratio * current market price of the stock

Conversion ratio = Bond's current price / Bond's conversion price = $790 / ($790 / 17) = $790 / $46.47 = 17

Conversion value = 17 * $33.79 = $574.43

d)
Conversion premium = Bond's current price - Conversion value
= $790 - $574.43
= $215.57

e)
Bond's payback period = Conversion premium / (Annual interest - Annual dividend)
= $215.57 / ($790 * 5% - 17 * 0.56)
= $215.57 / ($39.5 - $9.52)
= $215.57 / 29.98
= 7.2 years

f)
Investment value = Present value of all the bond cash flows
Rate = 7%
Nper = 20
PMT = 1000 * 5% = 50
FV = 1000

Present value can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(7%,20,-50,-1000)
= $788.12

The investment value of the convertible = $788.12