A certain ​% annual coupon rate convertible bond​ ($1,000 par​ value, maturing in 20​ years) is convertible at the​ holder's option into shares of common stock. The bond is currently trading at ​$. The stock​ (which pays ​¢ a share in annual​ dividends) is currently priced in the market at ​$ a share. a. What is the​ bond's conversion​ price? b. What is its conversion​ ratio? c. What is the conversion value of this​ issue? What is its conversion​ parity? d. What is the conversion​ premium, in dollars and as a​ percentage? e. What is the​ bond's payback​ period? f. If comparably​ rated, nonconvertible bonds sell to yield what is the investment value of the​ convertible?

Full word "A certain 6% annual coupon rate convertible bond​ (maturing in 20​ years) is convertible at the​ holder's option into 20 shares of common stock. The bond is currently trading at $800. The stock​ (which pays 82 ¢a share in annual​ dividends) is currently priced in the market at $34.35 a share."

a. The conversion price = Face value / Number of the shares it can be converted into

= 1,000 / 20 shares

= $50

b. The conversion ratio is 1:5 as 1 bonds convertible into 5 equity shares

c. Conversion value = Value of the shares it can be converted into

= 20 shares * Price of $34.35

= $687

Conversion parity = Price of the bond / Number of shares its convertible into

Conversion parity = $800 / $20

Conversion parity = $40

d. Conversion premium = Current price of bond - Conversion price

= $800 - $687

= $113

Conversion premium percentage = $113/$687*100

= 16.44832%

= 16.45%

e. Bonds payback period = Conversion premium /(Annual coupon interest - Annual common dividend)

= 113/(6%*1000 - 20*0.82)

= 113/(60 - 16.4)

= 113/43.60

= 2.59 years

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