Pentos International (PI) is in the heavy equipment industry. The debt rating for PI is AA, and the yield spread on AA-rated bonds for five-year maturity is 3% per year. The yield on a five-year treasury is 4% per year. The company recently announced that it would issue convertible bonds. The bonds will have no coupons and will have a maturity of five years and will pay $1000 at the end of five years. The bond can be converted to 20 shares of PI stock at the end of two years. The price of PI stock is $35. A call option on PI stock with an exercise price of $50 and maturity of five years is priced at $18. What is the fair value of the bond? Use simple compounding and ignore any dilution effects. Hint: Convertible bond price = (bond Price without options) + (Convertible Option)

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Answer:

$1072.99

Explanation:

We have the

Risk Free Rate to be = 4%

Also, the Default Premium on AA Rated Bonds is = 3%

We calculate the YTM on AA Rated Bond as 4% + 3% = 7%

Maturity years = 5

Face Value, fv is given as = $1000

Price of Bond without option = 0 + fv / (1 + YTM)^Years to Maturity

= 1000 / (1 + 0.07)⁵ = $712.99

Next we calculate the Value of Conversion Option:

The Number of Shares that can be converted into is 20

Price of conversion= Fv / No. of Shares

= 1000 / 20 = $50

We have that a call option with 5 years to maturity with a strike price of $50 has its worth to be $18, so the conversion option is also going to be $18.

Value of Conversion Option = 20 x 18 = $360

Next we get the Fair Value of Convertible Bond:

= 712.99 + 360 = $1072.99

Therefore the Fair Value of Convertible Bond would be $1072.99

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