Question

Piglet Pies has issued a zero-coupon 10-year bond that can be converted into 10 Piglet shares. Comparable straight bonds are yielding 8%. Piglet stock is priced at $64 a share.(Assume a face value of $1,000 and semi-annual compounding.)

a. Suppose that you had to make a now-or-never decision on whether to convert or to stay with the bond. Which would you do?

	Convert the bond
	Stay with the bond

b. If the convertible bond is priced at $552, how much are investors paying for the option to buy Piglet shares? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Option value            $ ____

c. If after one year the value of the conversion option is unchanged, what is the value of the convertible bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Bond value            $ _____

Answer 1

a). If the fair rate of return on a 10-year zero-coupon non convertible bond is 8%, then the price would be:

$1,000/1.08¹⁰ = $463.19

The conversion value is: 10 x $64 = $640

You would convert. By converting, you would gain:

$640 - $463.19 =$176.81

That is, you could convert, sell the ten shares for $640, and then buy a comparable straight bond for $463.19. Otherwise, if you do not convert, and the bond is no longer convertible in the future, you will own a non-convertible bond worth $463.19.

b). The value of the conversion option = the price of a convertible bond – the price of an equivalent straight bond

= $552 – $463.19 = $88.81 investors are paying for the option to buy ten shares.

c). In one year, bond value = $1000/1.08⁹ = $500.25 (i.e.,the value of a comparable non-convertible bond)

Then, the value of the convertible bond = $500.25 + $88.81 = $589.06