Sweeney pies has issued a zero-coupon 10-year bond that can be converted into 10 Sweeney shares. Comparable straight bonds are yielding 9%. Sweeney stock is priced at $63 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?
1. Convert the bond
2. Stay with the bond
B. If the convertible bond is priced at $476, how much are investors paying for the option to buy Sweeney shares?
C. If, after one year, the value of the conversion option is unchanged, what is the value of the convertible bond?

A.Convert the bond

B.$53.59

C. $514.01

Explanation:

a. Calculation for whether to convert or to stay with the bond.

First step

In a situation where the fair rate of return on a 10 year zero-coupon non-convertible bond is 9%, which means the price would be calculated as:

Using this formula

Price =(Face value/(1+Non-convertible bond)^Numbers of years

Let plug in the formula

Price =($1,000/1.09)^10

Price = $422.41

Second step is to calculate for the conversion value

Conversion value = 10×$63 shares

Conversion value= $630

If we convert the gain will be :

Gain=$630 - $422.41

Gain= $207.59

Based on the above calculation this mean you may convert and sell the $10 shares for the amount of $630 which will help you to buy a bond for the amount of $422.41

And in a situation were you decide not to convert, you will own a non-convertible bond of the amount of $422.41, based on this i will convert the bond.

b. Calculation for how much are investors paying for the option to buy Sweeney shares

Amount to be paid = ($476.00-$422.41)

Amount to be paid= $53.59

This means the Investors are paying the amount of $53.59

c. Calculation for the value of the convertible bond

First is to calculate for the value of a comparable non-convertible bon

Bond value = $1,000/1.09^9

Bond value = $460.42

Now let calculate for the value of the convertible bond

Value of the convertible bond = $460.42+ $53.59

Value of the convertible bond= $514.01

Therefore the Value of the convertible bond will be $514.01