Chapter 20, Problem 3P

a)

Summary Introduction

To calculate: The exercise value of the warrant at different stock prices

Explanation of Solution

(1)

Formula to calculate exercise price:

$\text{Exercise}\text{price}=\text{Current}\text{price}-\text{Strike}\text{price}$

Substitute $20 for current price and $25 for strike price to calculate the exercise price.

Calculation of exercise price:

$\begin{array}{c}\text{Exercise}\text{price}=\$20-\$25\\ =-\$5\end{array}$

Exercise price cannot be negative therefore; the exercise price is $0

(2)

Formula to calculate exercise price:

$\text{Exercise}\text{price}=\text{Current}\text{price}-\text{Strike}\text{price}$

Substitute $25 for current price and $25 for strike price to calculate the exercise price.

Calculation of exercise price:

$\begin{array}{c}\text{Exercise}\text{price}=\$25-\$25\\ =\$0\end{array}$

Therefore; the exercise price is $0

(3)

Formula to calculate exercise price:

$\text{Exercise}\text{price}=\text{Current}\text{price}-\text{Strike}\text{price}$

Substitute $30 for current price and $25 for strike price to calculate the exercise price.

Calculation of exercise price:

$\begin{array}{c}\text{Exercise}\text{price}=\$30-\$25\\ =\$5\end{array}$

Therefore; the exercise price is $5

(4)

Formula to calculate exercise price:

$\text{Exercise}\text{price}=\text{Current}\text{price}-\text{Strike}\text{price}$

Substitute $100 for current price and $25 for strike price to calculate the exercise price.

Calculation of exercise price:

$\begin{array}{c}\text{Exercise}\text{price}=\$100-\$25\\ =\$75\end{array}$

Therefore; the exercise price is $75

b)

Summary Introduction

To calculate: The coupon rate and interest amount in dollars attached to the bonds

Explanation of Solution

Formula to calculate value of straight bonds:

$\text{Value}\text{of}\text{bonds}\text{with}\text{warrants}=\text{Value}\text{of}\text{straight}\text{bonds}+\text{Value}\text{of}\text{warrants}$

Substitute $1,000 for value of bonds with warrants and number of warrants, 50 and price per warrant $3 to calculate the value of warrants in order to calculate the value of straight bonds.

Calculation of value of straight bonds:

$\begin{array}{c}\text{Value}\text{of}\text{bonds}\text{with}\text{warrants}=\text{Value}\text{of}\text{straight}\text{bonds}+\text{Value}\text{of}\text{warrants}\\ \$1000=\text{Value}\text{of}\text{straight}\text{bonds}+\left(50\text{warrants}\times \$3\text{per}\text{warrant}\right)\\ \text{Value}\text{of}\text{Straight}\text{bonds}=\$1,000-\$150\\ =\$850\end{array}$

Formula to calculate coupon interest amount:

$\text{Value}\text{of}\text{straight}\text{bonds}=\left(\begin{array}{l}\left(\text{Coupon}\text{interest}\text{amount}\times \text{PVIFA}\left(12\%,20\text{years}\right)\right)\\ +\left(\text{Value}\text{of}\text{stock}\text{with}\text{warrants}\times \text{PVIF}\left(12\%,20\text{years}\right)\right)\end{array}\right)$

Substitute $850 for value of straight bonds, 7.4694 for the value of PVIFA at 12% rate for 20 years, $1,000 for value of stock with warrants and 0.1037 for the value of PVIF at 12% rate for 20 years to calculate the coupon interest amount.

Calculation of coupon interest amount:

$\begin{array}{c}\text{Value}\text{of}\text{straight}\text{bonds}=\left(\begin{array}{l}\left(\text{Coupon}\text{interest}\text{amount}\times \text{PVIFA}\left(12\%,20\text{years}\right)\right)\\ +\left(\text{Value}\text{of}\text{stock}\text{with}\text{warrants}\times \text{PVIF}\left(12\%,20\text{years}\right)\right)\end{array}\right)\\ \$850=\left(\text{Coupon}\text{interest}\text{amount}\times 7.4694\right)+\left(\$1,000\times 0.1037\right)\\ \text{Coupon}\text{interest}\text{amount}=\frac{\$850-\$103.70}{7.4694}\\ =\$99.91\end{array}$

Therefore, the coupon rate is 9.91% and coupon amount is $9.91 on each bond.