Atchley Enterprises' stock price is $42 per share. The company wants to sell some 20-year, annual interest, $1,000 par value bonds. Each bond would have 75 warrants attached to it, each exercisable into one share of stock at an exercise price of $47. The firm's straight bonds yield 10%. Each warrant is expected to have a market value of $2.00 given that the stock sells for $42. What coupon interest rate must the company set on the bonds in order to sell the bonds-with-warrants at par?

Question

Quizplus · Accepted Answer

The first step is to calculate the total value of the bonds-with-warrants package:

Bonds: $1,000 par value with a coupon rate of C, and a maturity of 20 years. The price of the bond can be calculated using the formula:

PV(Bonds) = C * (1 - 1/(1+R)^n)/R + 1000/(1+R)^n

where R is the required rate of return (yield to maturity) on the bonds, and n is the number of periods (years).

The problem tells us that the bonds sell at par, so the PV(Bonds) = $1,000. Plugging in the given values, we can solve for the coupon rate C:

$1,000 = C * (1 - 1/(1+0.10)^20)/0.10 + 1000/(1+0.10)^20

C = $129.28

Warrants: Each warrant is worth $2. The total value of 75 warrants is 75 x $2 = $150.

Bonds-with-warrants: The total value of the bonds-with-warrants package is therefore:

$1,000 + $150 = $1,150

If the firm can sell the bonds-with-warrants at par ($1,150), it must offer a coupon rate that makes the present value of the bond cash flows equal to $1,150.

PV(Bonds) + PV(Warrants) = $1,150

C * (1 - 1/(1+R)^n)/R + 1000/(1+R)^n + 75 x $2/(1+R)^n = $1,150

Solving for the required rate of return (yield to maturity) on the bonds-with-warrants, R = 10.50%.

Now that we know the required rate of return, we can calculate the coupon rate that will make the bonds sell at par:

$1,000 = C * (1 - 1/(1+0.105)^20)/0.105 + 1000/(1+0.105)^20

C = $114.34

Therefore, the coupon interest rate must be 114.34/1000 = 11.434% or 8.24% rounded to two decimal places.

The answer is B.

Atchley Enterprises' Stock Price Is $42 Per Share