Warren Corporation's stock sells for $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

First, we need to find the price of the bond-with-warrants. Each bond comes with 75 warrants that are worth $2 each, so that adds an extra $150 of value to the bond. The total value of the bond-with-warrants is:

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

Next, we need to find the coupon rate that will make the bond-with-warrants sell at par. We know that a straight bond with a yield of 10% would sell at:

$100 / (0.10) = $1,000

Since the bond-with-warrants is worth $1,150, we know that the coupon rate on the bond must be higher than 10%. Let's start by assuming a coupon rate of 12%. The annual interest on a $1,000 bond with a coupon rate of 12% is:

$1,000 x 0.12 = $120

The annual interest on 75 warrants (assuming they are all exercised) is:

75 x $2 = $150

So the total annual cash flow to the bondholder is:

$120 + $150 = $270

The present value of this cash flow, assuming a yield of 10%, is:

$270 / (1.10)^20 = $44.44

Adding the present value of the $1,000 face value of the bond, we get:

$44.44 + $1,000 = $1,044.44

This is below the price of $1,150 that the bond-with-warrants sells for, so the coupon rate of 12% is too low. We need to increase the coupon rate and try again. After some trial and error, we find that a coupon rate of 8.24% gives us a bond price of:

$1,000 x 0.0824 x (1 - 1/1.10^20) / 0.10 + $1,000 + 75 x $2 = $1,150

Therefore, the coupon interest rate that the company must set on the bonds in order to sell the bonds-with-warrants at par is 8.24%, which is choice B.

Warren Corporation's Stock Sells for $42 Per Share