ABC stock sells for $22 bucks a share. The company wants to sell 20 year annual interest $1000 par value bonds. Each bond will have 75 warrants attached to it which is exercisable into one share of stock. The exercise price is $47.00. The stock sells for $42. The firm’s straight bond yields 10%. Each warrant has a market value of $2 given that the stock sells for 42.00. What coupon interest rate should the company set on the bonds in order to sell the bonds with the warrants at par?
To determine the coupon interest rate that the company should set on the bonds to sell them with the warrants at par, we first need to understand the concept of the bond's "at par" value.
The "par" value of a bond refers to its face value or the amount of money the bondholder will receive at maturity. In this case, the par value of the bond is $1000.
We also need to understand the components of the bond with warrants. Each bond comes with 75 warrants attached to it, which can be exercised to obtain one share of stock. The exercise price for these warrants is $47.00. Additionally, the stock is currently selling for $42.00.
The market value of each warrant is given as $2, based on the stock price of $42.00. This means that the warrant provides an additional value of $2 per warrant.
Now, let's break down the value of the bond with warrants:
1. Bond value: The bond itself has a par value of $1000. To determine its value, we need to calculate the present value of the bond's future cash flows using the straight bond yield.
2. Warrant value: Each bond comes with 75 warrants, and the market value of each warrant is $2. So the total value of the warrants is 75 * $2 = $150.
3. Stock value: Each warrant can be exercised to obtain one share of stock. The exercise price is $47.00, and the stock is currently selling for $42.00. Since the exercise price is higher than the stock price, the warrants are currently out of the money and have no intrinsic value. Hence, the stock value in this case is $0.
4. Total value of the bond with warrants: The total value of the bond with warrants is the sum of the bond value and the warrant value. Therefore, it is $1000 + $150 = $1150.
Now, to sell the bonds with warrants at par, the coupon interest rate should be set in a way that the total value of the bond with warrants equals its par value of $1000.
Letting 'x' be the coupon interest rate, we can use the present value formula to solve for 'x'.
PV = [C / (1 + r)^1] + [C / (1 + r)^2] + ... + [C / (1 + r)^n] + [F / (1 + r)^n]
Where:
PV = Present value (par value)
C = Coupon payment (annual interest payment)
r = Discount rate (required yield)
n = Number of periods
In this case, assuming the bonds are annual interest bonds, we have:
PV = $1000
C = x * $1000 (Coupon payment is the coupon interest rate multiplied by the par value)
r = 10% (Straight bond yield)
n = 20 (Number of years)
We need to solve for 'x' in the equation. To do this, we can use financial calculator functions like the NPV (Net Present Value) or IRR (Internal Rate of Return) functions. Alternatively, we can use an Excel spreadsheet or online financial calculators to find the value of 'x' that makes the present value equal to $1000.
By adjusting the coupon interest rate until the present value matches the par value, we can determine the exact coupon interest rate that the company should set on the bonds in order to sell them with the warrants at par.