Zabberer Corporation bonds pay a coupon rate of interest of 12 percent annually and have a maturity value of $1000. The bonds are scheduled to mature at the end of 14 years. The company has the option to call the bonds in 8 years at the premium of 12 percent above the maturity value you believe the company will exercise its option to call the bonds at that time. If you require a pretax return of 10 percent on bonds of this risk, how much would you pay for one of these bonds today?

Question

Zabberer Corporation bonds pay a coupon rate of interest of 12 percent annually and have a maturity value of $1000. The bonds are scheduled to mature at the end of 14 years. The company has the option to call the bonds in 8 years at the premium of 12 percent above the maturity value you believe the company will exercise its option to call the bonds at that time. If you require a pretax return of 10 percent on bonds of this risk, how much would you pay for one of these bonds today?

Answer 1

To calculate the present value of the bond, we need to discount the future cash flows (coupon payments and maturity value) at the required rate of return.

Let's break down the calculation into two parts:

1. Calculate the present value of the remaining coupon payments:
The bond pays a coupon rate of 12% annually, and since the maturity is 14 years, there will be 14 coupon payments. The formula for calculating the present value of an annuity is:

PV = C * (1 - (1 + r)^(-n)) / r

Where:
PV = Present Value
C = Coupon Payment
r = Required rate of return
n = Number of periods

Using the given information:
C = 0.12 * $1000 = $120
r = 0.10 (pre-tax return required)
n = 14 (number of remaining coupon payments)

Calculating the present value of the remaining coupon payments:

PV_coupon = $120 * (1 - (1 + 0.10)^(-14)) / 0.10

2. Calculate the present value of the maturity value:
The maturity value of the bond is $1000, but the company has the option to call the bonds in 8 years at a premium of 12% above the maturity value. This means that after 8 years, the bonds will be called, and we will receive the maturity value plus a premium.

Since we are assuming that the company will exercise its option, we need to calculate the present value of this premium amount after 8 years. To do this, we will discount the premium at the required rate of return for 8 years:

Premium = $1000 * 0.12 = $120 (premium amount)
PV_premium = $120 / (1 + 0.10)^8

Finally, to calculate the total present value of the bond, we sum the present value of the remaining coupon payments (PV_coupon) and the present value of the maturity value plus the premium (PV_premium):

Total PV = PV_coupon + PV_premium

By plugging in the calculated values, you will be able to determine the price you should pay for one of these bonds today.