You own a bond with a make-whole call provision. The bond matures in 11 years, but is being called today. The coupon rate is 8% with interest paid semiannually. What is the current call price if the discount rate is 7.2% and the make-whole call provision?

Question

Quizplus · Accepted Answer

To calculate the current call price, we need to find the present value of the bond's remaining cash flows.

First, we need to calculate the semiannual coupon payments. The annual coupon payment is 8% * $1,000 = $80. Since the interest is paid semiannually, the semiannual coupon payment is $40.

Next, we need to calculate the number of semiannual periods remaining until maturity. The bond has 11 years to maturity, which is 22 semiannual periods (11 years * 2 semiannual periods per year). However, since the bond is being called today, we only need to calculate the present value of 10 semiannual coupon payments.

Using the present value formula with a 7.2% discount rate, we get:

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

where:
C = semiannual coupon payment = $40
r = discount rate = 7.2% / 2 = 3.6% per semiannual period
n = number of semiannual periods remaining = 10
FV = face value = $1,000

PV = ($40 / 0.036) * (1 - 1 / (1 + 0.036)^10) + $1,000 / (1 + 0.036)^10
PV = $449.127 + $630.9539
PV = $1,080.08

Next, we need to calculate the make-whole call price. This is the present value of the remaining coupon payments plus the present value of the face value, discounted at the make-whole yield. To calculate the make-whole yield, we need to solve for the yield that would make the present value of the remaining cash flows equal to the call price. We can use Excel's RATE function to do this.

Using Excel's RATE function with the following inputs:
Nper = 10
Pmt = 40
Fv = 1,000
Pv = -1,080.08
Type = 0

We get a make-whole yield of 8.6168% per year, or 4.3084% per semiannual period.

Using the present value formula with a 4.3084% discount rate, we get:

Make-whole call price = ($40 / 0.043084) * (1 - 1 / (1 + 0.043084)^10) + $1,000 / (1 + 0.043084)^10
Make-whole call price = $401.23 + $658.85
Make-whole call price = $1,060.08

Therefore, the current call price with the make-whole call provision is $1,060.08. The answer is C.

You Own a Bond with a Make-Whole Call Provision