A 25-year maturity mortgage-backed bond is issued.The bond has a par value of $10,000 and promises to pay an 8 percent annual coupon.At issue,bond market investors require a 12 percent interest rate on the bond.What is the initial price on the bond?

Question

Quizplus · Accepted Answer

To calculate the initial price of the bond, we need to use the present value formula, which takes into account the future cash flows of the bond and the required rate of return by investors:

PV = C / (1 + r)^t + C / (1 + r)^(t-1) + ... + C / (1 + r) + F / (1 + r)^t

Where:
PV = Present value of the bond
C = Annual coupon payment = par value * coupon rate = $10,000 * 8% = $800
r = Required rate of return = 12%
t = Number of periods = 25 years
F = Face value or par value = $10,000

So plugging in the numbers, we get:
PV = $800 / (1 + 0.12)^1 + $800 / (1 + 0.12)^2 + ... + $800 / (1 + 0.12)^25 + $10,000 / (1 + 0.12)^25
PV = $6,863.22

Therefore, the initial price of the bond is $6,863.22, which is closest to option C.

A 25-Year Maturity Mortgage-Backed Bond Is Issued