If an investor requires a 10 percent return on a $1000 bond with a 7% coupon rate, what will the investor be willing to pay for the bond today if it matures in 8 years and interest is paid semiannually? What if interest is compounded and paid annually?

Question

Quizplus · Accepted Answer

First, we need to calculate the semi-annual coupon payments. The coupon rate is 7% and the face value is $1000, so the semi-annual coupon payment is $35 ($1000 x 0.07 / 2).

To calculate the present value of the bond with semi-annual payments, we need to use the following formula:
PV = (C / r) x [1 - 1 / (1 + r)^n] + FV / (1 + r)^n

where PV is the present value, C is the coupon payment, r is the required rate of return (10% or 0.05 in decimal form), n is the number of periods (8 years or 16 semi-annual periods), and FV is the face value of the bond ($1000).

Using this formula, we get:
PV = ($35 / 0.05) x [1 - 1 / (1 + 0.05)^16] + $1000 / (1 + 0.05)^16
PV = $837.43

Therefore, the investor would be willing to pay $837.43 for the bond today if interest is paid semi-annually.

To calculate the present value of the bond with annual compounding, we need to use the same formula but adjust the number of periods to 8 and divide the required rate of return by 2 (since interest is now compounded annually instead of semi-annually).

Using this formula, we get:
PV = ($70 / 0.05) x [1 - 1 / (1 + 0.05)^8] + $1000 / (1 + 0.05)^8
PV = $839.95

Therefore, the investor would be willing to pay $839.95 for the bond today if interest is compounded and paid annually.

If an Investor Requires a 10 Percent Return on a $1000