Your client has been offered a 5-year,$1,000 par value bond with a 10 percent coupon.Interest on this bond is paid quarterly.If your client is to earn a simple rate of return of 12 percent,compounded quarterly,how much should she pay for the bond?
A) $800
B) $926
C) $1,025
D) $1,216
E) $981

Question

Quizplus · Accepted Answer

To determine the price, we need to calculate the present value of the future cash flows (interest payments and principal repayment).
First, we need to determine the quarterly payment:
Coupon payment = $1,000 x 10% x 1/4 = $25
Next, we need to determine the number of periods:
5 years x 4 quarters per year = 20 periods
Using the formula for present value of an annuity:
PV = PMT x (1 - 1/(1 + r)^n) / r
where PV is the present value, PMT is the payment, r is the interest rate per period, and n is the number of periods.
Plugging in the numbers:
PV = $25 x (1 - 1/(1 + 0.03)^20) / 0.03
PV = $25 x 14.877 = $372.93
To determine the present value of the principal repayment, we can simply discount it back to present using the quarterly compound interest rate:
PV = $1,000 / (1 + 0.03)^20
PV = $567.43
Finally, we add the present values of the coupon payments and the principal repayment:
Price = $372.93 + $567.43 = $940.36
Therefore, the answer is B) $926, which is the closest option.

Your Client Has Been Offered a 5-Year,$1,000 Par Value Bond