A bond has a maturity value of $300,000 payable in 4 years. These bonds have a 7% coupon rate payable semi-annually, and the market yield was 4% when the bonds were purchased. How much premium or discount will be recorded upon purchase (rounded)?
A)$32,668 premium.
B)$32,668 discount.
C)$32,965 discount.
D)$32,965 premium.

Question

Quizplus · Accepted Answer

To determine the premium or discount, we calculate the present value of the bond's cash flows (interest payments and the principal repayment) and compare it to its face value. The bond pays semi-annual interest, so the coupon payment is $300,000 * 7% / 2 = $10,500 every six months. The market yield is 4% annually, or 2% per period semi-annually. There are 4 * 2 = 8 periods. The present value of the interest payments (an annuity) is calculated using the formula PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the payment per period, r is the market interest rate per period, and n is the total number of periods. The present value of the principal (a lump sum) is calculated using the formula PV = FV / (1 + r)^n, where FV is the future value. Adding these two present values gives the bond's price. If the price is higher than the bond's face value, the difference is a premium; if it's lower, it's a discount. In this case, the bond's price exceeds its face value, indicating a premium. Calculating the exact amount requires financial calculator or spreadsheet software, but the correct choice is a premium of $32,965.

A Bond Has a Maturity Value of $300,000 Payable in 4