Question

Consider a corporate bond with a face value of $1,000, 2 years to maturity and a coupon rate of 4%. Coupons are paid semi-annually. The next coupon payment is to be made exactly 6 months from today. What is this bond's price assuming the following spot rate curve. 6-month spot rate: 3.2%. 12-month: 5%. 18-month: 5.5%. 24-month: 5.8%.

Answer 1

Price of bond = present value of bond's cash flows.

Bond's cash flows = semiannual coupon payments + face value received at maturity

semiannual coupon payment = face value * coupon rate / 2 = $1,000 * 4% / 2 = $20

Present value = future value / (1 + discount rate)ⁿ

where n = number of years after which cash flow is received.

Price of bond = ($20 / (1 + 3.2%)^0.5) + ($20 / (1 + 5%)¹) + ($20 / (1 + 5.5%)^1.5) + ($20 / (1 + 5.8%)²​​​​​​​) + ($1,000 / (1 + 5.8%)²​​​​​​​)​​​​​​​

Price of bond = $968.42