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

The price of the corporate bond is sum of the present value of all the future cash flows. The future cash flows will be discounted at respective spot rates for that period to calculate the preset value

Therefore,

Price of two-year corporate bond = PV of four coupon payments + PV of principal payment at the end of period

Where,

Value at maturity, or par value of bond = $1,000

Coupon payment is 4%; therefore coupon = 4% * $1000 = $40; semiannual coupon = $40/2 = $20

n = number of payments = 1, 2, 3 and 4 for 4 semiannual payments

Therefore we have,

Price of the bond = $20/ (1+ 6-month spot rate) ^ 1 + $20/ (1+ 12-month spot rate) ^ 2 + $20/ (1+ 18-month spot rate) ^ 3 + $20/ (1+ 24-month spot rate) ^ 4 + $1000/ (1+ 24-month spot rate) ^ 4

= $20/ (1+3.2%) ^1 + $20/ (1+5%) ^2 +$20/ (1+5.5%) ^3 + $20/ (1+5.8%) ^4 + $1000/ (1+5.8%) ^4

= $19.38 + $18.14 + $17.03 + $15.96 +$798.10

= $868.61

Price of two-year corporate bond is $868.61