Manufacturing Company has a large number of ten-year $1,000 face value bonds on the market with a 7% coupon paid annually and an 8% YTM. Which of the following would be the current price of an individual $1,000 bond?

• A. $932.91
• B. $970.50
• C. $1,000
• D. $1,067.00

Answer: (A)

The price of a bond is the present value of its future cash flows discounted at the yield to maturity. In this case, the bond pays a 7% annual coupon on a 1000 face value, so 70 per year for 10 years, plus 1000 at the end of year 10. Discount these at 8%: the present value of the coupons is 70 times the annuity factor [ (1 − (1.08)^−10) / 0.08 ] ≈ 70 × 6.710 ≈ 469.70. The present value of the face value is 1000 × (1.08)^−10 ≈ 463.19. Adding them gives about 469.70 + 463.19 ≈ 932.89, which rounds to 932.91. Since the yield (8%) is higher than the coupon rate (7%), the bond trades below its par value, matching the observed price.