CFA Level IFixed IncomeMedium
A 3-year annual-pay bond has a 5% coupon rate, a face value of $1,000, and a market yield to maturity of 6%. The bond's price is closest to:
- A$960.00
- B$973.40
- C$946.50
- D$1,000.00
Show answer & explanationAnswer & explanation
Correct answer: B. $973.40
Price = 50/1.06 + 50/1.06² + 1,050/1.06³ = 47.17 + 44.50 + 881.77 = $973.44, closest to $973.40. Since the coupon (5%) is below the YTM (6%), the bond trades at a discount to par.
Why the other options are wrong
- A. Close but understates the correct discounted sum.
- C. Too low; recheck discounting of the final cash flow.
- D. This would be the price only if coupon equaled YTM.
Bond Pricing (Discounted Cash Flow)
A bond's price equals the present value of its future coupon and principal payments discounted at the market yield to maturity.
- Coupon < YTM → bond trades at a discount
- Coupon > YTM → bond trades at a premium
- Coupon = YTM → bond trades at par
Memory trick: Discount cash flows to find the true price today.