gen-define-bond-pricing-and-yield-and-give-one-short-worked-exam-0cd7

Define bond pricing and yield and give one short worked example.

# Bond Pricing and Yield ## Definitions **Bond Pricing** is the present value of all future cash flows from a bond, including periodic coupon payments and the face value at maturity, discounted at an appropriate rate. **Yield** (Yield to Maturity - YTM) is the total return anticipated on a bond if held until maturity, expressed as an annual rate. It's the discount rate that equates the bond's price to the present value of its cash flows. ## Relationship - **Inverse relationship**: When yields rise, bond prices fall, and vice versa - When yield = coupon rate → bond trades at par - When yield > coupon rate → bond trades at a discount - When yield < coupon rate → bond trades at a premium ## Worked Example **Given:** - Face value: $1,000 - Coupon rate: 6% (annual payments) - Time to maturity: 3 years - Market yield (YTM): 8% **Find the bond price:** Price = PV of coupons + PV of face value Annual coupon = $1,000 × 6% = $60 Price = $60/(1.08)¹ + $60/(1.08)² + $60/(1.08)³ + $1,000/(1.08)³ Price = $55.56 + $51.44 + $47.63 + $793.83 **Price = $948.46** The bond trades at a **discount** ($948.46 < $1,000) because the market yield (8%) exceeds the coupon rate (6%).