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fixed incomeintermediate25 min
Bond Valuation Step-by-Step
A complete workflow for pricing bonds, finding YTM, and understanding the price-yield relationship.
What You'll Learn
- ✓Price a bond with annual or semi-annual coupons
- ✓Find YTM using trial and error
- ✓Explain premium, par, and discount pricing
1. Identify Bond Cash Flows
Coupon bonds pay periodic interest plus face value at maturity. Zero-coupon bonds pay only face value.
Key Points
- •Annual coupon = coupon rate × face value
- •Semi-annual: halve coupon, double periods
- •Face value is typically $1,000
2. Discount to Find Price
PV the coupon stream as an annuity and PV the face value as a lump sum. Add both for the bond price.
Key Points
- •Use YTM as the discount rate
- •Annuity factor for coupons
- •Single PV factor for face value
3. Price-Yield Relationship
Bond price and yield move inversely. Higher yields mean lower prices. The relationship is convex.
Key Points
- •Coupon rate = YTM means price = par
- •Coupon > YTM means premium
- •Coupon < YTM means discount
4. Finding YTM
YTM is the rate that makes price equal to PV of cash flows. Solve by trial and error or financial calculator.
Key Points
- •YTM assumes reinvestment at same rate
- •Between two trial rates, interpolate
- •Calculator TVM keys: N, PMT, PV, FV solve for I/Y
Key Takeaways
- ★Duration measures price sensitivity to yield changes
- ★Longer maturity = more price sensitivity
- ★Pull-to-par: premium bonds decline toward par as maturity approaches
Practice Questions
1. A bond with 8% coupon trades at $1,050. Is YTM above or below 8%?
Below 8%. The bond trades at a premium, so yield is less than the coupon rate.
2. What is the price of a zero-coupon bond with $1,000 face, 10 years, 6% yield?
1000/1.06^10 = 1000/1.7908 = $558.39.
FAQs
Common questions about this topic
Halve the annual coupon and YTM, then double the number of periods.
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