What is Bond Pricing and Valuation?
Bond pricing calculates the current market value of a bond by discounting all future cash flows (coupon payments and principal repayment) back to present using the required rate of return. This determines whether a bond is fairly valued, overpriced, or underpriced.
Bond price is the present value of all future coupons and principal: P = C/(1+y)¹ + C/(1+y)² + … + (C+FV)/(1+y)ⁿ, where C is coupon, y is yield, FV is face value, and n is years to maturity.
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Step-by-step worked examples
Bond: FV=$1000, coupon=$50/year, YTM=5%, 10 years. Price?
P = Σ[C/(1+y)^t] + FV/(1+y)^n PV of coupons ≈ 50 × [1−(1.05)^-10]/0.05 ≈ $386 PV of principal = 1000/(1.05)^10 ≈ $614 P ≈ $1000 (par, coupon rate = YTM)
Same bond, YTM rises to 7%. New price?
PV of coupons ≈ 50 × [1−(1.07)^-10]/0.07 ≈ $348 PV of principal = 1000/(1.07)^10 ≈ $508 P ≈ $856 (discount, price < FV)
Bond: FV=$1000, coupon=$60/year, YTM=4%, 10 years. Price?
PV of coupons ≈ 60 × [1−(1.04)^-10]/0.04 ≈ $541 PV of principal = 1000/(1.04)^10 ≈ $676 P ≈ $1217 (premium, price > FV)
Flashcards
Quick quiz
Q1.Higher yield to maturity means…
Q2.Coupon payment is…
Q3.Bond trading at premium means…
Q4.When interest rates rise, existing bond prices…
The full card deck, worked steps and AI-tutor support for “What is Bond Pricing and Valuation?” are in Notek — study by hand before your exam.
Common mistakes
Forgetting that discount rate increases as yields rise. — Correct: Higher yields = lower present value → lower bond price.
Confusing coupon rate with yield to maturity. — Correct: Coupon rate is fixed; YTM changes based on market interest rates.
Ignoring time value of money in bond valuation. — Correct: Bond price requires discounting all cash flows—later payments worth less today.
Assuming bond price always equals face value. — Correct: Bond price fluctuates; equals face value only when coupon rate = market yield.
FAQ
What is the bond pricing formula?
P = Σ[C/(1+y)^t] + FV/(1+y)^n—sum of discounted coupons and principal.
What happens when interest rates rise?
Bond prices fall because future cash flows are discounted at a higher rate.
Premium bond vs discount bond?
Premium: price > FV (coupon > YTM). Discount: price < FV (coupon < YTM).
How to find fair bond price?
Calculate present value of all coupons and principal using market yield to maturity.