Understanding bond valuation
A bond's worth today depends on two things: the stream of coupon payments you'll receive, and the face value you get back at maturity. The calculator discounts all these future cash flows to today's dollars using the market yield—the return investors currently demand for that level of risk.
The formula
Bond Price = (C / y) × [1 − (1 + y)^(−n)] + FV / (1 + y)^n
Where:
- C = annual coupon payment (face value × coupon rate)
- y = market yield (as a decimal)
- n = years to maturity
- FV = face value (par value)
Worked example
Suppose you're evaluating a corporate bond with these terms:
- Face value: $1,000
- Coupon rate: 5% (paid annually)
- Market yield: 4%
- Years to maturity: 10
Step 1: Calculate annual coupon payment
- C = $1,000 × 0.05 = $50 per year
Step 2: Find the present value of all coupon payments
- PV of coupons = ($50 / 0.04) × [1 − (1.04)^(−10)]
- = $1,250 × [1 − 0.6756]
- = $1,250 × 0.3244
- = $405.50
Step 3: Find the present value of the face value at maturity
- PV of face value = $1,000 / (1.04)^10
- = $1,000 / 1.4802
- = $675.56
Step 4: Add them together
- Bond price = $405.50 + $675.56 = $1,081.06
This bond trades at a premium because its 5% coupon exceeds the 4% market yield. If the market yield were 6% instead, the bond would trade at a discount (below $1,000).
Why the relationship matters
Bond prices and yields move in opposite directions. When market yields rise, existing bonds become less attractive, so their prices fall. When yields drop, existing bonds' fixed coupons look more valuable, pushing prices up. This inverse relationship is fundamental to bond investing and crucial when deciding whether to buy, hold, or sell.
Common mistakes
Using annual coupon rate without converting to decimal: Always divide the percentage by 100 before plugging it into the formula. A 5% coupon becomes 0.05.
Forgetting that coupon rate and market yield are different: The coupon rate is fixed when the bond is issued. The market yield changes daily based on supply, demand, and interest rates. Use the current market yield to price a bond today, not the original coupon rate.
Mismatching payment frequency: If coupons are paid semi-annually (common in US bonds), divide the annual coupon by 2, the annual yield by 2, and double the number of periods. For a 10-year bond with semi-annual coupons, use n = 20 and y = 0.02 (if the annual yield is 4%).
This calculator provides an estimate, not professional investment advice. Bond prices are also affected by credit risk, callability, liquidity, and tax treatment. Consult a financial advisor before making investment decisions.