Bond Calculator
Determine a bond's fair market value or its Yield to Maturity (YTM). Calculate essential risk and interest rate sensitivity metrics like Macaulay duration, modified duration, and convexity, and see the full schedule of coupons and principal repayments.
Cash Flow Schedule
| Period | Year | Cash Flow | Present Value (PV) | Cumulative Cash Flow |
|---|---|---|---|---|
| 1 | 0.50 | $25.00 | $24.45 | $25.00 |
| 2 | 1.00 | $25.00 | $23.91 | $50.00 |
| 3 | 1.50 | $25.00 | $23.39 | $75.00 |
| 4 | 2.00 | $25.00 | $22.87 | $100.00 |
| 5 | 2.50 | $25.00 | $22.37 | $125.00 |
| 6 | 3.00 | $25.00 | $21.88 | $150.00 |
| 7 | 3.50 | $25.00 | $21.39 | $175.00 |
| 8 | 4.00 | $25.00 | $20.92 | $200.00 |
| 9 | 4.50 | $25.00 | $20.46 | $225.00 |
| 10 | 5.00 | $25.00 | $20.01 | $250.00 |
| 11 | 5.50 | $25.00 | $19.57 | $275.00 |
| 12 | 6.00 | $25.00 | $19.14 | $300.00 |
How is a bond valued?
A bond is valued by discounting its future cash flows (coupon payments and the principal returned at maturity) to their present value. The formula for the price of a standard, option-free bond is:
Where C is the annual coupon payment (Face Value × Coupon Rate), f is the coupon frequency, YTM is the annual Yield to Maturity, t is the period index, FV is the face value, and N is the total number of periods (Years × f).
Worked example
Consider a $1,000 face value bond with a 5% coupon rate paid semi-annually ($25 every 6 months) and 10 years to maturity:
- If the market demand requires a 4.5% YTM, the bond trades at a premium price of $1,039.91 (representing a price of 103.99% of par).
- If interest rates rise and market demand requires a 6.0% YTM, the price of the bond falls to a discount of $925.61 (representing a price of 92.56% of par).
Frequently asked questions
What is the difference between bond price and face value?
Face value (or par value) is the amount the issuer promises to pay back to the bondholder at maturity. The bond price is what the bond currently trades for in the secondary market. If the price is above face value, the bond trades at a premium; if below, it trades at a discount.
How do interest rates affect bond prices?
Bond prices and interest rates have an inverse relationship. When market interest rates rise, newly issued bonds pay higher yields, making existing bonds with lower coupon rates less valuable, causing their prices to fall. When market rates drop, existing bonds with higher coupons become more valuable, causing their prices to rise.
What is Yield to Maturity (YTM)?
Yield to Maturity (YTM) is the estimated annual rate of return an investor will receive if they purchase a bond at its current market price and hold it until it matures, assuming all coupon payments are received on time and reinvested at that same rate.
What do Macaulay and Modified Duration measure?
Macaulay Duration measures the weighted average time (in years) until an investor receives all the bond's cash flows. Modified Duration measures a bond's price sensitivity to interest rate changes; for instance, a bond with a Modified Duration of 5 years is expected to experience a 5% price change for every 1% change in yield.
What is bond convexity?
Convexity measures the curvature of the bond price-yield relationship. Because the relationship between a bond's price and its yield is curved rather than linear, convexity adjusts for the error in the duration estimate for larger changes in interest rates. A higher convexity is generally preferred by investors.