liminfoBondcalc
Free web tool: Bondcalc
Bond Price
10,445.18
Macaulay Duration
4.5571yrs
Modified Duration
4.3818
Convexity
24.4766
Cash Flow Table
| Period | Year | Cash Flow | Present Value |
|---|---|---|---|
| 1 | 1 | 500 | 480.77 |
| 2 | 2 | 500 | 462.28 |
| 3 | 3 | 500 | 444.5 |
| 4 | 4 | 500 | 427.4 |
| 5 | 5 | 10,500 | 8,630.23 |
About Bondcalc
The Bond Price Calculator is a free, browser-based fixed income analysis tool for finance students, bond traders, portfolio managers, and CFA exam candidates. It computes the theoretical fair value (clean price) of a bond by discounting all future cash flows — periodic coupon payments and the face value repayment at maturity — back to the present using the market yield as the discount rate.
Beyond price, the calculator also computes three key risk metrics: Macaulay duration (the weighted average time to receive the bond's cash flows, expressed in years), modified duration (a measure of price sensitivity to yield changes, equal to Macaulay duration divided by 1 + periodic yield), and convexity (the second-order correction to the price-yield relationship, which accounts for the curvature that modified duration alone cannot capture).
The tool supports annual, semi-annual, and quarterly coupon payment frequencies, which reflects real-world bond conventions. It also generates a full cash flow table showing each period's coupon payment, the present value of that payment, and the cumulative discount. This makes it useful not just for pricing but also for understanding the time structure of bond cash flows and building intuition about duration.
Key Features
- Theoretical bond price calculation by discounting all coupon and principal cash flows
- Macaulay duration: weighted average time to receive cash flows (in years)
- Modified duration: percentage price change per 1% yield change
- Convexity: second-order price-yield relationship for more accurate risk estimation
- Supports annual, semi-annual, and quarterly coupon payment frequencies
- Full cash flow table: period, year, nominal cash flow, and present value for each period
- Handles zero-coupon bonds (coupon rate = 0) correctly
- Real-time recalculation as any input changes — no page reload needed
Frequently Asked Questions
How is the bond price calculated?
The bond price equals the sum of present values of all future cash flows discounted at the market yield. For each period t from 1 to n: PV(t) = cash_flow(t) / (1 + y)^t, where y is the periodic yield (annual yield / payment frequency) and n is the total number of periods. The cash flow in the last period includes both the coupon and the face value.
What does Macaulay duration measure?
Macaulay duration is the weighted average time (in years) until the investor receives the bond's cash flows, where each weight is the proportion of the bond's price represented by that cash flow's present value. A longer Macaulay duration means more of the bond's value is tied up in distant cash flows, making it more sensitive to interest rate changes.
What is modified duration and how is it used?
Modified duration estimates the percentage change in bond price for a 1% (100 basis point) change in yield: %ΔPrice ≈ -ModDuration × ΔYield. For example, a bond with a modified duration of 5 will fall in price by approximately 5% if yields rise by 1%. It is computed as: ModDuration = MacDuration / (1 + periodic yield).
What is convexity and why does it matter?
Convexity measures the curvature of the price-yield relationship. Modified duration provides a linear approximation of price changes, but the actual relationship is curved (convex). A higher convexity bond loses less value when yields rise and gains more value when yields fall, relative to a lower convexity bond with the same duration. Convexity improves the accuracy of price change estimates for large yield moves.
When does a bond trade at a premium or discount?
A bond trades at a premium (price > face value) when its coupon rate exceeds the market yield, because investors are paying extra for above-market income. It trades at a discount (price < face value) when the coupon rate is below market yield. It trades at par (price = face value) when the coupon rate equals the market yield.
What is the difference between Macaulay duration and modified duration?
Macaulay duration is a time measure (in years) representing when, on average, you receive the bond's cash flows. Modified duration is a price sensitivity measure (unit: % per 1% yield change). Modified duration = Macaulay duration / (1 + y/m), where y is the annual yield and m is the payment frequency. For a 1x/year bond, they are related by simply dividing by (1 + y).
How does payment frequency affect bond price and duration?
More frequent coupon payments (quarterly vs. annual) generally reduce duration slightly, because investors receive cash flows sooner. They also change the periodic compounding rate, which affects the discounted price. The calculator adjusts all formulas for the selected payment frequency: annual yield is divided by frequency to get the periodic rate.
Can I use this for zero-coupon bonds?
Yes. Set the coupon rate to 0 and the tool will correctly calculate the zero-coupon bond price as: Price = Face Value / (1 + yield)^maturity. The Macaulay duration of a zero-coupon bond equals its maturity, because the only cash flow occurs at maturity. Modified duration will be slightly less than maturity.