Cash flow schedule and discounted values
The table below shows each coupon period, cash flows and their discounted present values based on the selected yield.
Estimate bond price and yield to maturity with a full cash flow schedule
Understand bond yield and pricing with a detailed cash flow view
The Bond Yield and Pricing Tool helps you evaluate fixed income investments by combining both price and yield calculations with a clean, period-by-period cash flow schedule. By entering a bond’s face value, coupon rate, time to maturity, payment frequency and either a market yield or an observed market price, you can quickly understand how each cash flow contributes to the overall value of the bond.
How bond cash flows determine price
A traditional fixed coupon bond pays a series of coupon payments followed by repayment of the principal at maturity. Each of these cash flows is discounted back to the present using a market yield. The present value of the bond is the sum of these discounted cash flows, often written as:
\[ P = \sum_{t=1}^{N} \frac{C}{(1 + y/m)^{t}} + \frac{F}{(1 + y/m)^{N}} \]
Where \(P\) is the bond price, \(C\) is the coupon per period, \(F\) is the face value, \(y\) is the annual yield, \(m\) is the number of coupon payments per year and \(N\) is the total number of periods until maturity. When the yield is higher, each future cash flow is discounted more heavily, which lowers the price. When the yield is lower, the present value of the cash flows increases and the bond price rises.
Yield to maturity versus current yield
Investors often talk about bonds using several different yield measures. The Bond Yield and Pricing Tool focuses on two practical concepts: yield to maturity and current yield.
- Yield to maturity (YTM) is the internal rate of return that equates all future cash flows to the current price. It assumes the bond is held until maturity and that coupons can be reinvested at the same yield. Conceptually, YTM solves the equation \[ P = \sum_{t=1}^{N} \frac{C}{(1 + y/m)^{t}} + \frac{F}{(1 + y/m)^{N}} \] for the unknown \(y\).
- Current yield is simpler and looks only at the income component. It is the annual coupon divided by the current price: \[ \text{Current Yield} = \frac{C_{\text{annual}}}{P}. \] It does not capture capital gains or losses at maturity.
By displaying both measures, the calculator helps you understand whether a bond’s income return and total return profile are aligned with your investment objectives.
Using market price to infer yield
Sometimes you know the price of a bond but not its yield. The Bond Yield and Pricing Tool can estimate an implied yield to maturity by solving for the rate that makes the discounted cash flows equal the observed price. Because this equation does not have a closed-form solution for most coupon bonds, the calculator uses numerical methods to find a yield that satisfies:
\[ 0 = \sum_{t=1}^{N} \frac{C}{(1 + y/m)^{t}} + \frac{F}{(1 + y/m)^{N}} - P_{\text{market}}. \]
This approach is similar to how professional pricing systems back out yields from market quotes. It is particularly useful when you are comparing bonds offered at different prices or when you want to see how a premium or discount price affects the expected return.
Interpreting the cash flow schedule
The detailed cash flow table in the tool shows, for every period, the coupon payment, any principal repayment, the total cash flow, the discount factor and the present value of that cash flow. The cumulative present value column sums all discounted cash flows up to that period, converging to the bond price at maturity. The final row, where the principal is repaid, is visually highlighted so that you can easily see how much of the value comes from the final cash flow versus the stream of coupons.
Reviewing this schedule provides insight into the bond’s interest rate sensitivity and risk profile. For example, when a large portion of the present value is concentrated in the final payment, the bond tends to have a longer effective duration and greater sensitivity to changes in yield.
Practical applications for investors and analysts
The Bond Yield and Pricing Tool is designed to support a wide range of fixed income decisions:
- Comparing similar bonds with different coupons and maturities.
- Evaluating whether a quoted market price is attractive given your target yield.
- Understanding the trade-off between premium and discount bond pricing.
- Visualizing how each coupon period contributes to overall return.
By combining bond pricing formulas, yield estimation and a transparent cash flow breakdown, the tool offers a practical way to deepen your understanding of fixed income instruments and make more informed portfolio decisions.
Limitations and assumptions
Like any financial model, this calculator relies on simplifying assumptions. It assumes that coupon payments are made exactly on schedule, that the bond is held to maturity, and that coupons can be reinvested at the yield to maturity. Real-world factors such as default risk, call features, taxes and transaction costs are not included. Nonetheless, the underlying mathematics of discounting cash flows and solving for yields provide a solid foundation for evaluating most plain-vanilla bonds and comparing their relative value.