How this calculation works
The annual coupon is divided equally across m payments. Each coupon and the final principal are discounted using the periodic required yield y/m. The valuation date is immediately after a coupon payment, with the next cash flow one whole period later.
Price = Σ coupon ÷ (1+y/m)ᵏ + face value ÷ (1+y/m)ᴺA worked example
A ₹10,000 bond with an 8% annual coupon, 8% required yield and half-yearly payments is priced at ₹10,000 under this model.
Good to know
Regular fixed coupons and repayment in full at maturity. Whole years only, valuation on a coupon date after payment. No accrued interest, settlement-date adjustments, day-count conventions, calls, defaults, fees, tax or market feed.
Reference: Investor.gov: bond terms and risks (opens in a new tab) ↗
Coupon rate and required yield play different roles
The coupon rate determines the contractual coupon amount from the face value. The required yield is the discount rate used to value the future cash flows. Changing the yield in this model changes the price without changing the coupon payment.
A bond with ₹10,000 face value and an 8% annual coupon pays ₹400 each half-year when it has two equal payments per year. At an 8% nominal required yield on the same basis, this regular bond is valued at face value.
If the required yield rises while the promised cash flows remain fixed, their present values fall. Compare yields above and below the coupon rate to see discount and premium prices. These are model outcomes, not an estimate of a particular security’s tradable quote.
The valuation date is part of the model
This tool values the bond on a coupon date immediately after a coupon due then has been paid. The next coupon is one full payment period away. Between coupon dates, accrued interest and settlement conventions can change how a quoted clean price relates to the cash paid.
The cash-flow table separates coupons from principal. At maturity, the final row includes both the last coupon and the face-value repayment. Forgetting either amount understates the present value.
The model assumes every promised payment arrives in full and on time. It does not price default risk, calls, floating coupons, irregular first periods or taxes. A zero-coupon bond is supported by setting the coupon rate to zero; its value comes entirely from the discounted maturity amount.
A few questions, answered
Is this a yield-to-maturity solver?
No. You enter the required yield and the tool calculates a price. Solving for yield from a market price is the reverse problem and is not done here.
What happens at zero required yield?
All discount factors equal one, so the price is the sum of every coupon plus the face value. The entered annual coupon does not become zero.
Why may the displayed row values not sum exactly to the headline price?
Rows are rounded to paise for display. The headline price sums unrounded present values and is then rounded once.