A gilt's NPV column discounts each future payment at the gilt's own gross redemption yield, which is why the column adds up to the dirty price per £100 nominal — and why the two curve columns do not.
A gilt's cash-flow schedule carries an NPV column, and the rows of it add up to the dirty price per £100 nominal. That is not a coincidence or an approximation: it is the arithmetic that defines the column, and it is the quickest check that a figure copied out of the page is the figure the site means.
What the column is
NPV is the present value of one flow, discounted at the gilt's own gross redemption yield. Each row of the schedule carries one future payment — a coupon or the redemption — and the column discounts that payment back to the page's settlement date at the yield on the gilt's own page, on the same convention the yield itself is quoted on. The two agree by construction rather than by rounding.
Which is why the column sums to the dirty price. The gross redemption yield is the rate at which the gilt's remaining cash flows, discounted to settlement, equal the cash paid for it — and the cash paid is the dirty price, clean plus accrued.
The two curve columns are a different question
| Column | Discounted at | Sums to the dirty price? |
| NPV | The gilt's own gross redemption yield, one rate for every flow. | Yes. That is what the yield was solved for. |
| NPV (par curve) | The report's fitted par curve, at each flow's own term. | No. An estimate from the curve, not a contractual amount. |
| NPV (zero-coupon) | The report's bootstrapped zero-coupon curve, at each flow's own term. | No. An estimate from the curve, not a contractual amount. |
The two curve columns are marked as curve-derived on the page, and they are there to show what the coupon effect is worth: the difference between discounting every flow at one yield and discounting each at the rate the curve gives for its own term. They are a reading of the curve, so they will not reconcile with a price, and they are not meant to.
The check, in steps
- Open the gilt from the list and choose Cash flows. The schedule lists every coupon and redemption the gilt has left, per £100 nominal, from the page's settlement.
- Note the report date the card names. Every figure in the table belongs to that report.
- Add the NPV column. On a conventional gilt the sum is the dirty price per £100 nominal.
- Compare it with Mid price (dirty) on the gilt's Prices card. They agree at the rounding the page shows.
- Working in pounds rather than per £100, scale both sides by the same nominal. The identity holds at any quantity, because every row and the price are per £100.
Where it disagrees
Three ordinary reasons for a mismatch, and all three are visible on the page rather than hidden.
- A projection. An index-linked gilt's future coupons are the real coupon scaled at the latest published index ratio, with no further inflation assumed. Rows that are projected are marked, and the sum is then an estimate rather than a contractual total.
- A different settlement. The dirty price and the discounting both start from the page's settlement date. Change the settlement, or compare with a price from the list, and the two sides are describing different days.
- Rounding. The column is money shown to a fixed number of decimals. Adding displayed values and comparing with a displayed price can leave a penny or two, which is display rounding rather than a difference in the arithmetic.
Where the column is not
It is not on the list, which has no room for a schedule: the list carries the price, the yields and the trend. The curve is where the two fitted rates behind the other two columns come from, and the price-in-pounds guide takes the dirty price itself through a worked example.
The terms this page draws on are the glossary's npv, npv-par-curve, npv-zero-coupon, clean-price, accrued-interest, dirty-price and gross-yield.