Apple Numbers XNPV: Present Value of Dated Cash Flows

• Introduced: The first supported release and introduction date are not established by the checked sources.
• Availability: Currently documented in Apple’s Formulas and Functions Help 15.4 documentation edition; no final support endpoint is established.
• Scope: Shared iWork function reference. This edition number does not establish a Numbers app version or identical behavior across older Mac, iPad, iPhone and iCloud clients.
• Checked: October 14, 2026, against the official XNPV reference. Documentation and independent numerical models; no native Numbers test.

=XNPV(discount, payments, dates)

All three arguments are required. Payments and dates are matching ranges of the same length. Apple’s reference requires at least one positive and one negative payment, with a negative initial payment when the first entry is an outflow. The first date starts the timeline; all later entries must have dates after it.

Use real date values rather than ambiguous date-looking text. The DATE function constructs dates from numeric year, month and day arguments. Keep each amount on the same row as its date, particularly when sorting.

The rate used below is an annual discount assumption in the accompanying actual-days/365 model. Apple’s short XNPV entry does not explicitly state its day-count denominator. That evidence limit is explained beside the calculation rather than silently borrowing another application’s rule.

Create a table named DatedFlows, with at least eight columns A:H and eight rows. Enter Date, Cash flow, Days from start and Discounted model in A1:D1. Enter these formulas in A2:A6 and numbers in B2:B6:

Enter the printed integer day counts into C2:C6. They are independently counted calendar gaps for this specific dataset, not a formula that updates when a date changes.

Put Discount in G1 and 8% in G2. In H2 enter =XNPV(G2,B2:B6,A2:A6). Apple’s documented expected result is approximately 1220.67. Format H2 as currency or a number with two decimals; the currency symbol follows the document’s regional settings and does not perform a currency conversion.

The initial −7000 is included in XNPV’s payment range at the starting date. Do not subtract it a second time after computing H2.

An actual-days/365 compound-discount model reproduces Apple’s published result:

cash flow / (1 + discount rate) ^ (days from first date / 365)

In D2 enter =B2/(1+$G$2)^(C2/365) and fill through D6. Expected model values, rounded to six decimals, are:

Put =D2+D3+D4+D5+D6 in H3; the full model sum is approximately 1220.672986231. Its two-decimal value matches the official 1220.67.

Model scope: This agreement supports a useful check for this example. The reference does not explicitly certify the denominator, leap-year treatment or every boundary case, and this guide does not present the model as a native-observed implementation rule. If a workbook depends on precise day-count conventions, verify those conventions in its target Numbers version.

Create a separate table named Delay, with at least six columns A:F and five rows. Put Date and Payment in A1:B1. Enter =DATE(2026,1,1) in A2 and -1000 in B2; enter =DATE(2027,1,1) in A3 and 1100 in B3.

Put Date and Payment in D1:E1. Enter =DATE(2026,1,1) in D2 and -1000 in E2; enter =DATE(2028,1,1) in D3 and 1100 in E3. These timelines span 365 and 730 actual days, respectively.

In C2 enter =XNPV(10%,B2:B3,A2:A3); in F2 enter =XNPV(10%,E2:E3,D2:D3). The same explicit model gives comparison targets of 0 and approximately -90.909090909.

Enter the arithmetic checks =-1000+1100/1.1 in C4 and =-1000+1100/1.1^2 in F4. The delay reduces present value by approximately 90.91 at this assumed annual rate, although the receipt amount is unchanged. These are independently calculated targets under the stated model, not additional Apple-published outputs.

For real projects, examine whether a delayed payment also changes costs, taxes or other flows. XNPV only processes the amounts and dates provided to it.

• Different range lengths: Apple explicitly says unequal payment/date counts produce an error. Use matching row boundaries.
• Invalid dates or nonnumeric inputs: The reference lists these as errors. DATE-generated values avoid ambiguity between month/day text conventions.
• A later entry at or before the starting date: Apple’s stated rule requires every later date to be after the first. The worked tables use increasing dates; same-day later payments and arbitrary ordering are not established here.
• Missing signs: Preserve the documented positive-and-negative requirement. Do not replace missing payment records with invented receipts or costs merely to satisfy it.

Apple does not assign precise error labels or exhaustive discount-rate bounds on this page. Diagnose the underlying input problem instead of copying another product’s error taxonomy. For an equal-period sequence see NPV; to solve for a dated return rate rather than an amount, see XIRR. For a constant annuity model, compare PV.