The payback period is the length of time it takes an investment’s cumulative net cash inflows to equal its initial outlay. When the same inflow arrives every year, the formula for payback period is initial investment divided by annual net cash inflow. When the inflows vary, the answer is read off a cumulative cash table instead, and only cash belongs in either version.
The Formula for Even Cash Flows
payback period = initial investment / annual net cash inflowInitial investment is the cash outlay at the start, before any inflow arrives. Annual net cash inflow is the cash the investment produces in a year, after the cash costs of running it. Both inputs are cash amounts, and neither one is a profit figure.
Payback is the length of time it takes the net cash revenue or cash cost savings of a project to pay back the initial investment, and only relevant cash flows belong in the calculation, so a noncash charge such as depreciation is excluded (ACCA, Payback and discounted payback).
That exclusion is where a profit figure and a payback figure part company. A project reported as profitable after depreciation needs that charge added back first, because straight-line depreciation spreads an outlay that already happened rather than moving cash this year. The bottom line it lands in is net income, which is not a cash measure.
The Formula for Uneven Cash Flows
The shortcut above holds only while the same inflow arrives every year and starts in the first year. Delay the first inflow, or let the amounts move, and it stops working. Build the cumulative balance and read the crossover off it.
payback period = A + (B / C)
A the last full year in which the cumulative balance is still negative
B the amount still unrecovered at the end of year A
C the net cash inflow in the year that follows year AB divided by C is the fraction of the following year needed to close the gap, and multiplying that fraction by twelve states the answer in months (ACCA, Payback and discounted payback).
One assumption decides whether the answer is a whole number. Cash treated as arriving at the end of each year makes payback the whole year in which the balance turns positive, while cash treated as arriving through the year leaves the fraction standing and the answer carries months (ACCA, Payback and discounted payback).
A Worked Example
Say a firm buys equipment on the inputs below, and the inflows rise as it comes into full use.
Initial investment (60,000)
Year Net cash inflow Cumulative
1 15,000 (45,000)
2 18,000 (27,000)
3 21,000 (6,000)
4 24,000 18,000
A = 3 last year the cumulative balance is negative
B = 6,000 unrecovered at the end of that year
C = 24,000 net cash inflow in the year that follows
payback period = 3 + (6,000 / 24,000) = 3.25 yearsOn end-of-year cash the answer is the fourth year, because nothing closes the gap until that year’s inflow lands. On cash arriving through the year it is three years and three months, so say which reading is in use before two projects are set side by side.
Discounted Payback Is a Separate Metric
Discounted payback discounts each cash flow before the cumulative balance is built, so it reports the moment the discounted inflows have covered the outlay, which is the point at which net present value turns positive (ACCA, Payback and discounted payback). It is the version that accounts for the time value of money, the principle that cash arriving later is worth less than the same cash arriving now. Plain payback does not consider it at all.
The plain version is defined by that omission. In the federal rules for life cycle cost analysis of building energy and water systems, estimated simple payback time is the number of years required for the cumulative value of energy or water cost savings less future non-fuel or non-water costs to equal the investment costs of that system, without consideration of discount rates (10 CFR 436.23).
Discounting only shrinks each inflow, so at any positive discount rate the discounted answer never lands earlier than the plain one. When one project carries two payback figures, check whether they are two metrics before treating them as a disagreement.
Where a Firm Meets the Calculation
Payback is a screen rather than a decision. It is often the first question asked about a new project, an organization may hold a target period and reject anything longer, and it puts weight on the earlier cash flows, which are both more certain and more important when liquidity is tight (ACCA, Payback and discounted payback).
That screening role is also the blind spot. Cash flows after the payback point are ignored, so the effect of the whole project on the organization’s cash flows is not considered (ACCA, Payback and discounted payback).
Inside a CPA firm the outlay may be a capital asset purchase or a system implementation, and the return often arrives as a cost saving rather than new revenue. A saving is not revenue, so it has to be stated as cash before either formula can run. That firm level calculation, applied to an outsourcing decision with the cost lines built out, is worked through in the ROI of accounting outsourcing.
What Payback Period Is Not
Return on Investment
Return on investment is a ratio of return to cost, and payback is a duration. One comes out as a percentage and the other as a number of years, so they cannot be compared or substituted for each other. A project can pay back quickly and still return little over its life, because payback stops counting at the moment the outlay is recovered.
Net Present Value
Payback produces no value figure at all. The increase or decrease in the investor’s wealth arising from a project is not considered by payback, and net present value is one measure that would be calculated to assess the effect on shareholder wealth (ACCA, Payback and discounted payback).
Common Questions
Simple payback is the undiscounted version, the one both formulas above produce, and the word simple marks what has been left out rather than how easy the sum is.
There is no universal figure, and the honest benchmark is the asset rather than the calendar. The federal rule treats it as a rough measure rather than a test: an energy or water conservation measure is likely to be cost effective if estimated payback time is significantly less than the useful life of that system, and of the Federal building in which it is to be installed (10 CFR 436.18). Payback needs a target to be judged against at all, and that target can be difficult to set and is arbitrary, which is one of the method’s known weaknesses (ACCA, Payback and discounted payback).
Accountably places trained offshore accountants and tax preparers inside US CPA and EA firms, and a trial task lets a firm grade a real block of its own work before a live engagement depends on it.
