The Payback Cutoff Rule

What the Payback Cutoff Rule Decides

A simple payback period measures how long it takes for a project’s cumulative cash inflows to recover its initial investment. The payback cutoff rule turns that measure into a screening decision: accept a project if its payback period is no greater than a stated maximum, and reject it if the payback period exceeds that maximum. The cutoff must be specified; payback alone does not determine whether a project passes.

This rule uses simple payback: cash flows are added without discounting. Assume the initial investment occurs at time 0 and the listed project cash flows are net inflows received after that date. When a fractional-year calculation is requested, assume the inflow for the recovery year is received evenly through that year. If the problem instead specifies that cash flows arrive only at year-end, do not assume partial-year recovery.

Definition: Let $I_0$ be the amount of the initial investment, and let $C_t$ be the project’s net cash inflow in year $t$. The simple payback period is the time required for cumulative inflows to equal the initial investment. If a maximum payback cutoff $T$ is stated, accept the project under this rule when $P \leq T$, where $P$ is its payback period; reject it when $P > T$. A project that does not recover its initial investment during the period being evaluated does not pass a finite cutoff within that period.

The comparison is inclusive at the boundary: a project with payback exactly equal to the maximum is accepted under the rule. The cutoff is a decision criterion, not a feature of the cash flows. Thus, changing the cutoff can change a project’s decision even when its investment and inflows remain exactly the same.

Finding Payback and Applying the Cutoff

First identify the year in which cumulative inflows reach or exceed the initial investment. If recovery occurs partway through year $k$, the balance still unrecovered after year $k-1$ is recovered by a fraction of year $k$. Under the even-inflow assumption, that fraction is the remaining balance divided by the inflow during year $k$.

P=(k-1)+\frac{I_0-\sum_{t=1}^{k-1} C_t}{C_k}

Here $k$ is the first year for which $\sum_{t=1}^{k} C_t \geq I_0$, and the formula assumes $C_k>0$. The numerator is the unrecovered investment at the start of year $k$; dividing by that year’s inflow gives the fraction of the year needed for recovery. If cumulative inflows equal the investment exactly at the end of a year, the fraction for that year is 1, so payback is that whole number of years. After calculating $P$, compare it with the stated cutoff $T$, using the same time units.

Build cumulative inflows.
Add the project’s inflows in order, beginning with year 1. Track the initial investment separately as the amount that must be recovered.

Locate the recovery year.
Find the first year in which cumulative inflows equal or exceed the initial investment. If there is no such year in the available cash-flow schedule, recovery is not shown within that schedule.

Calculate the recovery time.
For fractional-year payback, divide the balance unrecovered at the start of the recovery year by that year’s inflow, then add the preceding whole years.

Apply the stated rule.
Accept under the cutoff rule if payback is less than or equal to the maximum; otherwise reject. Do not round the payback before deciding if rounding could alter the comparison.

Worked Example: Classifying Projects at a 3.5-Year Cutoff

A firm screens three hypothetical projects using a maximum simple-payback period of 3.5 years. Project A requires $120,000 and has annual net inflows of $35,000, $45,000, and $50,000. Project B requires $150,000 and has inflows of $50,000, $40,000, and $60,000. Project C requires $100,000 and has inflows of $20,000, $30,000, $25,000, and $40,000. Calculate each payback period and state its decision under the cutoff rule. No interest rate is used because this is simple, undiscounted payback.

Method. For each project, add inflows until the investment is recovered. If recovery occurs during a year, divide the remaining balance by that year’s inflow. Then compare the result with 3.5 years.

Project A. After year 1, cumulative inflows are $35,000, leaving $120,000 − $35,000 = $85,000 unrecovered. After year 2, cumulative inflows are $35,000 + $45,000 = $80,000, leaving $120,000 − $80,000 = $40,000. Year 3 contributes $50,000, so the fraction of year 3 required is $40,000 ÷ $50,000 = 0.8. Payback is 2 + 0.8 = 2.8 years. Since 2.8 ≤ 3.5, accept Project A under the rule.

Project B. Cumulative inflows are $50,000 after year 1, $50,000 + $40,000 = $90,000 after year 2, and $90,000 + $60,000 = $150,000 after year 3. The investment is recovered exactly at the end of year 3, so payback is 3.0 years. Since 3.0 ≤ 3.5, accept Project B.

Project C. Cumulative inflows are $20,000 after year 1, $50,000 after year 2, and $75,000 after year 3. The balance at the start of year 4 is $100,000 − $75,000 = $25,000. The required fraction of year 4 is $25,000 ÷ $40,000 = 0.625, giving payback of 3 + 0.625 = 3.625 years. Since 3.625 > 3.5, reject Project C under the rule.

Check. By the calculated recovery point, each project’s cumulative inflows equal its initial investment: for A, $80,000 + 0.8($50,000) = $120,000; for B, the three annual inflows total $150,000; for C, $75,000 + 0.625($40,000) = $100,000. This method avoids treating the first year that reaches recovery as the payback period when recovery occurs partway through that year.

Why the Fractional-Year Calculation Works

At the start of the recovery year, the initial investment has not yet been fully recovered. Write the remaining balance as $R=I_0-\sum_{t=1}^{k-1}C_t$. If the year-$k$ inflow is received evenly, then the fraction $f$ of that year produces $fC_k$ of inflow. Recovery occurs when this amount just equals the remaining balance:

fC_k=R \qquad\Longrightarrow\qquad f=\frac{R}{C_k}

There are $k-1$ complete years before the recovery year, so total payback is $(k-1)+f$. This reasoning also shows why the denominator must be the inflow in the year recovery occurs—not the initial investment or the sum of all project inflows. The fraction measures how much of that particular year’s inflow is needed to cover the balance still outstanding.

Theorem: Under the stated simple-payback convention, a project passes a maximum cutoff $T$ exactly when its calculated payback satisfies $P \leq T$. If the decision depends on a close comparison, retain sufficient precision in $P$ until after applying the inequality.

Worked Example: Changing the Cutoff, Not the Cash Flows

A hypothetical review committee first considers a maximum payback of 2.5 years and later considers a maximum of 2.75 years. Project M requires $90,000 and returns $30,000, $40,000, and $40,000 over its first three years. Project N requires $120,000 and returns $20,000, $40,000, and $80,000. Determine both paybacks and the decisions at each cutoff. Assume the annual inflows are received evenly for any fractional-year calculation; no interest rate is applied.

Method. Calculate each project’s payback once from its unchanged cash flows. Then apply each cutoff separately; do not recalculate the cash flows when the decision standard changes.

Project M. Its cumulative inflows are $30,000 after year 1 and $30,000 + $40,000 = $70,000 after year 2. The remaining balance is $90,000 − $70,000 = $20,000. Year 3’s $40,000 inflow recovers that balance in $20,000 ÷ $40,000 = 0.5 years. Thus, $P_M=2.5$ years.

Project N. Its cumulative inflows are $20,000 after year 1 and $20,000 + $40,000 = $60,000 after year 2. The remaining balance is $120,000 − $60,000 = $60,000. Year 3’s $80,000 inflow recovers that balance in $60,000 ÷ $80,000 = 0.75 years. Thus, $P_N=2.75$ years.

At a cutoff of 2.5 years, M passes because 2.5 ≤ 2.5, while N fails because 2.75 > 2.5. At a cutoff of 2.75 years, both pass: M has 2.5 ≤ 2.75, and N has 2.75 ≤ 2.75. The projects’ cash flows and payback periods did not change; only the maximum allowed period changed.

Check. M recovers $70,000 + 0.5($40,000) = $90,000. N recovers $60,000 + 0.75($80,000) = $120,000. This comparison avoids the boundary error of rejecting a project whose payback is exactly equal to the stated maximum.

Worked Example: Testing a Close Cutoff Boundary

A hypothetical equipment project costs $240,000 and is expected to produce annual net inflows of $55,000, $65,000, $70,000, and $80,000 over its first four years. The decision rule permits a maximum payback of 3.60 years. Calculate payback and decide whether the project passes. Assume even inflow during the recovery year, with no discounting.

Method. Identify the first year that takes cumulative inflows to at least $240,000, then calculate the fraction of that year needed to recover the remaining balance.

Cumulative inflows are $55,000 after year 1, $55,000 + $65,000 = $120,000 after year 2, and $120,000 + $70,000 = $190,000 after year 3. The remaining balance at the start of year 4 is $240,000 − $190,000 = $50,000. The required fraction of year 4 is $50,000 ÷ $80,000 = 0.625. Therefore, payback is 3 + 0.625 = 3.625 years.

Because 3.625 > 3.60, reject the project under the stated cutoff rule. The difference is 0.025 year, so rounding payback to one decimal place before deciding would make the result appear to be 3.6 years and could obscure the comparison. The unrounded value should be used.

Check. Cumulative inflows at the computed recovery time are $190,000 + 0.625($80,000) = $240,000, matching the initial investment. A common mistake is to divide the $50,000 remaining balance by the total $270,000 of all four inflows. That gives a fraction unrelated to the recovery-year inflow and does not measure the portion of year 4 needed for recovery.

Common Mistakes and Decision Checks

The cutoff rule is a comparison, so both the payback calculation and the comparison must be correct. Before making a decision, check that the recovery year was identified from cumulative inflows, that any partial year uses the inflow during that recovery year, and that the cutoff and payback are expressed in the same units.

Using a single-year inflow instead of cumulative inflows. Recovery depends on inflows accumulated from the start of the project, not on whether one year’s inflow alone equals the initial investment.
Using the wrong denominator for a fraction of a year. Divide the unrecovered balance by the inflow during the recovery year. Do not divide by the initial investment or by the total inflows across all years.
Ignoring the cutoff boundary. The stated rule accepts at equality: $P=T$ passes because the condition is $P \leq T$.
Rounding too early. Preserve precision through the comparison, especially when payback is close to the cutoff.
Changing the project calculation when the cutoff changes. The cutoff changes the decision standard, not the project’s cash flows or calculated payback.

The cutoff rule is useful when a decision maker wants a clearly stated maximum time to recover an investment. Its output is a pass-or-fail result relative to that chosen standard. A cutoff should therefore be stated explicitly, and a conclusion should identify both the payback period and the comparison that supports acceptance or rejection.

Check Your Understanding

For each hypothetical project, calculate or use the simple payback period as needed, then apply the stated maximum. Assume even inflows during a recovery year when fractional-year payback is used; no interest rate is applied.

A project costs $84,000 and produces inflows of $24,000, $30,000, and $40,000. Find its fractional-year payback and decide under a 2.8-year cutoff. (Answer: Payback = 2.75 years; accept.)
A project costs $160,000 and has inflows of $40,000, $45,000, $50,000, and $55,000. Find payback and decide under a 3.5-year cutoff. (Answer: Payback = 3.4545 years; accept.)
A project costs $200,000 and has four annual inflows of $60,000 each. Find its payback and decide under a 3.25-year cutoff. (Answer: Payback = 3.3333 years; reject.)
A project costs $150,000 and returns $50,000, $50,000, and $70,000 over three years. State the decision at a 2.70-year cutoff and at a 2.75-year cutoff. (Answer: Payback = 2.7143 years; reject at 2.70 years and accept at 2.75 years.)
A project costs $180,000 and returns $30,000, $40,000, $50,000, $40,000, and $50,000 over five years. Find payback and decide under a 4.25-year cutoff. (Answer: Payback = 4.4 years; reject.)

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