6.3 Payback, Profitability Index & Other Methods

Payback Period

The payback period is the number of years required to recover the initial investment from a project's cash inflows. For even cash flows:

Payback period = Initial investment / Annual cash inflow

For uneven flows, accumulate inflows year by year until the investment is recovered, prorating the final partial year.

Worked Example

A $40,000 project returns $12,000 in year 1, $16,000 in year 2, and $20,000 in year 3.

• After year 1: $12,000 recovered ($28,000 remaining).
• After year 2: $28,000 recovered ($12,000 remaining).
• Year 3: $12,000 / $20,000 = 0.6 of the year.
• Payback = 2.6 years.

Limitations

• Ignores the time value of money — a dollar in year 3 is treated like a dollar in year 1.
• Ignores all cash flows after payback, so it can reject highly profitable long-lived projects.
• It is a liquidity/risk screen, useful when speed of cash recovery matters, not a measure of value.

Despite these flaws, payback survives in practice because it is simple, intuitive, and emphasizes liquidity. Firms operating in fast-changing or capital-constrained environments use a short payback cutoff as a first-pass filter — a project that takes too long to return cash is risky regardless of its NPV. Payback is often used alongside NPV, not instead of it.

Discounted Payback

Discounted payback fixes the first flaw by discounting each inflow to present value before accumulating. It tells you how long until the discounted inflows recover the investment, so it always equals or exceeds simple payback. However, it still ignores cash flows beyond the payback point, so it remains inferior to NPV as a value measure.

Worked Discounted-Payback Example

A $40,000 project returns $20,000 per year and the rate is 10%. Discounted inflows: year 1 = $20,000 × 0.9091 = $18,182; year 2 = $20,000 × 0.8264 = $16,528 (cumulative $34,710); year 3 = $20,000 × 0.7513 = $15,026. After year 2, $5,290 remains, so discounted payback = 2 + $5,290 / $15,026 ≈ 2.35 years — longer than the simple payback of 2.0 years, because discounting shrinks later inflows.

Profitability Index (PI)

The profitability index (also called the benefit-cost ratio) scales NPV to the size of the investment:

PI = PV of future cash inflows / Initial investment = 1 + (NPV / Initial investment)

Decision Rule

• PI > 1: accept (PV of inflows exceeds the cost — equivalent to NPV > 0).
• PI < 1: reject.

Worked Example

A project costs $80,000 and has PV of inflows of $92,000. PI = $92,000 / $80,000 = 1.15, and NPV = $12,000. Each dollar invested returns $1.15 of present value, creating $0.15 of value per dollar.

Capital Rationing and Ranking

Capital rationing exists when limited funds prevent a firm from accepting every positive-NPV project. The goal shifts from "accept all NPV > 0" to "choose the combination that maximizes total NPV within the budget."

The profitability index is the best ranking tool here because it measures NPV per dollar invested. Ranking by raw NPV can favor a large project that consumes the whole budget, whereas PI helps fit several smaller, high-return projects into the same capital limit. Caution: PI can mislead when projects are indivisible or when leftover funds cannot be reinvested — then test feasible combinations directly by total NPV.

A quick illustration: with a $100,000 budget, Project X (cost $100,000, PI 1.20, NPV $20,000) competes against Projects Y and Z (each cost $50,000, PI 1.30, NPV $15,000). Ranking by PI selects Y + Z for a combined NPV of $30,000, which beats X's $20,000 even though X is larger — exactly the outcome PI is designed to surface.

Accounting Rate of Return (ARR)

The accounting rate of return (also called the unadjusted or book rate of return) uses accrual figures:

ARR = Average annual accounting net income / Average (or initial) investment

Its weaknesses: it relies on accrual net income rather than cash flows and ignores the time value of money. It survives because it ties to reported ROI and is simple.

Worked ARR Example

A $100,000 asset depreciated straight-line to zero over 5 years has an average book value of ($100,000 + $0) / 2 = $50,000. If it produces average annual accounting net income of $9,000, then ARR = $9,000 / $50,000 = 18% on average investment, or $9,000 / $100,000 = 9% on initial investment. Always read whether the question wants the average or the initial investment in the denominator — the two answers differ sharply, and the choice is a common exam trap.

Comparing the Methods

NPV is the gold standard; PI ranks under rationing; payback screens liquidity and risk.