Benefit-Cost and Payback Analysis

Benefit-Cost and Payback Analysis

$Learning Objectives$

Compute a conventional benefit-cost ratio using equivalent benefits and costs on the same time basis.
Apply the $B/C\ge1$ rule to independent public projects under stated assumptions.
Use incremental benefit-cost analysis for mutually exclusive alternatives.
Distinguish simple payback from discounted payback.
Explain why payback is a screening measure rather than a complete measure of economic value.

$Benefit-Cost Ratio$

A benefit-cost ratio compares the equivalent monetary benefits of a project with its equivalent monetary costs, evaluated at a stated discount rate and on the same time basis.

$B/C Rule by Project Relationship$

Project relationship	Comparison	Decision use
Independent project	Conventional $B/C=PW(B)/PW(C)$ under a stated convention	$B/C\ge1$ is an economic screen at the stated rate
Mutually exclusive alternatives	Order by equivalent cost; compare incremental $\Delta B/\Delta C$	Move to a higher-cost alternative when the incremental ratio meets the stated rule
Modified B/C convention	Reclassify specified O&M, disbenefits, or residual value only as defined by the governing framework	State the framework; do not mix numerator/denominator conventions

Conventional Benefit-Cost Ratio

Ratio of equivalent benefits to equivalent costs, commonly expressed using present worth.

B/C=\frac{PW(B)}{PW(C)}

Variables

Symbol	Description	Unit
$B/C$	Conventional benefit-cost ratio	-
$PW(B)$	Present worth of benefits	-
$PW(C)$	Positive magnitude of present worth of costs	-

$Independent-Project B/C Rule$

If $B/C>1$ , equivalent benefits exceed equivalent costs.
If $B/C=1$ , the project is economically break-even at the stated discount rate.
If $B/C<1$ , equivalent benefits are less than equivalent costs.

$Incremental Benefit-Cost Ratio$

Incremental B/C compares the additional equivalent benefits of a higher-cost alternative with the additional equivalent costs required to obtain those benefits.

Incremental Benefit-Cost Ratio

Economic return on the additional public-project investment when comparing mutually exclusive alternatives.

\Delta B/\Delta C=\frac{PW(B_{\text{challenger}}-B_{\text{defender}})}{PW(C_{\text{challenger}}-C_{\text{defender}})}

Variables

Symbol	Description	Unit
$\Delta B$	Incremental equivalent benefits	-
$\Delta C$	Incremental equivalent costs	-

$Do Not Rank Mutually Exclusive Alternatives by Individual B/C$

A lower-cost alternative can have a higher individual B/C while a higher-cost alternative produces greater net benefits. Order by equivalent cost and evaluate incremental benefits versus incremental costs.

$Simple Payback Period$

Simple payback is the elapsed time required for cumulative undiscounted net cash inflows to recover the initial investment.

$Discounted Payback Period$

Discounted payback is the elapsed time required for cumulative cash inflows discounted at a stated rate to recover the initial investment.

$What the Payback Measures Include$

Measure	Cash-flow treatment	Time value	What it can screen	Main limitation
Simple payback	Accumulate undiscounted net inflows	No	Liquidity/recovery time	Ignores time value and usually post-recovery flows
Discounted payback	Discount inflows at stated rate before accumulation	Yes	Recovery within a specified hurdle/horizon	Still ignores value after recovery and may not rank NPV
NPV/PW	Discount the full signed stream	Yes	Total modeled value at MARR	Depends on forecast, rate, and study assumptions

$Interactive B/C and Payback Laboratory$

Compare conventional B/C, simple payback, and discounted payback for the same project to see that they answer different questions.

Common study life7 years

Discount rate8.00%

Lower-cost alternative — defender

Initial sponsor costPHPAnnual public benefitPHP/yearAnnual sponsor O&MPHP/yearTerminal salvage / benefitPHP

Higher-cost alternative — challenger

Initial sponsor costPHPAnnual public benefitPHP/yearAnnual sponsor O&MPHP/yearTerminal salvage / benefitPHP

Defender conventional B/C

1.065

Passes the independent-project B/C ≥ 1 screen.

Challenger conventional B/C

1.085

Do not use this stand-alone ratio by itself to choose between mutually exclusive alternatives.

Incremental B/C — challenger minus defender

1.151

Extra investment is economically justified at the stated discount rate. ΔB(PW) = ₱2,140,897; ΔC(PW) = ₱1,860,319.

Alternative	Simple payback	Discounted payback
Defender	5.00 years	6.48 years
Challenger	4.89 years	6.34 years

Fractional payback values shown here linearly interpolate within the recovery year. That is appropriate only when the analyst assumes the year's recovery cash flow accrues approximately uniformly. If cash flows occur strictly at year-end, report the first whole year-end at which cumulative recovery reaches the initial investment.

This laboratory uses the conventional classification in which sponsor first cost and O&M are negative cost cash flows, while annual public benefits and terminal salvage are benefits. Modified B/C conventions can classify items differently and must be stated explicitly.

Payback remains a screening metric: simple payback ignores time value, and both payback measures disregard much of the economic value after recovery. Use PW/AW/NPV or the required public-project criterion for the final decision.

MARR10.00%

Common study life8 years

Alternative A

First costPHPAnnual net cash flowPHP/yearSalvagePHP

Alternative B

First costPHPAnnual net cash flowPHP/yearSalvagePHP

PW — Alternative A

₱1,741,625

Meets the MARR screen.

PW — Alternative B

₱1,968,658

Meets the MARR screen.

Preferred on this common basis

Alternative B

PW(B) − PW(A) = ₱227,033.

For unequal lives, do not force a common-life comparison without stating the repeatability assumption. Annual worth or a fixed study period is often clearer.

$Why Simple Payback Is Incomplete$

Simple payback ignores the time value of money and normally ignores cash flows after the recovery date. A project can have a short payback yet destroy value at the MARR, or a long payback yet have strongly positive NPV because of large later benefits.

$Modified B/C Conventions$

Some practice frameworks move recurring O&M, disbenefits, or other items between the numerator and denominator to define a modified B/C. The resulting ratio is meaningful only when its convention is stated and used consistently. Do not mix conventional and modified ratios without defining them.

$Benefit Identification Must Be Defensible$

Avoid counting transfers, double-counting related benefits, or assigning unsupported monetary values merely to raise the ratio. Define viewpoint and benefit categories before discounting.

$Public-Project B/C Workflow$

STEP-BY-STEP

Define viewpoint, alternatives, study period, and discount rate.
Classify benefits, costs, and any disbenefits consistently.
Convert all amounts to the same equivalent time basis.
Screen an independent project using B/C if required.
For mutually exclusive alternatives, order by cost and form incremental benefit and cost differences from the current defender, including an eligible do-nothing baseline.
Use incremental B/C only when the additional equivalent cost is positive. At equal cost, compare equivalent benefits under the stated convention; if ΔC is negative, correct the cost order before comparing.
When ΔC > 0, promote the challenger only if incremental B/C is at least 1; otherwise retain the defender. When ΔC = 0, retain the alternative with greater equivalent benefit. Then compare the next eligible alternative.
Report net present value or another value measure alongside ratios when possible.

$Payback Workflow$

STEP-BY-STEP

Define the initial investment magnitude.
List net cash inflows by period.
For simple payback, accumulate undiscounted inflows.
For discounted payback, discount each inflow first at the stated rate.
Interpolate within the recovery period only when the within-period flow assumption permits it.
State explicitly that payback does not replace a full PW/AW/NPV decision.

Benefit–Cost and Payback Analysis Route

Route the question to independent-project B/C, incremental B/C, or payback while preserving each measure's assumptions and limits.

B/C numerator and denominator conventions vary by framework and must be stated. The independent screen uses the stated B/C ≥ 1 rule. For mutually exclusive alternatives, cost-order options, including an eligible do-nothing/no-action baseline, and compute challenger-minus-defender ΔB and ΔC. Use incremental B/C only for ΔC > 0; at ΔC = 0 compare equivalent benefits under the stated convention; if ΔC < 0, correct the cost order. Advance or retain the defender and repeat until the candidate set is exhausted. Payback is a screen; interpolation within a period requires a supported flow assumption.

Start → Set viewpoint, study period, and discount rate; Set viewpoint, study period, and discount rate → B/C or payback question?; B/C or payback question? — B/C → Define benefits, costs, disbenefits, and convention; B/C or payback question? — Payback → Accumulate inflows; discount first if required; Define benefits, costs, disbenefits, and convention → Independent or exclusive alternatives?; Independent or exclusive alternatives? — Independent → Compute independent B/C and apply stated ≥1 screen; Independent or exclusive alternatives? — Exclusive → Cost-order options; compute challenger − defender ΔB, ΔC; Compute independent B/C and apply stated ≥1 screen → Report screen result and basis; Cost-order options; compute challenger − defender ΔB, ΔC → Incremental cost ΔC > 0?; Incremental cost ΔC > 0? — Yes → Compute ΔB/ΔC for positive additional cost; Incremental cost ΔC > 0? — No → Incremental cost ΔC = 0?; Incremental cost ΔC = 0? — Yes → Compare equivalent benefits at equal cost; Incremental cost ΔC = 0? — No → Correct order, then restart ΔB and ΔC comparison; Compute ΔB/ΔC for positive additional cost → Incremental B/C ≥ 1?; Incremental B/C ≥ 1? — Yes → Promote challenger to defender; Incremental B/C ≥ 1? — No → Retain current defender; Promote challenger to defender → Higher-cost alternative remains?; Retain current defender → Higher-cost alternative remains?; Compare equivalent benefits at equal cost → Keep higher-benefit option as defender; Keep higher-benefit option as defender → Higher-cost alternative remains?; Higher-cost alternative remains? — Yes → Cost-order options; compute challenger − defender ΔB, ΔC; Higher-cost alternative remains? — No → Report final alternative and cross-check value; Accumulate inflows; discount first if required → Report recovery or none; state screening limits

Start: terminator
Set viewpoint, study period, and discount rate: process
B/C or payback question?: decision
Define benefits, costs, disbenefits, and convention: process
Independent or exclusive alternatives?: decision
Compute independent B/C and apply stated ≥1 screen: process
Report screen result and basis: terminator
Cost-order options; compute challenger − defender ΔB, ΔC: process
Incremental cost ΔC > 0?: decision
Incremental cost ΔC = 0?: decision
Compute ΔB/ΔC for positive additional cost: process
Incremental B/C ≥ 1?: decision
Promote challenger to defender: process
Retain current defender: process
Compare equivalent benefits at equal cost: process
Keep higher-benefit option as defender: process
Correct order, then restart ΔB and ΔC comparison: terminator
Report final alternative and cross-check value: terminator
Accumulate inflows; discount first if required: process
Report recovery or none; state screening limits: terminator
Higher-cost alternative remains?: decision

Key Takeaways

B/C compares equivalent benefits with equivalent costs at a stated rate.
Independent public projects pass the conventional screen when $B/C\ge1$ .
Mutually exclusive public alternatives require incremental B/C, not ranking by stand-alone ratios.
Simple payback ignores time value; discounted payback includes discounting but still ignores much of the value after recovery.
Payback is a liquidity/risk-screening measure, not a complete value metric.
Benefit definitions and viewpoint are as important as the arithmetic.

$References$

Engineering Economy, 18th edition — William G. Sullivan, Elin M. Wicks, and Joseph H. Wilck, Pearson, 2024; chapters 5 and 10 cover project screening, payback, and benefit-cost comparisons.
Benefit-Cost Analysis Guidance, 2025 Update II — U.S. Department of Transportation, 2025; current guidance for U.S. discretionary grant applicants only, illustrating why benefit/cost categories and conventions must be stated.