8.5Lesson 8.5 · Module 8 — Capital Budgeting

Useful Shortcuts, Wrong Decisions

IRR, payback, profitability index, EPS accretion, and ROIC each answer a narrower question than NPV. Learn what each reveals, what it omits, and when it can lead to the wrong decision.

The highest return is not the best investment
Payback and discounted payback — and what they miss
IRR: when it agrees with NPV and when it does not
Multiple IRRs, scale conflicts, and timing problems
Profitability index, EPS accretion, and ROIC as diagnostic tools
One investment evaluated through all six metrics

Start

Central question

If NPV measures value creation, what information do IRR, payback, profitability index, EPS accretion, and ROIC provide — and when can those measures lead to the wrong decision?

8.5.1Section 1 · The highest return is not the best investment

A return percentage does not measure total value

Two mutually exclusive projects: one has 30% return on $1M, the other has 20% return on $100M. Which looks better?

8.5.2Section 2 · Why companies use shortcuts

Alternative metrics are popular because they summarize real concerns

The problem is not that these measures contain no information. The problem is treating one narrow measure as if it answers the entire investment decision.

“20% IRR” is easy to summarize. “Five-year payback” is intuitive. EPS accretion is familiar to public-company analysts. These metrics travel well in meetings and press releases.

The problem is not that these measures contain no information. The problem is treating one narrow measure as if it answers the entire investment decision.

8.5.3Section 3 · Payback period

How quickly is capital recovered?

The payback period is the time required for cumulative cash inflows to recover the initial investment.

Initial investment$100

Year 1

$30

Year 2

$40

Year 3

$35

Year 4

Year 5

Cumulative cash recovery

Year 0

−$100

Year 1

$30

Year 2

$70

Year 3

$105

Year 4

$105

Year 5

$105

Target

Initial investment recovered: $100

Payback period

2.9 years

Recovered during Year 3

The project recovers its initial $100 investment during Year 3. This measures speed of capital recovery — not value created. Cash flows after recovery are not considered.

8.5.4Section 4 · What payback reveals

Legitimate uses of a narrow measure

Payback answers a specific question: how long is the company's capital exposed before the forecast cash inflows recover the initial commitment?

Payback reveals

Liquidity exposure
Speed of capital recovery
Dependence on distant forecasts
Risk of obsolescence before recovery
Flexibility to reinvest recovered cash

Payback does not reveal

How much value the project creates
Cash flows after the recovery date
The time value of money (without discounting)
Risk-adjusted return
Total economic benefit

8.5.5Section 5 · Payback problem 1: ignoring time value

Basic vs. discounted payback

Two projects recover $100 by Year 2. But one receives cash sooner. Basic payback treats them as equivalent; discounted payback corrects the timing.

Discount rate10%

Project A · early cash

Yr 1

$90

Yr 2

$10

Yr 3

Yr 4

Basic payback2.0 yrs

Discounted payback (10%)—

NPV (10%)−$9.9

Project B · late cash

Yr 1

$10

Yr 2

$90

Yr 3

Yr 4

Basic payback2.0 yrs

Discounted payback (10%)—

NPV (10%)−$16.5

What discounting reveals

Basic payback treats both projects as equivalent — each recovers $100 by the end of Year 2. But Project A receives most of its cash sooner. Once cash flows are discounted, Project A recovers its investment faster and has a higher NPV. Early cash flows receive greater weight because of the time value of money.

Discounted payback corrects the timing problem, but does not solve every payback limitation.

8.5.6Section 6 · Payback problem 2: ignoring post-payback cash flows

The blind spot after recovery

Projects with identical payback can create very different value. Payback can ignore both valuable later inflows and costly later obligations.

Same payback as A, but continues producing substantial cash in Years 3–4.

Payback period: 2.0 years (all three projects share this).

Year 0

−$100

Year 1

+$50

Year 2

+$50

Year 3

???

hidden

Year 4

???

hidden

Payback can ignore both valuable later inflows and costly later obligations. A project that looks identical by payback period can create very different amounts of value.

8.5.7Section 7 · IRR: definition and interpretation

The break-even discount rate

IRR is the discount rate that makes a project's NPV equal to zero. It is an internal property of the cash flows.

IRR definition

0 = - C F_{0} + \frac{C F _{1}}{1 + I R R} + \frac{C F _{2}}{( 1 + I R R ) ^{2}} + \dots + \frac{C F _{T}}{( 1 + I R R ) ^{T}}

IRR is the discount rate at which the present value of expected future cash flows exactly equals the initial investment.

IRR is determined entirely by the project's own cash-flow pattern. The required return (opportunity cost of capital) is a separate, externally determined benchmark.

Initial investment$100

Expected payoff (1 yr)$115

Required return10%

IRR definition

0 = - C F_{0} + \frac{C F _{1}}{1 + I R R} + \frac{C F _{2}}{( 1 + I R R ) ^{2}} + \dots + \frac{C F _{T}}{( 1 + I R R ) ^{T}}

IRR is the discount rate that makes the project's NPV equal to zero.

$100.00 = \frac{$115.00}{1 + I R R}

I R R = \frac{$115.00}{$100.00} - 1 = 15.00%

IRR

15.00%

Required return

10.00%

NPV at required return

+$4.55

At a 15.00% discount rate, the present value of the expected payoff exactly equals the initial investment. Since IRR exceeds the 10.00% required return, NPV is positive. IRR is an internal property of the cash flows. The required return is an external benchmark set by the opportunity cost of capital.

I R R > r ⟺ N P V > 0

8.5.8Section 8 · When IRR and NPV agree

IRR is not inherently wrong

For conventional independent projects, IRR and NPV usually point in the same direction.

Conditions for agreement

One initial cash outflow
Positive later inflows only
One independent project
One economically meaningful IRR
Required return is appropriate for the project
Decision rule: accept if IRR exceeds the required return

Note

IRR becomes unreliable as a universal ranking rule when projects differ in scale, timing, sign pattern, or financing structure. For a simple conventional independent project, IRR and NPV agree: IRR above the required return is equivalent to positive NPV.

8.5.9Section 9 · IRR problem 1: scale

Return per dollar vs. total dollars created

IRR tells us return per dollar. NPV tells us total dollars of value created.

Project A scale (IRR 30%)$1M

Project B scale (IRR 20%)$100M

Metric	Project A	Project B
Investment	$1.00M	$100.00M
IRR	30%	20%
NPV	$0.18M	$9.09M
Ranking winner	Higher IRR	Higher NPV

IRR says

Project A has a higher return per dollar invested. But it does NOT create the most total value.

NPV says

Project B creates $9.09M of value versus $0.18M. If the projects are mutually exclusive, select Project B.

IRR tells us return per dollar. NPV tells us total dollars of value created. If projects are independent and capital is available, both may be acceptable. If mutually exclusive, choose the highest positive NPV.

8.5.10Section 10 · IRR problem 2: cash-flow timing

The NPV profile and the crossover rate

Two equal-cost projects can rank differently depending on the discount rate. Higher discount rates favor earlier cash flows.

Required return (discount rate)10%

NPV_A at current rate

$6.6

NPV_B at current rate

$12.4

IRR_A

15.9%

IRR_B

16.9%

At a 10% discount rate, Project B has the higher NPV. At low discount rates, Project B benefits more because its larger later cash flows are discounted less heavily. As the rate rises, earlier cash flows are favored. The crossover occurs at approximately 18.8%. IRR alone cannot identify which project is better — the answer depends on the required return.

8.5.11Section 11 · IRR problem 3: multiple or nonexistent IRRs

When 'one project, one return' breaks down

Nonconventional cash flows — where signs change more than once — can produce multiple IRRs or no economically meaningful IRR at all.

Nonconventional cash flows

Yr 0

-100

Yr 1

+230

Yr 2

-132

Signs change twice: outflow, inflow, outflow. The NPV curve can cross zero more than once.

IRRs found: 10.0% and 20.0%

Conventional cash flows

Yr 0

-100

Yr 1

+50

Yr 2

+80

One outflow, then positive inflows. The NPV curve crosses zero exactly once.

IRR: 17.9%

NPV profile: NPV vs. discount rate

The nonconventional project's NPV curve crosses zero twice. Two IRRs exist (10.0% and 20.0%). The rule “accept if IRR > required return” breaks down — which IRR should be used? The conventional project has exactly one IRR (17.9%) and the standard rule applies cleanly.

8.5.12Section 12 · IRR problem 4: investment vs. financing

'Higher IRR is better' is not a universal rule

The interpretation of IRR depends on the direction of the cash flows.

Investment pattern

Cash outflow today, inflows later. Higher IRR is generally preferred.

Financing pattern

Cash inflow today, outflows later. A lower rate is generally preferred — the borrower wants to pay less.

A company pays $100 today to build a factory, then receives positive operating cash flows for ten years.

Cash flows: −100, +20, +20, +20, …

A bank lends $100 today and receives $110 in one year.

Cash flows: −100, +110

A company borrows $100 today and repays $108 in one year.

Cash flows: +100, −108

A mining project requires an initial investment, generates positive cash flows during production, then requires a large environmental remediation payment at shutdown.

Cash flows: −100, +40, +40, +40, −50

A company enters a derivative contract that produces complex cash flows depending on future interest-rate movements.

Cash flows: Unknown pattern

“Higher IRR is better” is not a universal rule. The interpretation depends on the direction of the cash flows.

8.5.13Section 13 · Profitability index

Value per dollar invested

PI measures capital efficiency: how much present value is produced per dollar committed.

Profitability index

P I = \frac{PV of future cash inflows}{Initial investment}

Each dollar invested produces this much present value. PI above 1 generally corresponds to positive NPV for a conventional independent project.

PI is useful when considering how much present value is created per dollar committed — especially under capital constraints.

PV of future cash inflows$120

Initial investment$100

Profitability index

P I = \frac{PV of inflows}{Initial investment} = \frac{$120.00}{$100.00} = 1.20

N P V = $120.00 - $100.00 = $20.00

Profitability index

1.20

Value per $1 invested

$1.20

NPV

+$20.00

Each $1 invested produces $1.20 of present value. PI > 1 generally corresponds to positive NPV for a conventional independent project. PI measures capital efficiency: how much present value is created per dollar committed.

8.5.14Section 14 · Profitability index and scale

Efficient per dollar is not the same as most value

PI measures efficiency but can misrank mutually exclusive projects of different scale.

Project A

Investment$1

PV of inflows$2

PI2.0

NPV$1M

Project B

Investment$100M

PV of inflows$130M

PI1.30

NPV$30M

Which project is more capital-efficient (higher PI)?

Which project creates more total value (higher NPV)?

If mutually exclusive, which should be selected?

Project A is more efficient per dollar. Project B creates far more total value. If projects are mutually exclusive, select based primarily on NPV. If capital is constrained, PI may provide useful evidence — but the company must still identify the combination of projects that maximizes total NPV.

8.5.15Section 15 · EPS accretion

Accounting result, not economic proof

An acquisition is EPS accretive when post-transaction EPS exceeds pre-transaction EPS. But EPS accretion does not prove value creation.

Definition · EPS accretion

An acquisition is EPS accretive when expected post-transaction earnings per share exceed the buyer's pre-transaction EPS. This is an accounting result. It can arise from debt financing, multiple differences, share-issuance effects, or near-term earnings — none of which determine whether the purchase price was economically attractive.

Simplified instructional acquisition model

Buyer EPS$5

Buyer shares (M)100

Target earnings$30M

Synergy earnings$10M

Integration cost$5M

Purchase price$400M

Financing method

Buyer share price$50

Pre-deal EPS

$5.00

Post-deal EPS

$4.95

EPS change

-0.93%

Est. acquisition NPV

$-5.00M

EPS accretion vs. economic value

Both EPS and NPV are negative. The deal is dilutive and value-destroying.

N P V = V_{target} + V_{synergies} - integration - price

EPS accretion answers an accounting question. NPV answers an economic value question. They can disagree.

8.5.16Section 16 · ROIC

Realized capital efficiency, not forward-looking NPV

ROIC measures operating return relative to invested capital. It is useful for evaluating realized performance — but it is not identical to a project's forward-looking NPV.

ROIC (simplified)

R O I C = \frac{After-tax operating profit}{Invested capital}

ROIC compares the operating profit a company generates with the capital committed to its operations.

ROIC above the cost of capital is generally consistent with value creation; ROIC below suggests inadequate returns. But ROIC is an accounting snapshot that does not capture full cash-flow timing or provide a dollar value estimate.

After-tax operating profit$15M

Invested capital$100M

Cost of capital10%

ROIC calculation

R O I C = \frac{$15.0 M}{$100.0 M} = 15.0%

ROIC

15.0%

Cost of capital

10.0%

Spread

+5.0%

ROIC exceeds the cost of capital by 5.0 percentage points. This is consistent with value creation — the company is earning more on its invested capital than that capital costs.

Important limitations

Accounting measurement: book values may differ from economic values.
One-year ROIC may not reflect full-life project economics.
Early ramp-up can depress ROIC temporarily even for value-creating projects.
Aggregate ROIC mixes old and new investments — strong old projects can conceal weak new ones.
ROIC does not show full cash-flow timing or a dollar value estimate.

NPV is primarily a forward-looking decision framework. ROIC is primarily an operating-performance measure.

8.5.17Section 17 · One investment, six metrics

The practical center of the lesson

Evaluate one restaurant expansion program through all six metric lenses. Each answers a different question.

Restaurant expansion program

Initial capital

$100M

PV of cash flows

$115M

Required return

10%

NPVSupports thesis

Question answered

How many dollars of economic value are expected to be created?

What it reveals

Total estimated value creation after accounting for cash flow, timing, risk, and scale.

What it omits

Nothing fundamental — NPV is the primary economic measure. It does depend on uncertain estimates.

8.5.18Section 18 · How to use the metrics together

Anchor in NPV, diagnose with the rest

Step 1: anchor the decision in NPV. Step 2: use supplementary metrics diagnostically. Step 3: investigate contradictions.

The discipline

Contradictions between metrics should trigger investigation rather than mechanical metric selection. Do not simply pick the favorable number — ask what the conflict reveals.

Positive NPV, but an eight-year payback period.

High IRR (35%), but low NPV ($0.5M on a $1M investment).

EPS accretive, but negative estimated NPV.

Strong current ROIC (18%), but weak NPV on a new project ($2M).

Low first-year ROIC (4%), but positive NPV ($10M).

8.5.19Section 19 · Management incentives and selective metrics

Why was this metric selected?

Management may emphasize the measure that presents a decision most favorably. The investor should ask what it leaves out.

Management may emphasize the measure that presents a decision most favorably. The investor should ask why this metric was selected and what it leaves out. This is analytical discipline, not an assumption of deception.

"This acquisition has a compelling 25% IRR."