Learning Objectives

By the end of this lesson, learners should be able to:

• Explain the payback period.
• Calculate and interpret payback.
• Distinguish traditional payback from discounted payback.
• Explain the Accounting Rate of Return.
• Explain the Profitability Index.
• Identify the strengths and limitations of traditional investment appraisal techniques.
• Compare payback, ARR, PI and NPV.
• Apply these techniques appropriately in executive capital-allocation decisions.

1. Introduction

Although NPV and IRR are fundamental discounted cash-flow techniques, executives often encounter other investment appraisal methods.

The major methods include:

• Payback Period
• Discounted Payback Period
• Accounting Rate of Return (ARR)
• Profitability Index (PI)

These methods can provide useful supplementary information, but they should be understood within their limitations.

2. Payback Period

The payback period measures how long it takes for cumulative project cash flows to recover the initial investment.

For equal annual cash flows:

Payback = Initial Investment ÷ Annual Cash Flow

For unequal cash flows, cumulative cash flows must be calculated year by year.

3. Payback Example

An investment requires $600,000.

Expected cash flows:

Year	Cash Flow	Cumulative
1	$150,000	$150,000
2	$200,000	$350,000
3	$250,000	$600,000
4	$180,000	$780,000

The investment is fully recovered at the end of:

Year 3

Therefore:

Payback Period = 3 years

4. Fractional Payback

Suppose the initial investment is $700,000.

Cash flows:

• Year 1: $200,000
• Year 2: $250,000
• Year 3: $300,000

At the end of Year 2:

$450,000 has been recovered.

Remaining:

$700,000 − $450,000 = $250,000

Year 3 generates $300,000.

Therefore:

Payback = 2 + ($250,000 ÷ $300,000)

Payback ≈ 2.83 years

5. Advantages of Payback

Payback can be useful because it:

• Is simple to understand.
• Emphasizes speed of capital recovery.
• Provides a basic liquidity perspective.
• Can be useful when investment uncertainty is high.
• Helps identify projects with prolonged capital exposure.

Executives may therefore use payback as a supplementary decision measure.

6. Limitations of Traditional Payback

Traditional payback has important weaknesses.

It generally:

• Ignores the time value of money.
• Ignores cash flows after the payback point.
• Does not directly measure value creation.
• Can favour short-lived projects.
• Depends heavily on the selected payback threshold.

Consider two projects with identical payback periods.

One generates substantial cash flows immediately after payback.

The other generates almost nothing.

Traditional payback may treat them similarly despite their very different economic value.

7. Discounted Payback Period

Discounted payback improves on traditional payback by discounting project cash flows before calculating recovery.

This incorporates the time value of money.

However, discounted payback still has a major limitation:

It ignores cash flows after the discounted payback point.

Therefore, it does not replace NPV.

8. Accounting Rate of Return

The Accounting Rate of Return (ARR) measures investment performance using accounting profit rather than project cash flows.

A common formulation is:

ARR = Average Annual Accounting Profit ÷ Average Investment × 100

Different organizations and textbooks may use different conventions for the denominator, so executives must understand the methodology being applied.

9. ARR Example

Suppose:

• Initial investment = $1,000,000
• Average annual accounting profit = $180,000
• Average investment = $900,000

Then:

ARR = $180,000 ÷ $900,000 × 100

ARR = 20%

The project generates an accounting return of 20% under the specified ARR methodology.

10. Advantages of ARR

ARR can:

• Be relatively easy to calculate.
• Use familiar accounting information.
• Connect investment analysis with reported profitability.
• Assist managers who are evaluated using accounting performance measures.

However, these advantages do not eliminate its conceptual limitations.

11. Limitations of ARR

ARR can be problematic because it:

• Uses accounting profit rather than cash flow.
• Does not inherently recognize the time value of money.
• Can be affected by accounting policies.
• May use arbitrary definitions of average investment.
• Does not directly measure economic value creation.

Therefore, a project can have an attractive ARR while having a weak NPV.

12. Profitability Index

The Profitability Index (PI) measures the present value of future cash inflows relative to the initial investment.

A common formula is:

PI = Present Value of Future Cash Flows ÷ Initial Investment

For a conventional project:

PI > 1 → Generally attractive

PI = 1 → NPV approximately zero

PI < 1 → Generally unattractive

13. PI Example

A project requires an initial investment of $2 million.

Present value of expected future cash flows:

$2.6 million

Therefore:

PI = $2.6m ÷ $2.0m

PI = 1.30

The project generates approximately $1.30 of present value for every $1 of initial investment.

14. Relationship Between PI and NPV

For a conventional project:

PI > 1

corresponds to:

Positive NPV

because:

PV of Future Cash Flows > Initial Investment

Similarly:

PI < 1

corresponds to:

Negative NPV

This makes PI useful as a relative investment measure.

15. PI and Capital Rationing

Profitability Index can be particularly useful when capital is constrained.

Suppose an organization has limited investment funds.

Project	Investment	PI
A	$2m	1.50
B	$5m	1.30
C	$8m	1.15

PI helps management assess the relative value generated per unit of initial investment.

However, executives should not automatically rank projects exclusively by PI when projects are indivisible or strategically interdependent.

16. PI Limitations

PI can create problems when comparing:

• Projects of very different sizes.
• Mutually exclusive projects.
• Projects with different risk profiles.
• Projects with strategic interdependencies.

A smaller project can have a higher PI but generate less total economic value.

Therefore:

PI measures relative efficiency, not necessarily absolute value creation.

17. Comparing the Methods

Method	Time Value of Money?	Uses Cash Flow?	Value Creation?
Payback	No	Yes	Limited
Discounted Payback	Yes	Yes	Limited
ARR	No	No	Limited
PI	Yes	Yes	Relative
NPV	Yes	Yes	Strong
IRR	Yes	Yes	Indirect

This comparison demonstrates why different techniques should be interpreted differently.

18. Executive Use of Multiple Techniques

An executive investment proposal might present:

• NPV.
• IRR.
• Payback.
• Discounted payback.
• PI.
• Strategic benefits.
• Risk analysis.

This provides a more comprehensive decision picture.

For example:

NPV: Value creation

IRR: Percentage return

Payback: Speed of capital recovery

PI: Value relative to initial investment

Each metric answers a different question.

19. When Payback May Be Useful

Payback may be particularly useful where:

• Liquidity is constrained.
• Technology becomes obsolete quickly.
• Forecast uncertainty is significant.
• Management places importance on rapid capital recovery.

However, this should not be confused with evidence that the project necessarily creates greater economic value.

20. Executive Interpretation

Suppose two projects have:

Project A

• NPV = $3m
• IRR = 22%
• Payback = 2 years

Project B

• NPV = $6m
• IRR = 18%
• Payback = 4 years

If the projects are mutually exclusive, Project A’s faster payback and higher IRR do not automatically make it superior.

Project B may create significantly more economic value.

The executive must determine whether the additional value justifies:

• Longer capital recovery.
• Greater capital commitment.
• Additional risk.
• Greater resource requirements.

21. Investment Appraisal Hierarchy

A practical executive framework is:

Primary Question

Does the investment create economic value?

→ NPV

Supporting Question

What rate of return does it generate?

→ IRR

Liquidity Question

How quickly is capital recovered?

→ Payback

Accounting Performance Question

What accounting return does the investment produce?

→ ARR

Capital Efficiency Question

How much present value is generated relative to initial investment?

→ PI

This prevents executives from treating all appraisal methods as equivalent.

22. Post-Appraisal Governance

Executives should document:

• Appraisal method.
• Key assumptions.
• Forecast cash flows.
• Discount rate.
• Risk assessment.
• Approval rationale.
• Performance thresholds.

After implementation, actual results can be compared with original projections.

This helps identify:

• Forecasting errors.
• Overly optimistic assumptions.
• Unexpected costs.
• Revenue shortfalls.
• Risk events.

Lesson Summary

Payback, ARR and PI provide useful information but serve different purposes.

Payback focuses on capital recovery.

Discounted Payback adds the time value of money.

ARR focuses on accounting profitability.

PI measures present value relative to initial investment.

None should automatically replace NPV.

For major executive investment decisions, these measures are most effective when used as complementary indicators within a broader capital-allocation framework.

Key Principle

No single appraisal metric provides a complete picture of an investment; executives should understand what each measure captures, what it ignores and how it contributes to the overall capital-allocation decision.

References

1. CFA Institute — Capital Budgeting and Investment Analysis
   CFA Institute
2. Brealey, R. A., Myers, S. C., Allen, F., & Edmans, A. — Principles of Corporate Finance. McGraw Hill.
3. Ross, S. A., Westerfield, R. W., Jaffe, J., & Jordan, B. D. — Corporate Finance. McGraw Hill.
4. Damodaran, A. — Investment Valuation. Wiley.