comparison of investment appraisal methods, including their limitations

10.3 Investment Appraisal – Investment Appraisal Decisions

Objective

• Compare the main investment appraisal techniques used by businesses.
• Identify the advantages, limitations and the most appropriate circumstances for each technique.
• Integrate quantitative results with qualitative (non‑financial) considerations when making a final decision.

10.3.1 Concept of Investment Appraisal

Definition (Cambridge wording): Investment appraisal is the systematic process of evaluating the profitability and risk of a capital project before any resources are committed.

Why it is needed (three purposes):

• To estimate the expected profitability of the investment.
• To identify and assess the risk associated with the project.
• To provide a basis for an informed decision – accept, modify or reject the investment.

10.3.2 Basic Methods

1. Pay‑back Period (cumulative cash‑flow method)

What it measures: The length of time required for the cumulative cash inflows to recover the initial cash outlay.

Steps:

1. List the expected cash inflow for each year.
2. Calculate the cumulative cash‑flow at the end of each year.
3. Identify the year in which the cumulative cash‑flow becomes equal to or exceeds the initial investment.

Formula (when cash inflows are level):

\[ \text{Pay‑back Period} \;=\; \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}} \]

Assumptions

• Cash inflows are known and can be added year by year.
• The time value of money is ignored.

Advantages

• Very simple to calculate and easy to understand.
• Provides a quick indication of liquidity risk – useful when cash‑flow timing is critical.

Disadvantages

• Ignores any cash flows that occur after the pay‑back date.
• Does not consider the time value of money.
• No direct link to overall profitability or value added.

2. Accounting Rate of Return (ARR)

What it measures: The return generated by an investment expressed as a percentage of the average accounting (book) investment.

Formula

\[ \text{ARR} \;=\; \frac{\text{Average Annual Accounting Profit}}{\text{Average Book Value of Investment}} \times 100\% \]

where

• Average Annual Accounting Profit = \(\frac{\sum_{t=1}^{n} \text{Profit}_t}{n}\)
• Average Book Value of Investment = \(\frac{\text{Initial Cost} + \text{Residual Value}}{2}\) (or the average of opening book values each year).

Assumptions

• Profit is based on accounting figures (including depreciation).
• Cash‑flow timing is not considered.

Advantages

• Uses information readily available from the income statement and balance sheet.
• Provides a profitability measure expressed as a percentage, which can be compared with a required accounting return.

Disadvantages

• Depends on accounting policies (e.g., depreciation method), which can distort the result.
• Ignores the timing of cash flows and the time value of money.
• Does not incorporate risk directly.

3. Discounted Cash‑Flow (DCF) method – Net Present Value (NPV)

What it measures: The difference between the present value of all expected cash inflows and the present value of all cash outflows. NPV is the core DCF technique required by the syllabus.

Formula

\[ \text{NPV} \;=\; \sum_{t=1}^{n} \frac{C_{t}}{(1+r)^{t}} \;-\; C_{0} \]

where

• \(C_{0}\) = initial investment (cash outflow at \(t = 0\))
• \(C_{t}\) = cash flow in period \(t\)
• \(r\) = required rate of return (discount rate)
• \(n\) = life of the project (years)

Assumptions

• Future cash flows can be estimated with reasonable accuracy.
• The discount rate reflects the project's cost of capital and risk.
• Cash flows are reinvested at the discount rate.

Advantages

• Fully incorporates the time value of money.
• Gives a direct measure of the additional value created for the firm (positive NPV = value added).
• Allows comparison of projects of different sizes and durations.

Disadvantages

• Requires a reliable estimate of the discount rate, which can be subjective.
• Depends heavily on the accuracy of cash‑flow forecasts.
• Mathematically more complex than the simple methods.

4. Internal Rate of Return (IRR)

What it measures: The discount rate that makes the NPV of a project equal to zero.

Formula (implicit)

\[ 0 \;=\; \sum_{t=1}^{n} \frac{C_{t}}{(1+\text{IRR})^{t}} \;-\; C_{0} \]

Assumptions

• Cash‑flow pattern is known and can be discounted repeatedly.
• Interim cash flows are reinvested at the IRR (the “re‑investment assumption”).

Advantages

• Expresses profitability as a single percentage, making it easy to compare with the required rate of return.
• Considers the time value of money.

Disadvantages

• Projects with unconventional cash‑flow patterns (multiple sign changes) can produce multiple IRRs, creating ambiguity.
• Ignores the scale of the project – a small project with a high IRR may add less total value than a larger project with a lower IRR.
• The reinvestment assumption (re‑investing at the IRR) is often unrealistic.

10.3.3 Comparison of Methods

Method	Considers Time Value of Money?	Primary Focus	Ease of Use	Key Limitation
Pay‑back Period (cumulative cash‑flow)	No	Liquidity / short‑term risk	Very easy	Ignores cash flows after pay‑back and ignores TVM
Accounting Rate of Return (ARR)	No	Accounting profitability	Easy	Based on accounting profit; ignores cash‑flow timing and TVM
Net Present Value (NPV) – DCF method	Yes	Value added to the firm	Moderate (requires discounting)	Requires reliable discount rate & cash‑flow forecasts
Internal Rate of Return (IRR)	Yes	Rate of return (percentage)	Moderate (iterative calculation)	Multiple IRRs possible; assumes reinvestment at IRR; ignores project scale

10.3.4 Limitations of Investment Appraisal Methods (Summary)

1. Data accuracy: All techniques rely on projected cash flows, which are inherently uncertain.
2. Discount rate selection: An inappropriate discount rate can distort NPV and IRR results.
3. Non‑financial factors: Strategic fit, legal/ethical issues, environmental impact, and stakeholder concerns are not reflected in the quantitative analysis.
4. Scale sensitivity: Percentage‑based methods (ARR, IRR) may favour smaller projects.
5. Re‑investment assumptions: IRR assumes reinvestment at the IRR; NPV assumes reinvestment at the discount rate.
6. Complexity vs. simplicity: Simpler methods (pay‑back, ARR) are easy to apply but give limited insight; more sophisticated methods (NPV, IRR) are more reliable but require greater expertise.

10.3.5 Decision‑Making Process (including qualitative factors)

1. Initial liquidity screening: Calculate the Pay‑back Period. Reject projects that exceed the organisation’s maximum acceptable pay‑back.
2. Profitability assessment: Compute NPV and IRR for the remaining projects. Accept projects with NPV > 0 and IRR ≥ required rate of return.
3. Accounting return check: Compare ARR with the company’s required accounting return (if a benchmark exists).
4. Qualitative (non‑financial) review:
   • Strategic alignment – does the project support long‑term business objectives?
   • Legal and regulatory compliance.
   • Environmental and social impact.
   • Stakeholder pressure – customers, suppliers, community, shareholders.
   • Technological compatibility and operational risk.
5. Final decision: Choose the project that offers the best combination of quantitative value (positive NPV, acceptable IRR, reasonable pay‑back, satisfactory ARR) and qualitative fit.

10.3.6 Illustrative Example (All four methods)

Project data:

• Initial outlay: £120,000
• Expected cash inflows: £40,000 per year for 4 years
• Required rate of return (discount rate): 10 %
• Depreciation (straight‑line, zero residual value): £30,000 per year

Pay‑back Period (cumulative cash‑flow)

Year	Cash Inflow	Cumulative Cash‑flow
1	£40,000	£40,000
2	£40,000	£80,000
3	£40,000	£120,000

Pay‑back = 3 years. If the company’s maximum acceptable pay‑back is 4 years, the project passes the liquidity filter.

Accounting Rate of Return (ARR)

Average annual accounting profit = Cash inflow – Depreciation = £40,000 – £30,000 = £10,000

Average book value of investment = (Initial cost + Residual value) / 2 = (£120,000 + £0) / 2 = £60,000

\[ \text{ARR} = \frac{10,000}{60,000}\times100\% = 16.7\% \]

If the required accounting return is 12 %, the project meets the ARR criterion.

Net Present Value (NPV)

\[ \begin{aligned} \text{NPV} &= \frac{40{,}000}{(1+0.10)^{1}} + \frac{40{,}000}{(1+0.10)^{2}} + \frac{40{,}000}{(1+0.10)^{3}} + \frac{40{,}000}{(1+0.10)^{4}} - 120{,}000\\ &= 36{,}364 + 33{,}058 + 30{,}053 + 27{,}321 - 120{,}000\\ &= £6{,}796 \; (>0) \end{aligned} \]

Positive NPV indicates the project adds value.

Internal Rate of Return (IRR)

Solving

\[ 0 = \frac{40{,}000}{(1+\text{IRR})^{1}} + \frac{40{,}000}{(1+\text{IRR})^{2}} + \frac{40{,}000}{(1+\text{IRR})^{3}} + \frac{40{,}000}{(1+\text{IRR})^{4}} - 120{,}000 \]

by trial‑and‑error (or a financial calculator) gives \(\text{IRR} \approx 13.5\%\).

Since IRR > required rate of return (10 %), the project is acceptable on an IRR basis.

Overall appraisal

• Pay‑back: 3 years ≤ maximum 4 years → passes liquidity test.
• ARR: 16.7 % > required 12 % → passes accounting‑return test.
• NPV: £6,796 > 0 → creates value.
• IRR: 13.5 % > 10 % → meets required return.
• Qualitative check: aligns with the firm’s growth strategy, no legal barriers, moderate environmental impact – acceptable.

Result: The project would be recommended for acceptance.