Investment Appraisal: Evaluating a Capital Project Using NPV, IRR and Payback Period

Sample assignment — written by an AHC subject expert in Finance to a Distinction / First-class standard. All cash flows and figures below are illustrative and constructed solely for teaching purposes. This is an academic sample and does not constitute investment advice.

Introduction

Capital investment decisions are among the most consequential a firm can take. Because they commit substantial resources for several years and are frequently difficult to reverse, the quality of the appraisal process has a direct bearing on shareholder wealth (Watson and Head, 2019). Investment appraisal provides a structured means of deciding whether the future benefits of a project justify its up-front cost. This assignment applies three of the most widely used techniques — net present value (NPV), internal rate of return (IRR) and the payback period — to a single illustrative capital project. It sets out the full workings for each method, arrives at a reasoned accept or reject recommendation, and then evaluates the relative strengths, limitations and underlying assumptions of the three approaches. The central argument is that, while payback and IRR each offer useful supplementary information, NPV is theoretically the most defensible criterion because it is the technique most directly aligned with the objective of maximising shareholder wealth (Brealey, Myers and Allen, 2020).

The illustrative project

Consider Precision Components Ltd, a fictional mid-sized manufacturer evaluating the purchase of a new computer-controlled machining line. The proposal requires an immediate capital outlay of £250,000 at time zero and is expected to generate the following incremental net operating cash inflows over a five-year life, after which the equipment is assumed to have no residual value:

The company applies a discount rate of 10%, taken to represent its weighted average cost of capital (WACC) — the minimum return the project must earn to satisfy the providers of finance (Atrill and McLaney, 2019). All cash flows are assumed to arise at the end of each year, a standard simplifying convention in appraisal exercises. The figures above are illustrative and have been chosen to demonstrate the mechanics of each method rather than to reflect any real firm.

Method 1: Net present value

NPV discounts each future cash flow back to its present value using the cost of capital, then subtracts the initial outlay. A positive NPV indicates that the project is expected to add value to the firm over and above the return required by investors (Watson and Head, 2019). The discount factor for year t is 1 / (1 + r)^t, with r = 0.10.

NPV = Sum of present values − Initial outlay NPV = £304,702.86 − £250,000 = £54,702.86

The NPV is positive, so on this criterion the project should be accepted: it is expected to increase shareholder wealth by roughly £54,700 in today’s terms. A useful companion measure is the profitability index (PI), which expresses the present value of inflows relative to the outlay: PI = 304,702.86 / 250,000 = 1.22. A PI above 1.0 confirms the positive NPV and shows the project returns approximately £1.22 of present value for every £1 invested, a helpful ranking device when capital is rationed (Pike, Neale and Linsley, 2018).

Method 2: Internal rate of return

The IRR is the discount rate at which the NPV of the project equals zero — in effect, the project’s own break-even rate of return. A project is acceptable when its IRR exceeds the cost of capital (Brealey, Myers and Allen, 2020). Because the IRR cannot generally be solved algebraically for a multi-period project, it is estimated in practice either by financial software or, in an examination setting, by linear interpolation between two discount rates that bracket a zero NPV.

Discounting the cash flows at 15% and 20% gives:

• NPV at 15% = +£19,816.17
• NPV at 20% = −£9,085.65

Because the NPV changes sign between these rates, the IRR lies between them. Applying the standard interpolation formula:

IRR ≈ r₁ + [ NPV₁ / (NPV₁ − NPV₂) ] × (r₂ − r₁) IRR ≈ 0.15 + [ 19,816.17 / (19,816.17 − (−9,085.65)) ] × (0.20 − 0.15) IRR ≈ 0.15 + (19,816.17 / 28,901.82) × 0.05 IRR ≈ 0.15 + 0.0343 = 18.4% (approximately)

The precise IRR, confirmed by iterative computation, is 18.33%. The small difference between the interpolated estimate (18.4%) and the exact value illustrates a limitation of interpolation: because the NPV profile is a curve rather than a straight line, linear interpolation introduces a modest approximation error, and the error grows as the two chosen rates move further apart (Drury, 2018). At 18.33% the IRR comfortably exceeds the 10% cost of capital, so the project is again accepted. Reassuringly, the NPV and IRR rules agree — as they must for a single, conventional project with one initial outlay followed by positive inflows.

Method 3: Payback period

The payback period measures the time required for the cumulative cash inflows to recover the initial outlay. It is intuitive and widely used as a crude screen for liquidity risk (Atrill and McLaney, 2019). Accumulating the undiscounted cash flows:

The cumulative balance turns positive during year 3. At the end of year 2, £90,000 of the outlay remains unrecovered; year 3 brings in £95,000. Assuming inflows accrue evenly through the year:

Payback = 2 years + (90,000 / 95,000) = 2 + 0.947 = 2.95 years, or approximately 2 years and 11 months.

If the firm applied a decision rule requiring payback within, say, three years, the project would be accepted on this basis as well. It is instructive also to compute the discounted payback period, which uses the present values from the NPV table and therefore accounts for the time value of money. The discounted cumulative balance turns positive during year 4, giving a discounted payback of approximately 3.70 years. The discounted figure is necessarily longer than the simple payback because future inflows are worth less once discounted — a reminder that ordinary payback flatters a project by ignoring the cost of capital (Watson and Head, 2019).

Summary of results and recommendation

All three techniques point in the same direction, so the recommendation is to accept the project. The consistency across methods strengthens confidence in the decision, but it should not be mistaken for proof of robustness: the methods agree here because the project is conventional and clearly worthwhile, and they can conflict in less favourable circumstances, as discussed below.

Critical evaluation of the methods

Net present value

NPV is generally regarded as the theoretically superior criterion because it measures the absolute monetary contribution a project makes to shareholder wealth, is expressed in the currency of the firm’s objective, and correctly incorporates the time value of money across the whole life of the project (Brealey, Myers and Allen, 2020). It is additive — the NPVs of independent projects can be summed — and it uses a discount rate that reflects the risk-adjusted opportunity cost of capital. Its principal limitations are practical rather than conceptual. The technique depends heavily on the accuracy of forecast cash flows, which become increasingly uncertain the further into the future they extend, and it is sensitive to the chosen discount rate, which is itself an estimate. A small change in the WACC can materially alter the NPV, so sensitivity analysis is advisable. NPV also assumes that interim cash flows can be reinvested at the cost of capital, a more defensible assumption than the one implicit in IRR.

Internal rate of return

The IRR is popular with managers because it expresses return as a percentage, which is intuitive and permits easy comparison with the cost of capital or a hurdle rate (Pike, Neale and Linsley, 2018). However, it carries several well-documented weaknesses. First, it implicitly assumes that interim cash flows are reinvested at the IRR itself rather than at the cost of capital, which overstates the return when the IRR is high. Second, projects with unconventional cash flows — those where the sign of the net flow changes more than once — can produce multiple IRRs or none at all, rendering the measure ambiguous. Third, and most importantly for decision-making, IRR can rank mutually exclusive projects incorrectly because it measures return as a percentage and ignores scale: a project with a high IRR but a small outlay may add less absolute value than a larger project with a lower IRR. Where NPV and IRR conflict over mutually exclusive projects, NPV should prevail (Drury, 2018).

Payback period

Payback’s enduring appeal lies in its simplicity and its focus on liquidity: it tells managers how quickly their capital is at risk, which matters for cash-constrained firms and for projects in volatile or fast-changing markets (Atrill and McLaney, 2019). It is easily understood by non-financial staff and requires no assumption about a discount rate, which partly explains why surveys of practice consistently find it in widespread use alongside the discounting techniques. Yet as a standalone investment criterion it is seriously flawed. In its simple form it ignores the time value of money, weighting a pound received in year one identically to a pound received in year three. More damagingly, it disregards entirely all cash flows arising after the payback point, so a project with large but late returns may be rejected in favour of an inferior one that pays back sooner. The cut-off period against which payback is judged is also arbitrary, lacking any theoretical foundation, and different firms — or different managers within the same firm — may apply quite different thresholds. The discounted payback variant remedies the first defect but not the second. Payback is therefore best used as a supplementary screening device alongside NPV, not as a substitute for it.

Assumptions and limitations of the analysis

Several simplifying assumptions underpin the workings above and should be made explicit. Cash flows are treated as certain and as arising in discrete year-end lumps, whereas in reality they are uncertain and continuous. The discount rate is held constant at 10% throughout, though a firm’s cost of capital can change over a project’s life. Inflation, taxation, working-capital movements and any residual or scrap value have been excluded for clarity; a fuller appraisal would incorporate them, typically by discounting after-tax cash flows. The analysis also ignores real options — the managerial flexibility to expand, delay or abandon a project as circumstances unfold — which conventional NPV can undervalue (Brealey, Myers and Allen, 2020). The appraisal further assumes that the project can be evaluated in isolation, whereas in practice its cash flows may be correlated with those of the firm’s existing activities, and strategic considerations such as competitive positioning or capacity flexibility may weigh alongside the purely financial numbers. Finally, because the cash-flow forecasts are the most influential and least certain inputs, the results should be tested through sensitivity or scenario analysis before any decision is finalised; identifying the discount rate or the annual cash flow at which the NPV falls to zero gives management a clear sense of how much room for error the project can absorb.

Conclusion

Applying NPV, IRR and payback to the illustrative project produces a unanimous verdict: with an NPV of approximately £54,700, an IRR of 18.33% comfortably above the 10% cost of capital, and payback within three years, Precision Components Ltd’s proposed machining line is financially attractive on every measure. The wider lesson of the exercise, however, concerns the methods themselves. Payback offers a quick read on liquidity but ignores both the time value of money and later cash flows; IRR provides an intuitive percentage return but can mislead over scale, reinvestment and unconventional cash-flow patterns. NPV alone measures the project’s absolute contribution to shareholder wealth in a theoretically coherent way, and it should therefore serve as the primary decision criterion, with IRR and payback used to enrich rather than override its conclusion (Watson and Head, 2019).

References

Atrill, P. and McLaney, E. (2019) Accounting and Finance for Non-Specialists. 11th edn. Harlow: Pearson.

Brealey, R.A., Myers, S.C. and Allen, F. (2020) Principles of Corporate Finance. 13th edn. New York: McGraw-Hill Education.

Drury, C. (2018) Management and Cost Accounting. 10th edn. Andover: Cengage Learning.

Pike, R., Neale, B. and Linsley, P. (2018) Corporate Finance and Investment: Decisions and Strategies. 9th edn. Harlow: Pearson.

Watson, D. and Head, A. (2019) Corporate Finance: Principles and Practice. 8th edn. Harlow: Pearson.

Brealey, R.A., Myers, S.C. and Marcus, A.J. (2021) Fundamentals of Corporate Finance. 10th edn. New York: McGraw-Hill Education.

Arnold, G. and Lewis, D. (2019) Corporate Financial Management. 6th edn. Harlow: Pearson.