Investment Decisions and Recommendations using supporting data

(a) NPV −$5,000 → reject (negative). (b) IRR 16% > 11% → accept (above cost of capital). (c) Payback 3 years < 4-year target → accept. (d) ARR 12% < 15% target → reject.

All three methods support acceptance: the NPV is positive (+$22,000), so the project adds value after allowing for the time value of money; the payback of 3.2 years is within the 4-year target; and the ARR of 19% exceeds the 15% target. As all the methods agree, the business should accept the project (subject to the forecasts being reliable and any non-financial factors).

The two methods give conflicting signals: on NPV, Project B is preferable (+$40,000 vs +$28,000), but on payback, Project A is preferable (2.5 years vs 4.5 years).

This conflict arises because the methods measure different things: payback focuses on how quickly the initial outlay is recovered (liquidity and risk), favouring A's earlier cash flows, whereas NPV measures the total value added over the project's whole life, allowing for the time value of money, and favours B's larger discounted return.

NPV is generally the deciding method, because it gives the $ value added to the business and properly reflects the timing and whole life of the cash flows. On that basis, Project B should be chosen, as it adds $12,000 more value.

However, B's payback of 4.5 years is significantly longer than A's, meaning B's returns depend more heavily on later, more uncertain cash flows — so B carries greater risk. Recommendation: the business should choose Project B for its higher value added, provided it is confident in the reliability of B's later cash-flow forecasts and can afford to wait longer for repayment; if those forecasts are highly uncertain or the business needs faster cash recovery, the lower-risk Project A would be the safer choice. Non-financial factors should also be considered.

A business would usually rely on the NPV because it is the theoretically soundest measure of a project's worth. Unlike payback, NPV allows for the time value of money by discounting all the future cash flows to their present value, so it correctly reflects that earlier cash is worth more than later cash. It also uses the project's cash flows over its whole life — not just up to the point of recovery, as payback does — so it does not ignore the returns that come after the payback period. Finally, NPV produces a clear $ value of the gain, directly measuring the value added to the business, with a simple accept-if-positive (or highest-NPV) rule. Payback, by contrast, ignores the time value of money and all cash flows after the payback period, so it is a measure of risk/liquidity rather than of value. Where the two conflict, the NPV therefore gives the more complete and reliable basis for the decision — though the business should still consider payback as a risk indicator and any non-financial factors.

Investment appraisal has several limitations. First, the cash flows are forecasts/estimates of the future, which may prove inaccurate — particularly over a long project life where small errors compound; if the actual cash flows differ, a project that appeared acceptable could turn out to be unprofitable. Secondly, the NPV (and IRR comparison) depends on the chosen discount rate / cost of capital, which is itself an estimate and may change, so the NPV is sensitive to that assumption. Thirdly, the results consider only financial factors and ignore non-financial ones — such as effects on staff, customers, the environment and strategy — which can be decisive. Finally, the simpler methods have specific flaws (payback and ARR ignore the time value of money; ARR uses profit not cash; IRR can mislead with unconventional cash flows).

For these reasons, the appraisal should be used to inform the decision, not to make it automatically. A business should treat the figures as the main financial evidence but apply judgement about the reliability of the forecasts, the risk of the project, and the non-financial factors, and should be especially cautious where a project's NPV is only marginally positive.

Strictly by the NPV rule, a positive NPV means the project should be accepted. However, the NPV of +$3,000 is very small relative to the $200,000 investment — the project is marginal. Because the cash flows are based on optimistic sales forecasts, even a small shortfall in sales could easily turn the NPV negative, making the project loss-making in value terms. The business should therefore be cautious: it should re-examine and test the sales forecasts (e.g. consider a more prudent estimate or a sensitivity analysis), and only proceed if the forecasts are realistic and robust. Given the thin margin and the optimism in the forecasts, it may be safer to reject the project, or to defer it pending more reliable data, unless there are strong non-financial reasons to proceed.

Both projects have the same NPV (+$50,000) and both have an IRR above the cost of capital (P 18%, Q 14% vs 10%), so both are acceptable. Where the NPVs are equal, the IRR can be used as a tie-breaker: Project P has the higher IRR (18%), meaning it earns a higher percentage return and has a greater margin of safety above the cost of capital before its NPV would become negative. Recommendation: choose Project P, as it offers the same value added but with a higher rate of return and lower risk of falling below the required return — though the business should also consider the projects' risk profiles, sizes and any non-financial factors.

(1) I would state what each method shows, quoting the figures (NPV, payback, ARR). (2) I would apply the decision rule for each (positive NPV; payback within target; ARR above target) and identify whether they agree or conflict. (3) If they conflict, I would favour the NPV (as it measures value added using the time value of money) while noting the payback as a risk indicator, and I would acknowledge the limitations of the appraisal (forecast uncertainty, the discount rate, non-financial factors). (4) Finally, I would give a clear, justified recommendation — a definite decision supported by the strongest evidence, noting any conditions (e.g. 'provided the cash-flow forecasts are reliable').

The purpose of an investment appraisal is to support a decision, so the calculations are only the means to an end. On their own, the figures do not tell management what to do — they must be interpreted against the decision rules and weighed alongside risk, the reliability of the forecasts and non-financial factors. A clear, justified recommendation is therefore essential to complete the analysis and answer the actual question asked, and it is where a significant proportion of the marks are awarded.

The rule is to accept a project if its IRR exceeds the cost of capital (the required return), and reject it otherwise. (a) At a cost of capital of 10%, the IRR (13%) is higher, so the project earns more than the required return → accept. (b) At a cost of capital of 15%, the IRR (13%) is lower, so the project earns less than the required return → reject.