Investment appraisal techniques

Investment appraisal is where financial management earns its keep. A company that commits $450,000 to a new machine is betting that the cash the machine brings back is worth more than the cash it costs, and the techniques in this lesson are how a finance manager tests that bet before the money is spent. FM builds directly on MA: you will meet payback, discounted payback, net present value (NPV) and internal rate of return (IRR) again, joined by the accounting rate of return (ARR), and you are now expected to judge the methods as well as calculate them. The FM study guide says the two 20-mark constructed-response questions in Section C will come mainly from working capital, investment appraisal and business finance, so expect a full appraisal there, and short calculations or "which statement is correct" questions on the methods in Sections A and B. This lesson works before inflation and tax; the next lesson adds both.

Relevant cash flows

Every method except ARR works on cash, and every method is only as good as the figures you feed it. A cash flow is relevant if it is future, incremental (it happens only because the project goes ahead) and cash.

Three timing conventions apply unless the question says otherwise. "Now" is time 0 (T0). A cash flow arising during a year is treated as arising at the end of that year, so year 1's cash flows sit at T1. A payment made at the start of a year is treated as made at the end of the previous year: rent paid in advance for year 1 sits at T0.

Accounting rate of return

ARR, which the study guide also calls return on capital employed (ROCE), is the one method that uses accounting profit rather than cash:

ARR = average annual accounting profit ÷ average investment × 100%

• Accounting profit is the project's net cash inflow less depreciation. Over the whole life, total profit is total net cash inflow less total depreciation, which is initial cost less scrap value.
• Average investment = (initial investment + scrap value) ÷ 2. Working capital is tied up for the whole life and recovered in full at the end, so it is added in full, not halved.
• Some questions use the initial investment instead of the average. Use whichever the question asks for, and say which you used.

Accept the project if its ARR is above the company's target return. ARR is easy to understand and matches the return on capital employed that shareholders and analysts already watch. Against that, it ignores the time value of money and the timing of cash flows; it rests on profit, which depends on accounting choices such as the depreciation method; as a percentage it says nothing about the size of the gain; and there is no single agreed definition, so two analysts can produce different ARRs for the same project.

Payback and discounted payback

Payback is the time it takes for the project's cash inflows to repay the initial investment. Add the cash flows year by year until the cumulative total turns positive; if it turns positive part-way through a year, assume that year's cash arrives evenly. Accept the project if payback is within the company's target period.

Discounted payback does the same with discounted cash flows: it is the time until the cumulative present value turns positive. With a positive discount rate it is always longer than simple payback, because later dollars are worth less.

Payback is simple, uses cash, and favours projects that return cash quickly, which reduces risk and helps a company short of liquidity. Its weaknesses are serious: it ignores every cash flow after the payback date, so it can reject a project that adds a great deal of value; simple payback ignores the time value of money; and the target period is a matter of judgement, not a measure of wealth. Discounted payback cures the second weakness but not the first. Use payback alongside NPV, as a first screen or a measure of risk, not as the decision rule.

Net present value

NPV discounts every relevant cash flow to T0 at the cost of capital and adds them up. A positive NPV means the project earns more than investors require, so it increases shareholder wealth by that amount in today's money: accept it. A negative NPV means reject. Among mutually exclusive projects, choose the one with the highest NPV.

The exam gives you a present value table and an annuity table to three decimal places. These patterns cover almost every question:

The last row works because the perpetuity formula values a stream one year before its first cash flow, so a perpetuity starting at T3 is valued at T2 and must then be discounted for two years.

Internal rate of return

The IRR is the discount rate at which the project's NPV is exactly zero: the return the project itself earns. Accept the project if its IRR is above the cost of capital. You estimate it by linear interpolation: find the NPV at two rates, ideally one giving a positive NPV and one a negative NPV, and assume the NPV moves in a straight line between them.

IRR ≈ a + [NPVa ÷ (NPVa − NPVb)] × (b − a)

Here a is the lower rate, with NPVa, and b the higher rate, with NPVb. When NPVb is negative, the denominator NPVa − NPVb is the two NPVs added together, ignoring the sign. The NPV curve is not really a straight line, so the result is an estimate, and the closer the two rates are to the IRR, the better the estimate.

Why discounted methods are better, and why NPV beats IRR

Discounted cash flow (DCF) methods, NPV and IRR, are better than ARR and payback because they use cash rather than profit, they look at the whole life of the project, and they allow for the time value of money and, through the discount rate, for risk.

Between the two DCF methods, NPV is preferred:

IRR has genuine strengths: managers find a percentage easy to grasp, and it can be calculated without knowing the exact cost of capital. For a single, conventional project (an outflow followed by inflows), NPV and IRR always give the same accept or reject decision. They can disagree only when ranking projects, and then you follow NPV.

Worked example

Bwari Polymers Co is considering a moulding machine costing $400,000, payable now. It would be sold for $40,000 at the end of its five-year life and needs working capital of $50,000 from the start, released at the end. Net cash inflows from operations are expected to be $110,000, $140,000, $160,000, $120,000 and $90,000 in years 1 to 5. A market survey costing $15,000 has already been paid for. The machine would be financed by a bank loan at 8%. Depreciation is straight line. The cost of capital is 10%, the target payback period is three years and the target ARR is 15%.

Step 1: relevant cash flows. The survey is sunk and the loan interest is a finance cost, already reflected in the discount rate, so both are left out. T0 = $400,000 + $50,000 working capital = $450,000 outflow. T5 = $90,000 + $40,000 scrap + $50,000 working capital released = $180,000.

Step 2: ARR on average investment. Depreciation = ($400,000 − $40,000) ÷ 5 = $72,000 a year. Total operating inflows are $620,000, so total profit = $620,000 − $360,000 = $260,000, an average of $52,000 a year. Average investment = ($400,000 + $40,000) ÷ 2 + $50,000 = $270,000. ARR = $52,000 ÷ $270,000 = 19.3%, above the 15% target. On initial investment it would be $52,000 ÷ $450,000 = 11.6%, below it: the definition matters.

Step 3: NPV at 10%, payback and discounted payback.

NPV at 10% = $79,530. Payback = 3 + 40,000 ÷ 120,000 = 3.33 years, about 3 years 4 months, outside the three-year target. Discounted payback = 4 + 32,250 ÷ 111,780 = 4.29 years.

Step 4: NPV at 20%.

Step 5: IRR. IRR ≈ 10% + [79,530 ÷ (79,530 + 38,370)] × (20% − 10%) = 10% + 6.75% = 16.7%. The true IRR is about 16.3%. Interpolating between 15% (NPV $14,920) and 20% gives 16.4%, closer to the truth because the rates are nearer the answer.

Step 6: the decision. NPV is positive, IRR is above the 10% cost of capital and ARR beats its target, so the machine should be bought: it adds about $79,500 to shareholder wealth. Payback fails the three-year target, which shows its weakness exactly: much of the project's value arrives in years 4 and 5, which payback barely sees. A board relying on payback alone would turn down a project that makes its shareholders richer.

Common mistakes

• Including sunk costs, depreciation, allocated overheads or interest as cash flows.
• Forgetting the working capital, or forgetting to release it at the end; or halving it in the ARR average investment.
• Using cash flows instead of profit in ARR, or profit instead of cash in every other method.
• Valuing a delayed perpetuity or annuity with the wrong factor: a perpetuity starting at T3 is discounted with the year 2 factor.
• Getting the interpolation denominator wrong when the second NPV is negative: add the two NPVs, ignoring the sign.
• Arguing that IRR is better because it is a percentage. It is easier to communicate, but NPV is the better decision rule.

Exam technique

In a Section C answer, lay the NPV out as a table with the years across the top (T0, T1, T2 and so on), one row for each relevant cash flow, then rows for net cash flow, discount factor and present value. Put anything that does not fit the table, such as the ARR or depreciation, in labelled workings below it, and finish with a one-sentence recommendation: the decision earns marks, not just the number. Use the tables' three-decimal factors, because the answers and the objective test options are built on them. When asked to discuss a method, make specific points ("it ignores cash flows after the payback date") rather than vague ones ("it is not very accurate").

Study with AI

I am studying ACCA Financial Management (FM), investment appraisal techniques. Set me
one project with an initial cost, working capital, a scrap value, uneven cash inflows
for five years, a sunk cost and an interest charge. Ask me, one at a time, for the
relevant cash flows, ARR on average investment, payback, NPV at 10%, NPV at 20% and
IRR by interpolation. Use three-decimal discount factors from the ACCA tables. Wait
for each answer, then show the correct working and explain any mistake I made.

AI assistants can make arithmetic mistakes and can misstate the rules: check every answer against these notes and the ACCA tables before you rely on it.

Lecturer's note: Each method answers a different question. ARR asks how profitable the project looks in the accounts, payback asks how quickly the money comes back, IRR asks what rate the project earns, and NPV asks how much richer the shareholders become. Only the last is the objective of financial management, which is why NPV wins every argument in FM. Use the others as supporting evidence, payback especially for liquidity and risk, but let NPV make the decision.

Key points

• Relevant cash flows are future, incremental cash flows: exclude sunk costs, depreciation, allocated overheads and finance costs; include opportunity costs and working capital.
• ARR = average annual profit ÷ average investment, where average investment is (initial cost + scrap value) ÷ 2, plus working capital in full.
• Payback and discounted payback measure the speed of return, not value, and ignore cash flows after the payback date.
• Accept a project with a positive NPV; estimate IRR by interpolating between a positive and a negative NPV.
• NPV is preferred to IRR: it measures wealth in dollars, ranks mutually exclusive projects correctly, and copes with unconventional cash flows and changing discount rates.

Quick check

1. A project costs $120,000, has no scrap value and a four-year life, and is expected to earn an average annual profit after depreciation of $12,000. What is its ARR on average investment?
2. What is the present value at 10% of $20,000 a year in perpetuity, with the first receipt at the end of year 3?
3. A project has an NPV of $12,000 at 8% and an NPV of −$4,000 at 12%. Estimate its IRR.

Answers

1. Average investment = ($120,000 + $0) ÷ 2 = $60,000. ARR = $12,000 ÷ $60,000 = 20%.
2. Value at T2 = $20,000 ÷ 0.10 = $200,000. Present value = $200,000 × 0.826 = $165,200.
3. IRR ≈ 8% + [12,000 ÷ (12,000 + 4,000)] × (12% − 8%) = 8% + 3% = 11%.