What you'll learn
Investment appraisal is how a business decides whether a long-term project is worth committing money to. The decisions are large, irreversible and stretch over years, so the techniques have to deal with something the rest of accounting largely ignores: the fact that a dollar received in five years is worth less than a dollar received today.
Four methods are examined at CAPE, and they divide sharply. Payback and accounting rate of return are simple and widely used but ignore the time value of money. Net present value and internal rate of return discount future cash flows to what they are worth now, and are theoretically superior for exactly that reason.
Businesses in practice use more than one, and a good answer explains why. Payback tells a cash-constrained Caribbean business how long its money is locked up, which matters enormously to a firm with a thin overdraft, even though NPV is the better measure of whether the project creates value.
By the end of this topic you should be able to calculate all four measures, explain the strengths and weaknesses of each, and reach a recommendation that combines them rather than relying on one.
Key terms and definitions
Payback period — the time taken for cumulative net cash inflows to recover the initial investment.
Accounting rate of return (ARR) — average annual profit divided by average investment, expressed as a percentage. Also called return on capital employed for a project.
Time value of money — the principle that a sum received sooner is worth more than the same sum received later, because it could be reinvested in the meantime.
Discounting — converting a future cash flow into its present value using the required rate of return.
Discount factor — the multiplier that converts a cash flow in year n into its present value.
Net present value (NPV) — the sum of all discounted cash flows, including the initial outlay. Positive means the project adds value.
Internal rate of return (IRR) — the discount rate at which NPV is exactly nil. Accept where IRR exceeds the required return.
Cost of capital — the return the business must earn to satisfy those who funded it; the rate used for discounting.
Core concepts
Payback
Payback asks one question: how long before we get our money back? Add the net cash inflows year by year until the cumulative figure reaches the initial outlay, interpolating within the year where the recovery happens part-way through.
Its strengths are real. It is easy to calculate and explain, and it directly addresses liquidity risk, which is the risk that actually closes small businesses. A project paying back in two years exposes the firm to far less uncertainty than one paying back in seven, because forecasts four years out are largely guesswork.
Its weaknesses are equally real. It ignores everything after the payback point — a project that repays quickly and then stops is preferred to one that repays slowly and then earns for a decade. And it ignores the time value of money entirely.
Accounting rate of return
ARR is the only one of the four built on profit rather than cash flow, which makes it the odd one out. Average annual profit is divided by average investment, and average investment is normally (initial cost + residual value) ÷ 2.
Its appeal is that it speaks the same language as the financial statements, so it can be compared directly with the business's overall return on capital employed. Its weaknesses are that profit is affected by accounting policy, that it ignores the timing of returns completely, and that it can be computed several ways — always state the basis you used.
Discounting and NPV
A dollar next year is worth less than a dollar today, because today's dollar could be earning in the meantime. Discounting reverses that: a cash flow in year n is multiplied by the discount factor for year n at the business's cost of capital.
NPV sums every discounted cash flow, treating the initial outlay as a year-nil negative. A positive NPV means the project earns more than the cost of the money used to fund it, so it adds value and should be accepted. A negative NPV means it destroys value.
This is the theoretically soundest measure, because it accounts for the timing and the whole life of the project, and its answer is expressed in money rather than a percentage — $18,000 of value added is directly comparable across projects of different sizes.
Internal rate of return
IRR is the discount rate at which NPV is exactly nil — the return the project itself earns. Accept if it exceeds the cost of capital.
At CAPE level it is usually found by linear interpolation: calculate NPV at two rates, one giving a positive and one a negative, and interpolate between them. The result is an approximation, because the relationship between rate and NPV is a curve rather than a straight line.
Managers often prefer IRR because a percentage is intuitive and needs no cost of capital to interpret. Its drawbacks are that it can mislead when comparing projects of different sizes — a 40% return on $10,000 adds less value than 20% on $500,000 — and that unconventional cash flow patterns can produce more than one IRR.
Choosing between them
Where NPV and IRR disagree on ranking mutually exclusive projects, NPV is the one to follow, because it measures value added rather than a rate. Where NPV says accept and payback says the money is tied up longer than the business can bear, the constraint is real and the business may rationally decline.
That is the balanced conclusion an evaluation question is looking for: the techniques answer different questions, and a recommendation should say which question matters most for this business.
Worked examples
Example 1 — Payback period (5 marks)
A project costs $120,000 and generates net cash inflows of $40,000, $50,000, $45,000 and $30,000 over four years.
Cumulative after year 1: $40,000. Cumulative after year 2: $40,000 + $50,000 = $90,000. Still to recover at the start of year 3: $120,000 − $90,000 = $30,000. Year 3 brings in $45,000, so the fraction needed = $30,000 ÷ $45,000 = 0.67 of a year.
Payback = 2.67 years, or about 2 years and 8 months.
Note that the $30,000 arriving in year 4 played no part in the calculation at all. That is precisely the limitation of the method.
Example 2 — Accounting rate of return (5 marks)
The same project costs $120,000 with no residual value. Total cash inflows over four years are $40,000 + $50,000 + $45,000 + $30,000 = $165,000.
Depreciation over the life = $120,000, so total profit = $165,000 − $120,000 = $45,000. Average annual profit = $45,000 ÷ 4 = $11,250. Average investment = ($120,000 + $0) ÷ 2 = $60,000.
ARR = $11,250 ÷ $60,000 × 100 = 18.75%.
If the business requires 15%, the project passes on this measure. Note that profit was derived by deducting depreciation from cash flows — the step candidates most often skip.
Example 3 — Net present value (7 marks)
The same project, with a cost of capital of 10%. Discount factors at 10% are 0.909, 0.826, 0.751 and 0.683.
Year 1: $40,000 × 0.909 = $36,360. Year 2: $50,000 × 0.826 = $41,300. Year 3: $45,000 × 0.751 = $33,795. Year 4: $30,000 × 0.683 = $20,490.
Total present value of inflows = $36,360 + $41,300 + $33,795 + $20,490 = $131,945. Less the initial outlay of $120,000.
NPV = $11,945 positive.
The project earns $11,945 more, in today's money, than the cost of the funds used to finance it. On this measure it should be accepted.
Example 4 — IRR by interpolation (5 marks)
At 10% the NPV is $11,945 positive. Suppose at 20% the NPV is $6,000 negative.
The NPV falls by $11,945 + $6,000 = $17,945 across a 10 percentage point range.
IRR ≈ 10% + [$11,945 ÷ $17,945] × 10% = 10% + (0.6657 × 10) = 10% + 6.66 = 16.7%.
Since 16.7% comfortably exceeds the 10% cost of capital, the project is accepted on this measure too. State that the figure is an approximation, because interpolation draws a straight line through what is actually a curve.
Common mistakes and how to avoid them
Using profit in payback, NPV or IRR. Those three use cash flows. Only ARR uses profit.
Forgetting to deduct depreciation when finding profit for ARR. Cash inflow less depreciation gives profit.
Using initial investment instead of average investment in ARR. Average is (initial + residual) ÷ 2 — and state which basis you used.
Discounting the initial outlay. It occurs at year nil, so its discount factor is 1.
Ignoring cash flows beyond the payback point. They do not affect payback, but they do affect whether the project is worthwhile — say so.
Recommending on IRR alone when projects differ in size. A high percentage on a small outlay can add less value than a modest percentage on a large one.
Treating interpolated IRR as exact. It is an approximation of a curve.
Forgetting that all four rest on forecast cash flows. The technique cannot be more reliable than the estimates fed into it.
How this links to your Internal Assessment
Investment appraisal suits an Internal Assessment where the business is contemplating something substantial — a vehicle, a second location, new equipment. Build the cash flows from what the owner actually expects, and say clearly where each figure came from.
Apply at least two methods, because that is what lets you write the interesting part. If NPV says accept and payback says the money is committed for five years, set the two against each other and reach a judgement that reflects the firm's cash position rather than the textbook ranking.
Then test the forecast. Recalculate NPV with inflows 10% lower and say whether the decision changes. Sensitivity analysis of that kind is the single strongest addition available here, because it acknowledges that the whole calculation rests on estimates the owner supplied.
State the cost of capital you used and justify it — the rate on the loan the business would take out is usually the defensible choice for a small firm.
Exam technique for investment appraisal
Set cash flows out in a table with a row per year, and put the initial outlay in year nil. Most errors are timing errors, and a table makes them visible.
Where discount factors are given, use them rather than calculating your own, and show the multiplication for each year. Mark schemes award the working line by line, so a table of discounted figures picks up marks even if the total is added wrongly.
Label every result with its unit: years for payback, a percentage for ARR and IRR, dollars for NPV.
Command words divide the question. Calculate wants the workings. Explain why NPV is preferred to payback wants the time value of money and the whole-life coverage. Compare wants both methods applied and the difference in what they measure. Advise wants a recommendation, the measure it rests on, and the conditions attached — particularly whether the business can afford the payback period.
If asked to evaluate, never conclude that one method is simply best. Conclude which method matters most for the business in the question, and why.
Quick revision summary
- Payback = time to recover the initial outlay from cumulative net cash inflows; interpolate within the year.
- Payback ignores everything after the payback point and ignores the time value of money.
- ARR = average annual profit ÷ average investment × 100; average investment = (initial + residual) ÷ 2.
- ARR is the only method using profit rather than cash flow, so depreciation must be deducted first.
- NPV discounts every cash flow at the cost of capital; the initial outlay sits at year nil undiscounted.
- A positive NPV means the project earns more than the cost of the funds financing it — accept.
- IRR is the rate at which NPV is nil; accept where it exceeds the cost of capital.
- IRR by interpolation is an approximation, because the NPV line is a curve.
- Where NPV and IRR disagree on mutually exclusive projects, follow NPV.
- All four rest on forecast cash flows — test the forecast before trusting the answer.