Investment appraisal

Accounting A2 · Cost and management accounting. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Investment appraisal tests whether a long-term project is worth its cost. Payback, NPV and IRR use cash flows, so depreciation is left out. Only ARR uses profit, which is after depreciation.

Payback is simple and favours quick returns, but it ignores cash received after the payback point. Money received later is worth less than money received now. Net present value allows for this by multiplying each year’s net cash flow by a discount factor based on the cost of capital.

The internal rate of return is the discount rate at which the NPV is zero. Managers also weigh non-financial factors, such as the effect on staff, customers and the environment.

Rules to remember

Payback period = the time taken for the net cash inflows to repay the initial cost. Part year = amount still needed ÷ net cash flow of that year × 12 months.
ARR = average annual profit ÷ average investment × 100. Average investment = (initial cost + residual value) ÷ 2.
NPV = total present value of the net cash inflows − initial cost. Present value = net cash flow × discount factor.
Accept a project if its NPV is positive; between projects, choose the higher NPV.
IRR = lower rate + [NPV at lower rate ÷ (NPV at lower rate − NPV at higher rate)] × (higher rate − lower rate). A negative NPV is subtracted, so its size is added.
Accept a project if its IRR is higher than the cost of capital.
If NPV and IRR rank projects differently, follow NPV.

Common mistake

Students use profit after depreciation in payback and NPV. Depreciation is not a cash flow, so add it back to profit to get the net cash flow; only ARR uses profit.

Worked example

A machine costs $100 000. Net cash inflows are $40 000 in year 1, $40 000 in year 2, $30 000 in year 3 and $20 000 in year 4. The cost of capital is 10% (discount factors 0.909, 0.826, 0.751, 0.683). Calculate the payback period and the NPV.

After 2 years $80 000 is repaid; $20 000 more is needed: $20 000 ÷ $30 000 × 12 = 8 months. Payback = 2 years 8 months.
Present values: $40 000 × 0.909 = $36 360; $40 000 × 0.826 = $33 040; $30 000 × 0.751 = $22 530; $20 000 × 0.683 = $13 660.
Total present value = $36 360 + $33 040 + $22 530 + $13 660 = $105 590.
NPV = $105 590 − $100 000 = $5590.

Answer: Payback is 2 years 8 months and the NPV is $5590 positive, so the project is acceptable.

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