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3.8

Investment appraisal

Unit 3 · Finance and accounts · SL and HL

Should a business buy the machine, open the new outlet, or launch the product? Investment appraisal uses forecast cash flows to compare projects. SL and HL both calculate the payback period and the average rate of return (ARR); HL adds net present value (NPV), which accounts for the time value of money. Expect a calculation plus an evaluation that brings in qualitative factors.

🎯What you need to be able to do

  • Calculate and evaluate investment opportunities using the payback period and the average rate of return.
  • HL Calculate and evaluate investment opportunities using net present value (NPV), with discount factors provided.

📚The business management

Payback period

The payback period is the time it takes for the net cash inflows from an investment to repay its initial cost. Work out the cumulative net cash flow year by year; payback is when it reaches zero. If it happens part-way through a year:

\[ \text{months} = \frac{\text{amount still to be recovered}}{\text{net cash flow in that year}} \times 12 \]
Strengths
simple and quick; focuses on liquidity and risk (a short payback returns cash sooner and is less exposed to uncertain far-future forecasts); useful in fast-changing industries.
Limitations
ignores cash flows after payback (so ignores total profitability); ignores the time value of money; assumes cash flows are spread evenly within the year.

Average rate of return (ARR)

\[ \text{ARR} = \frac{(\text{total returns} - \text{capital cost}) \div \text{years of use}}{\text{capital cost}} \times 100 \]

The average annual profit as a percentage of the initial cost. Compare it with the interest rate (the opportunity cost of the money) and with other projects.

Strengths
uses all the cash flows; gives a percentage easy to compare with interest rates and targets.
Limitations
ignores the timing of cash flows (a return in year 5 counts the same as in year 1); ignores the time value of money; relies on long-term forecasts.

Net present value HL

Money received in the future is worth less than money today, because today’s money could be invested to earn interest (and because of inflation and risk). Discounting converts future cash flows into their present value by multiplying by a discount factor (provided in the exam) for the chosen interest rate and year.

\[ \text{NPV} = \text{sum of present values of future net cash flows} - \text{initial cost} \]

A positive NPV means the investment earns more than the discount rate: worth doing on financial grounds. A negative NPV means it would be better to invest the money at the discount rate.

Strengths
accounts for the time value of money; uses all cash flows; a clear decision rule.
Limitations
more complex; choosing the discount rate is subjective and changes the answer; still depends on uncertain forecasts.

Qualitative factors

Numbers are not the whole decision. Consider: how reliable the forecasts are; the business’s objectives (growth, CSR); risk and the economy; the impact on staff, customers and the environment; the source and cost of finance; competitors’ actions; and whether the project fits the strategy.

✏️Worked example

Ombak Boards is considering a new shaping machine costing $400 000, expected to generate net cash flows of $100 000, $120 000, $140 000, $140 000 and $100 000 over five years. (a) Calculate the payback period. (b) Calculate the ARR. (c) HL Using discount factors at 8% of 0.9259, 0.8573, 0.7938, 0.7350 and 0.6806, calculate the NPV. (d) Recommend whether to invest.

(a) Cumulative ($000): −400, −300, −180, −40, +100, +200. Payback falls in year 4: 40 ÷ 140 × 12 = 3.4 months, so about 3 years 4 months.

Cumulative net cash flow rising from minus 400 thousand dollars at year 0 to minus 300, minus 180, minus 40, plus 100 and plus 200 in years 1 to 5, crossing zero at about 3 years 4 months, the payback period.
Payback is where the cumulative cash flow crosses zero.

(b) Total returns = 600; profit = 600 − 400 = 200; per year = 200 ÷ 5 = 40.

\[ \text{ARR} = \frac{40}{400} \times 100 = 10\% \]

(c) Present values ($000): 100 × 0.9259 = 92.59; 120 × 0.8573 = 102.88; 140 × 0.7938 = 111.13; 140 × 0.7350 = 102.90; 100 × 0.6806 = 68.06. Total = 477.56.

\[ \text{NPV} = 477.56 - 400 = +77.56 \text{ thousand} = \$77\,560 \]

(d) The NPV is positive, the ARR (10%) exceeds an 8% cost of capital, and payback in under 3.5 years is reasonable for a machine lasting 5. Financially, Ombak should invest, provided the sales forecasts behind the cash flows are realistic (surf tourism can be volatile) and it can finance $400 000 without straining its cash flow; its low gearing (27.5%) suggests a loan is possible.

Check it. The sum of undiscounted flows (600) must exceed the sum of discounted flows (477.56); discounting always shrinks future values.
Forgetting to subtract the capital cost in ARR and NPV, or calculating payback months from the whole-year cash flow of the wrong year.

📝Practise

Work through these on paper, then reveal the answer.

1. [2 marks] A project costs $50 000 and returns $15 000 a year. Calculate the payback period.
After 3 years: $45 000 recovered; $5000 remains. 5000 ÷ 15 000 × 12 = 4 months. Payback = 3 years 4 months.
2. [2 marks] A $200 000 machine returns $260 000 in total over 4 years. Calculate the ARR.
Profit = 60 000; per year = 15 000. ARR = 15 000 ÷ 200 000 × 100 = 7.5%.
3. HL [3 marks] A project costs $100 000 and returns $60 000 in each of 2 years. Discount factors at 10%: 0.9091 and 0.8264. Calculate the NPV.
PV = 60 000 × (0.9091 + 0.8264) = 60 000 × 1.7355 = $104 130. NPV = 104 130 − 100 000 = +$4130.
4. [4 marks] Explain why a business might prefer a project with a shorter payback even if its ARR is lower.
A short payback returns the cash sooner, which matters if the business has limited cash or high borrowing, and reduces risk because near-term forecasts are more reliable than distant ones. In a fast-changing market (technology, fashion), later returns may never arrive if the product becomes obsolete.
5. HL [4 marks] Explain how a rise in interest rates could change an NPV decision.
A higher interest rate means a higher discount rate, so discount factors are smaller and the present value of future cash flows falls. A project with a small positive NPV at a low rate may have a negative NPV at a higher rate, so it would no longer be worthwhile: the money earns more elsewhere, or borrowing costs more.
6. [10 marks] A hotel is choosing between solar panels (cost $150 000, ARR 12%, payback 6 years) and refurbishing rooms (cost $150 000, ARR 9%, payback 3 years). Discuss which investment it should choose.

Solar: higher ARR, long-term energy savings, CSR and brand benefits with eco-conscious guests; but long payback, reliant on energy-price forecasts, technology risk.

Refurbishment: faster payback helps liquidity, directly raises room rates and occupancy; but lower overall return and rooms will need refurbishing again.

Judgment: depends on the hotel’s cash position and gearing, its objectives (sustainability positioning vs short-term recovery), reliability of forecasts, and financing options (green loans for solar). A hotel with weak cash flow might refurbish first; one targeting eco-tourists might choose solar.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • Khan Academy — Present value and the time value of money.
  • Investopedia — payback period, ARR and NPV with examples.
  • Tutor2u — investment appraisal revision notes and practice.