Investment appraisal techniques – Financial Management (Senior 4 Entrepreneurship) | Ganzaa

Financial Management

Lessons

Senior 4 · Entrepreneurship

Financial Management

5 lessons

Lesson 5 of 5

Investment appraisal techniques

25 min

Case: two ways to spend Frw 20 million on pineapples

A cooperative of pineapple growers in Ngoma District sells most of its fruit fresh, and in the peak season much of it spoils before it reaches buyers. The board has Frw 20 million to invest and two proposals. Project A is a small juice-pasteurising and bottling line, slow to win supermarket buyers but expected to earn more each year. Project B is a set of solar driers for dried pineapple, which earns quickly but whose market is expected to fill with competitors. Each would last five years. (The cooperative and its figures are illustrative.)

Net cash inflow (million Frw)	Year 1	Year 2	Year 3	Year 4	Year 5	Total
Project A: bottling line	4	6	7	8	8	33
Project B: solar driers	9	8	5	2	1	25

Think about it: B gets its money back faster; A brings in more in total. Which would you choose, and what else would you want to know?

Why appraise an investment?

An investment ties up a large sum for years, and it is hard to reverse: a bottling line cannot easily be sold for what it cost. Investment appraisal uses forecasts of cash flows to judge, before the money is spent, whether a project is worth it and which of several projects is best. Four techniques are used. The first two ignore the time value of money; the last two discount future cash to its value today.

Definition

Investment appraisal (capital budgeting): evaluating the expected costs and returns of a long-term project to decide whether to undertake it. Net cash inflow: cash received from a project minus the cash it costs to run, in a period.

Payback period: the time a project takes for its net cash inflows to repay the initial investment.

Accounting rate of return (ARR): the average annual accounting profit of a project as a percentage of the average (or initial) investment.

Definition

Discounting: converting a future amount to its present value (PV), its worth today, at a chosen rate called the discount rate or cost of capital:

PV = \frac{C_t}{(1 + r)^t}

Net present value (NPV): the sum of the present values of all future net cash inflows minus the initial investment. Internal rate of return (IRR): the discount rate at which the NPV is exactly zero.

The four techniques

Technique	Formula or rule	Accept if	Strength	Weakness
Payback period	Count the years until cumulative cash flow reaches zero	Shorter than the firm's target	Simple; shows liquidity and risk	Ignores cash after payback and the time value of money
ARR	$\frac{\text{average annual profit}}{\text{average investment}} \times 100\%$	Above the target rate	Uses the whole life; a familiar percentage	Uses profit, not cash; ignores timing
NPV	$\sum \frac{C_t}{(1 + r)^t} - C_0$	NPV $> 0$	Allows for time value and all cash flows; shows the gain in Frw	Depends on the discount rate chosen; harder to explain
IRR	The $r$ that makes NPV $= 0$	IRR $>$ cost of capital	A single rate, easy to compare with the cost of borrowing	Needs trial and error; can mislead when projects differ in size

For ARR, accounting profit is cash inflow minus depreciation. With straight-line depreciation and no scrap value, the total profit over the life is simply total inflows minus the cost, and the average investment is $\frac{\text{cost} + \text{scrap value}}{2}$ .

The graph shows the cooperative's dilemma. Project B's line crosses zero first, so it has the shorter payback; but it flattens out, while A keeps climbing to a cumulative Frw 13 million against B's Frw 5 million. Payback alone would pick B.

Tip

Time is money, so discount it. When methods disagree, NPV is the most reliable guide, because it counts every franc and when it arrives. Use payback as a second check when cash is tight or the future is very uncertain. In an exam, always end with a recommendation that names the method and the non-financial factors.

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Worked example 1: payback and ARR

Payback, Project A. Cumulative inflows: 4, 10, 17 after three years; 3 million is still needed from year 4's 8 million.

\text{Payback}_A = 3 + \frac{20 - 17}{8} = 3.375\ \text{years} \approx 3\ \text{years}\ 4.5\ \text{months}

Payback, Project B. Cumulative 9, 17 after two years; 3 million still needed from year 3's 5 million.

\text{Payback}_B = 2 + \frac{20 - 17}{5} = 2.6\ \text{years} \approx 2\ \text{years}\ 7\ \text{months}

ARR (no scrap value, so average investment $= \frac{20 + 0}{2} = 10$ million Frw):

\text{ARR}_A = \frac{(33 - 20) \div 5}{10} \times 100\% = \frac{2.6}{10} \times 100\% = 26\%

\text{ARR}_B = \frac{(25 - 20) \div 5}{10} \times 100\% = \frac{1.0}{10} \times 100\% = 10\%

So far: B wins on payback; A wins clearly on ARR.

Worked example 2: NPV and IRR at a 16% cost of capital

The cooperative would borrow at about 16% a year, close to Rwanda's 2025 average lending rate of 15.84% (BNR, March 2026), so it discounts at 16%. Discount factors $\frac{1}{1.16^t}$ , to 3 decimal places: 0.862, 0.743, 0.641, 0.552, 0.476.

Year	Factor at 16%	A: cash	A: PV	B: cash	B: PV
1	0.862	4	3.448	9	7.758
2	0.743	6	4.458	8	5.944
3	0.641	7	4.487	5	3.205
4	0.552	8	4.416	2	1.104
5	0.476	8	3.808	1	0.476
Total PV			20.617		18.487

\text{NPV}_A = 20.617 - 20 = +0.617\ \text{million Frw}, \qquad \text{NPV}_B = 18.487 - 20 = -1.513\ \text{million Frw}

IRR of A by interpolation. At 20% (factors 0.833, 0.694, 0.579, 0.482, 0.402) the PV of A is 18.621, so $\text{NPV} = -1.379$ . The NPV changes sign between 16% and 20%:

\text{IRR}_A \approx 16\% + \frac{0.617}{0.617 + 1.379} \times (20\% - 16\%) \approx 17.2\%

Recommendation: reject B, whose NPV is negative: at 16% it destroys about Frw 1.5 million of value despite its fast payback. A adds about Frw 0.6 million, and its IRR of about 17.2% is above the 16% cost of capital, but only just; if sales grow more slowly than forecast, A could fail too. Before investing, the board should test A with lower sales, check that supermarkets will really buy the juice, and remember that A's slow payback means a tight first two years for cash.

Warning

Common mistakes. Counting the initial cost as year 1 instead of year 0, which discounts it wrongly. Including depreciation as a cash outflow in NPV or payback: depreciation is not cash. Using profit instead of cash in payback. Rounding discount factors too roughly. Treating a positive NPV as certain: the result is only as good as the forecasts behind it.

Giles Gets Down To Business, "3.7.8 Investment Appraisal" (A-Level Business revision on ARR, NPV and payback). Pause after each method and redo its example in your notebook, then compare the method's verdict with the cooperative's.

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Practice

Define payback period, accounting rate of return and net present value.
Find the present value of Frw 1,000,000 received in 3 years' time at a discount rate of 10%.
A project costs Frw 12 million and earns net cash inflows of Frw 3, 4, 5 and 4 million in years 1 to 4, with no scrap value. Calculate its payback period and ARR (on average investment).
Using factors 0.893, 0.797, 0.712 and 0.636 (12%), calculate the NPV of the project in question 3. Should it go ahead?
A project's NPV is Frw +2.4 million at 10% and Frw −1.6 million at 18%. Estimate its IRR. Should it be accepted if the firm borrows at 15%?
Give two advantages and two disadvantages of the payback method.
"A business should always choose the project with the shortest payback." Evaluate this statement, using the pineapple cooperative's two projects.

Show answersHide answers

Payback: time for net cash inflows to repay the investment. ARR: average annual accounting profit as a percentage of the average (or initial) investment. NPV: the present value of future net cash inflows minus the initial investment.
$PV = \frac{1\,000\,000}{1.1^{3}} \approx 751\,315$ Frw (with the factor 0.751: 751,000 Frw).
Cumulative: −9, −5, 0 after year 3, so payback $= 3$ years exactly. Average profit $= \frac{16 - 12}{4} = 1$ million Frw; average investment $= \frac{12}{2} = 6$ million Frw; ARR $= \frac{1}{6} \times 100\% \approx 16.7\%$ .
PV $= 3 (0.893) + 4 (0.797) + 5 (0.712) + 4 (0.636) = 2.679 + 3.188 + 3.560 + 2.544 = 11.971$ ; NPV $= 11.971 - 12 = - 0.029$ million Frw (about −29,000 Frw). It does not quite earn 12%, so on financial grounds it should not go ahead, despite its acceptable payback.
IRR $\approx 10\% + \frac{2.4}{2.4 + 1.6} \times 8\% = 14.8\%$ . Since $14.8\% < 15\%$ , it does not cover the cost of borrowing: reject (narrowly).
Advantages: simple to calculate and explain; favours quick returns, which helps liquidity and limits risk in an uncertain market. Disadvantages: ignores cash after payback; ignores the time value of money (unless discounted).
Disagree. Project B has the shorter payback (2.6 against 3.4 years) but a negative NPV of about −1.5 million Frw at 16%, while A has a positive NPV and an IRR above the cost of capital. Payback is useful when cash is very tight or the future very uncertain, but it ignores the later years in which A earns most. A balanced decision uses NPV first, payback as a check, plus non-financial factors such as markets, skills and the environment.

Quick check

Key points

Investment appraisal judges a long-term project before money is committed, using forecast cash flows.
Payback = time to recover the cost; ARR = average annual profit ÷ average investment. Both ignore the time value of money.
$PV = \frac{C_t}{(1 + r)^t}$ ; NPV = total PV of inflows − cost; accept if NPV $> 0$ .
IRR is the discount rate that makes NPV zero; accept if it exceeds the cost of capital. Estimate it by interpolation.
When methods disagree, rely on NPV, check payback for risk and liquidity, and weigh non-financial factors.

1Case: two ways to spend Frw 20 million on pineapples

2Why appraise an investment?

3The four techniques

Case: two ways to spend Frw 20 million on pineapples

Why appraise an investment?

The four techniques