What is investment appraisal?
An investment is spending money now (on a machine, building, IT system, new product or new market) to get more money back later. Investment appraisal is how a business checks if the investment is worth it, and which of several projects is best.
You need: the initial cost (year 0) and the forecast net cash flows each year (cash in β cash out). These are forecasts, so they can be wrong.
Payback period
The payback period is the time it takes for the net cash inflows to repay the initial cost.
Steps: make a cumulative cash flow column (running total starting at βcost). Find the year where it turns positive. Then:
Payback = full years + (amount still needed Γ· cash flow in the next year) Γ 12 months
Example: β100, β70, β35, +5. After 2 years 35k is still needed; year 3 brings 40k. 35 Γ· 40 Γ 12 = 10.5 months. Payback = 2 years 10.5 months.
Good: simple, focuses on cash and on how fast risk is reduced. Bad: ignores cash after payback and ignores the time value of money.
Average rate of return (ARR)
ARR = (average annual profit Γ· initial investment) Γ 100%
Average annual profit = (total net cash inflows β initial cost) Γ· number of years.
Example: inflows 160k, cost 100k, 5 years. Profit = 60k; per year 12k; ARR = 12 Γ· 100 Γ 100 = 12%. Compare it with the interest rate or a target (for example 10%).
Good: uses all the years, gives a % that is easy to compare. Bad: ignores timing: a profit in year 5 counts the same as one in year 1. (Some courses divide by the average capital employed instead; follow your course.)
Net present value (NPV) and discounting
Money received later is worth less than money today, because today's money could earn interest and because of inflation and risk. This is the time value of money.
Discount factor = 1 Γ· (1 + r)βΏ, where r is the discount rate and n the year. At 10%: year 1 = 0.909, year 2 = 0.826, year 3 = 0.751, year 4 = 0.683, year 5 = 0.621.
Present value = cash flow Γ discount factor. NPV = total present values β initial cost.
If NPV > 0 the project earns more than the discount rate: accept on financial grounds. If NPV < 0, reject. Between projects, prefer the higher NPV. (The internal rate of return is the discount rate that makes NPV exactly zero.)
Good: includes timing and all cash flows. Bad: harder to work out; the right discount rate is a guess.
Sensitivity, risk and uncertainty
All the numbers are forecasts. Sensitivity analysis asks "what if?": change one input (sales β20%, cost +10%, interest rate up) and see if the decision changes. If a small change flips NPV from positive to negative, the project is risky.
Risks: wrong sales forecasts, new competitors, rising costs, exchange rates, interest rates, technology going out of date. Uncertainty grows the further ahead the forecast goes, which is one reason later cash flows are discounted more.
Non-financial factors and choosing a method
Numbers are not everything. Managers also ask: does it fit our strategy and objectives? What about staff (jobs, training, morale), ethics and the environment, brand image, quality, and the finance available (can we borrow, at what interest?)
Firms often use several methods together: payback for speed and cash, ARR for overall profitability, NPV for value. A cash-poor start-up may care most about payback; a big firm planning 10 years ahead may care most about NPV.
Try it: appraise a purchase at home
Imagine your family buys a solar water heater for 30,000 and saves 9,000 a year on electricity for 6 years. Work out the payback (3 years 4 months), the ARR ((54,000 β 30,000) Γ· 6 = 4,000 a year β 13.3%) and the NPV at 8%. Then ask: what if the savings are only 7,000? In the 3D free-play step, use the sliders to test your own "what if".
Key formulas and definitions
- Payback = full years + (cash still needed Γ· next year's cash flow) Γ 12 months
- Average annual profit = (total net inflows β initial cost) Γ· years
- ARR = average annual profit Γ· initial investment Γ 100%
- Discount factor = 1 Γ· (1 + r)βΏ
- Present value = cash flow Γ discount factor
- NPV = sum of present values β initial cost
Worked examples
1. A project costs 50,000 and brings in 10,000 every year. Find the payback period.
50,000 Γ· 10,000 = 5 years. (When yearly cash is equal, payback = cost Γ· yearly cash flow.)
2. Cost 100k; inflows 30k, 35k, 40k, 30k, 25k. Find the payback period.
Cumulative: β100, β70, β35, +5. After 2 years 35k is still needed; year 3 gives 40k. 35 Γ· 40 Γ 12 = 10.5 months. Payback = 2 years 10.5 months.
3. Using the same project, find the ARR.
Total inflows = 160k. Profit = 160 β 100 = 60k over 5 years = 12k a year. ARR = 12 Γ· 100 Γ 100 = 12%.
4. Find the NPV of the same project at 10% (factors 0.909, 0.826, 0.751, 0.683, 0.621).
PVs: 27.27 + 28.91 + 30.04 + 20.49 + 15.53 = 122.24k. NPV = 122.24 β 100 = +22.24k (about +22.3k with exact factors). Positive, so accept on money grounds.
5. A machine costs 80,000 and brings 25,000 a year for 4 years. Find ARR and NPV at 8% (factors 0.926, 0.857, 0.794, 0.735).
ARR: profit = 100,000 β 80,000 = 20,000; per year 5,000; ARR = 5,000 Γ· 80,000 = 6.25%. NPV: sum of factors = 3.312; 25,000 Γ 3.312 = 82,800; NPV = 82,800 β 80,000 = +2,800.
6. Project A: NPV +12k, payback 4 years. Project B: NPV +8k, payback 1.5 years. The firm is short of cash. Which should it choose?
On value alone A is better (higher NPV). But B pays back much faster, so cash returns quickly and risk is lower. A cash-short firm may choose B; a strong firm may choose A. A good answer weighs both and adds non-financial factors.
Common mistakes
- Forgetting to take away the initial cost when working out total profit for ARR.
- Writing payback months wrongly: 0.875 of a year is 10.5 months (Γ 12), not 8.75 months.
- Discounting the year-0 cost. The cost is paid today, so its discount factor is 1.
- Judging only on numbers. Exam answers need risk, sensitivity and non-financial factors too.