💡 What is it? The payback period tells you how many years it will take for an investment to recover its initial cost from the cash it generates. Think of it as the “time to get your money back” from a new gadget or a school project.
Imagine you set up a lemonade stand and spent £10 on lemons, sugar, and cups. Each day you earn £2. The payback period tells you how many days it takes to earn back that £10.
Formula for a constant cash flow: \$\text{Payback period} = \frac{\text{Initial investment}}{\text{Annual cash inflow}}\$
Suppose a company spends £10,000 on a new machine that will bring in £3,000 each year.
| Year | Cash Inflow (£) | Cumulative (£) |
|---|---|---|
| 1 | 3,000 | 3,000 |
| 2 | 3,000 | 6,000 |
| 3 | 3,000 | 9,000 |
| 4 | 3,000 | 12,000 |
The cumulative inflow reaches £10,000 during year 4. We need an additional £1,000 after the first 3 years (9,000). That extra £1,000 is one‑third of the £3,000 yearly inflow.
Payback period = 3 + (1,000 ÷ 3,000) = 3.33 years.
Exam Tip 💬
- Remember the formula: \$\text{Payback period} = \frac{\text{Initial investment} - \text{Cumulative cash flow at }(n-1)}{\text{Cash flow in year }n} + (n-1)\$
- Show the calculation steps clearly; examiners look for a logical flow.
- If the cash flows are not equal each year, use the cumulative method.
- Note that the payback method is a quick screening tool, not a definitive decision criterion.
While the payback period focuses on how fast you recover your investment, the Annual Rate of Return (ARR) looks at the average profit relative to the initial cost. ARR is calculated as:
\$\text{ARR} = \frac{\text{Average annual profit}}{\text{Initial investment}} \times 100\%\$
Both methods are simple, but remember:
Exam Tip 📚
- When asked to compare payback and ARR, highlight their advantages (simplicity, speed) and limitations (ignores time value, cash flows).
- Provide a short example for each to illustrate how they differ in practice.