the meaning, calculation and interpretation of payback as an investment appraisal method

10.3 Investment Appraisal – Payback and ARR

Payback Period

💡 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.

Step‑by‑Step Calculation

  1. Write down the initial investment (e.g., £10,000).
  2. List the expected cash inflows for each year.
  3. Accumulate the cash flows year by year.
  4. Find the year when the cumulative inflow first equals or exceeds the initial cost.
  5. If it happens partway through a year, calculate the fraction of that year needed.

Formula for a constant cash flow: \$\text{Payback period} = \frac{\text{Initial investment}}{\text{Annual cash inflow}}\$

Example

Suppose a company spends £10,000 on a new machine that will bring in £3,000 each year.

YearCash Inflow (£)Cumulative (£)
13,0003,000
23,0006,000
33,0009,000
43,00012,000

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.

Interpretation

  • Shorter payback = lower risk – you get your money back faster.
  • Longer payback = higher risk – the investment takes longer to recover.
  • It ignores cash flows after the payback point and does not consider the time value of money.

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.

Quick Comparison with ARR

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:

  • Payback ignores time value of money.
  • ARR ignores cash flows and only uses accounting profit.
  • Use them as quick checks before applying more robust methods like NPV or IRR.

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.

Key Take‑aways

  • Payback period = time to recover initial cost.
  • Calculated by adding yearly cash inflows until the sum ≥ initial investment.
  • Shorter period = lower risk.
  • Does not consider cash flows after payback or time value of money.