Revise Basic methods: payback, accounting rate of return (ARR) for Cambridge 9609 (10.3.2)

Investment appraisal refers to the quantitative techniques used by businesses to evaluate the potential financial viability of long-term capital investment projects. Before committing significant capital to projects such as purchasing new machinery, opening a new factory, or launching a new product line, managers need to assess the likely returns and risks involved. These techniques provide a framework for comparing different investment opportunities and making informed decisions. The primary goal is to determine whether a project's expected future cash flows or profits will be sufficient to justify the initial capital outlay. The two basic methods we will explore, the payback period and the accounting rate of return (ARR), offer different perspectives on a project's attractiveness, focusing on speed of return and overall profitability respectively.

The payback period is the time it takes for a project's net cash inflows to repay the initial capital cost of the investment. It is a measure of liquidity and risk, not profitability. To calculate it, you track the cumulative net cash flow year by year until the initial investment is recovered. If cash flows are uneven, identify the year in which the investment is paid back. Then, calculate the specific month using the formula: (Amount still to pay back / Net cash flow in that year) × 12 months. For example, if a £100,000 project returns £40,000 in Year 1 and £50,000 in Year 2, £10,000 is still outstanding. If Year 3's cash flow is £30,000, the payback is 2 years and (£10,000 / £30,000) × 12 = 4 months.

The primary strength of the payback method is its simplicity; it is easy to calculate and understand, making it accessible to managers without a deep financial background. It is also an effective tool for managing liquidity, as it prioritises projects that return cash quickly, which is particularly important for businesses with cash flow concerns. However, its weaknesses are significant. It completely ignores all cash flows received after the payback period has been reached, meaning a highly profitable long-term project may be rejected in favour of a less profitable short-term one. Furthermore, it does not actually measure profitability, only the speed of return. The choice of an 'acceptable' payback period is often arbitrary and lacks a clear theoretical basis.

The Accounting Rate of Return (ARR) measures the average annual profit of an investment project as a percentage of the initial investment cost. Unlike payback, it focuses on profitability. The formula is: ARR (%) = (Average Annual Profit / Initial Investment) × 100. To find the Average Annual Profit, you first calculate the total profit over the project's life (Total Cash Inflows - Total Costs, including the initial investment) and then divide by the number of years. For example, a 4-year project costing £200,000 with total inflows of £280,000 has a total profit of £80,000. The average annual profit is £80,000 / 4 = £20,000. The ARR is (£20,000 / £200,000) × 100 = 10%. This result is then compared against a pre-set target rate.

The main advantage of ARR is that it provides a clear measure of profitability for the entire duration of a project, using a percentage figure that is easily understood and compared. It allows a business to set a minimum target rate of return for all projects, ensuring they align with corporate objectives for profitability. However, ARR has two major drawbacks. Firstly, it completely ignores the timing of cash flows, treating profits in later years as equally valuable as profits in earlier years (ignoring the time value of money). Secondly, it relies on accounting profit, which is subject to depreciation rules and can be manipulated, rather than actual cash flow, which is less ambiguous. This can sometimes present a misleading picture of a project's financial performance.

List net cash flows by year and calculate cumulative totals. Payback occurs when cumulative flow reaches zero (investment recovered).

If recovery falls between two years, interpolate:

Payback = year before recovery + (unrecovered amount at start of year ÷ cash flow in recovery year)

ARR = $\frac{\text{Average annual profit}}{\text{Initial investment}} \times 100\%$

Average annual profit = $\frac{\text{Total profit over project life}}{\text{Number of years}}$