3.8 Investment appraisal

Payback period measures how long net cash inflows take to recover the initial investment. Average rate of return (ARR) expresses average annual accounting profit as a percentage of the initial investment.

For equal annual net cash inflows, payback $=\text{initial investment}/\text{annual net cash inflow}$. For uneven flows, add yearly net cash inflows until recovery; if $R$ remains at the start of the recovery year and that year's flow is $F$, payback $=\text{completed years}+R/F$. For ARR, calculate $\text{total profit}=\text{total returns}-\text{initial investment}$, then $\text{average annual profit}=\text{total profit}/\text{project life}$ and $\text{ARR}=\text{average annual profit}/\text{initial investment}\times100$.

Use currency units for the investment, returns and profit; report payback in years (and convert the fractional year consistently if months are required) and ARR as a percentage. A shorter payback improves liquidity exposure, while a higher ARR indicates a stronger average accounting return, but the two rankings can disagree because they measure different things.

Payback ignores cash flows after recovery and does not measure total return; ARR uses accounting profit and ignores when returns occur. Compare projects with consistent assumptions, then evaluate forecast risk, finance, capacity, strategic fit and non-financial effects before recommending one.

Net present value is the total of discounted future net cash flows minus the initial investment. Discounting reflects that money received later has a lower present value and that today’s funds could have been used elsewhere.

Multiply each future net cash flow by its discount factor, add the discounted values including the negative initial outlay, then interpret the sign. A positive NPV suggests value at the chosen rate; a negative NPV suggests the forecast return does not cover that opportunity cost.

For a £325,000 project with discounted future inflows of £100,100, £74,400, £56,250, £44,200 and £37,200, the total including the initial outlay is −£12,550. That is a warning under the 10% discount rate, not a guarantee that every non-financial benefit is worthless.

NPV depends on forecast cash flows and the discount rate. It can ignore environmental or strategic value and become misleading when assumptions are weak; show units, timing and sensitivity before accepting the result.