Investment Appraisal Methods

• Opportunity Cost of Capital: This represents the return foregone by investing in a specific project instead of an alternative investment of similar risk. It is typically used as the discount rate in financial calculations to ensure the project meets the minimum required return.

• Compounding and Discounting: Compounding calculates the future value of a current sum, while discounting is the reverse process, determining what a future sum is worth today. The relationship is defined by the formula $PV = \frac{FV}{(1+r)^n}$, where $r$ is the discount rate and $n$ is the number of periods.

• Incremental Analysis: Only cash flows that change as a direct result of the investment decision should be considered. Sunk costs (money already spent) and allocated overheads that do not change should be excluded from the appraisal.

Net Present Value (NPV)

• Methodology: NPV calculates the difference between the present value of cash inflows and the present value of cash outflows over the project's life.
• Decision Rule: If $NPV > 0$, the project is expected to add value to the firm and should be accepted; if $NPV < 0$, it should be rejected.

Formula: $NPV = \sum_{t=0}^{n} \frac{C_t}{(1+r)^t}$

Internal Rate of Return (IRR)

• Methodology: The IRR is the specific discount rate that makes the NPV of a project exactly zero. It represents the expected percentage return of the investment.
• Decision Rule: Accept the project if the IRR is greater than the company's hurdle rate or cost of capital.

Payback Period (PP)

• Methodology: This measures the time required for the cumulative cash inflows to equal the initial investment. It focuses on liquidity and risk rather than total value creation.
• Decision Rule: Accept if the payback period is shorter than a pre-determined maximum allowable timeframe.

• Check the Cash Flow Timing: Always verify if cash flows occur at the start (Year 0) or end (Year 1, 2, etc.) of a period. Initial investments are almost always at Year 0 and should not be discounted.

• Consistency in Units: Ensure that the discount rate matches the frequency of cash flows (e.g., use an annual rate for annual cash flows). If a rate is given as monthly, it must be converted or the periods adjusted accordingly.

• Sanity Check for IRR: If a project has an NPV of zero at a 10% discount rate, then its IRR is exactly 10%. Use this relationship to quickly verify your calculations; if the NPV is positive at 10%, the IRR must be higher than 10%.

• Common Error - Depreciation: Never include depreciation as a cash outflow in NPV or Payback calculations. However, do include it if you are calculating the Accounting Rate of Return (ARR), as ARR is based on profit.