Investment Evaluation: NPV and IRR

Key Concepts

• Internal Rate of Return (IRR): Measures the profitability of potential investments. Directly calculates the actual rate of return on an investment and compares it to a benchmark.
• Net Present Value (NPV): Measures the profitability of an investment against a benchmark rate expressed in dollar terms. If NPV > 0, the investment beats the benchmark.

Example Analysis

Simple Cash Flow Example

• Period 0: Invest $1,000
• Period 1: Return $1,200
• Benchmark Rate: 10%

NPV Calculation

• NPV = -$1,000 + $1,200 / (1 + 0.1) = $90.90
• Positive NPV means the investment is better than the 10% benchmark.

IRR Calculation

• Return on Investment (ROI) = (Return - Investment) / Investment = $200/$1,000 = 20%
• IRR is directly calculated and compared to the benchmark.
• If IRR > Benchmark, investment is considered good.

Multi-Period Cash Flows

• Complexity increases as returns spread over multiple periods; simple ROI calculation doesn't suffice.
• Use NPV set to zero to solve for IRR in multi-period scenarios.
• IRR is the discount rate that results in an NPV = 0.

Advantages of IRR

• Provides a percentage measure, which is more intuitive and communicable.
• Shows rate of return, helping compare directly to market rates.

Problems with IRR

Multiple IRRs

• Occur when cash flows change signs more than once.
• Multiple IRRs can make interpretation difficult; neither root may have financial meaning.

Modified Internal Rate of Return (MIRR)

• Adjusts cash flows to deal with multiple IRRs.
• IRR becomes dependent on the choice of discount rate, which violates the purpose of IRR.

Investment vs. Financing Projects

• IRR doesn't distinguish between investing (initial cash outflow) and financing (initial cash inflow) projects.
• For financing projects, a lower IRR than the benchmark indicates cheaper financing.

Independent vs. Mutually Exclusive Projects

Independent Projects

• Accept projects if they meet individual minimum criteria.
• Not constrained by mutual exclusivity.

Mutually Exclusive Projects

• Only one project can be chosen among alternatives.
• Use IRR for ranking; highest IRR preferred.

IRR Calculation with Spreadsheets

• Use Excel's IRR function to calculate IRR by entering a range of cash flows.
• No need for an assumed discount rate as IRR is calculated to make NPV = 0.

Visualizing IRR and NPV

• Net Present Value Profile: Plot of NPV against varying discount rates.
• The point where NPV = 0 on the graph is the IRR.

Conclusion

• NPV provides a reliable measure when IRR has limitations such as multiple IRRs.
• IRR, while intuitive, requires careful interpretation, especially with financing projects.
• Use tools like Excel for more complex IRR calculations over multiple periods.