Intro to Finance: Capital Budgeting - Internal Rate of Return, IRR Decision Rule IRR vs. NPV Conflicts

What This Is

The Internal Rate of Return (IRR) is a metric used to evaluate the profitability of investments or projects. It represents the rate at which the present value of expected cash flows equals the initial investment. For example, consider a project with an initial investment of $100,000 and expected cash flows of $30,000 in year 1, $40,000 in year 2, and $50,000 in year 3. If the IRR of this project is 15%, it means that an investor would be willing to pay $100,000 today to receive $30,000 in year 1, $40,000 in year 2, and $50,000 in year 3.

Key Formulas & Symbols

• IRR = r where IRR = internal rate of return, r = rate of return.
• NPV = ?(CFt / (1 + r)^t) where NPV = net present value, CFt = cash flow in period t, r = discount rate, t = time period.
• CF0 = -I where CF0 = initial cash flow, I = initial investment.
• CFt = EBIT(1 + t) - T where CFt = free cash flow in period t, EBIT = earnings before interest and taxes, T = taxes.
• WACC = (E/V x Re) + ((D/V x Rd x (1 - T)) where WACC = weighted average cost of capital, E = market value of equity, V = total market value, Re = cost of equity, D = market value of debt, Rd = cost of debt, T = tax rate.
• PV = FV / (1 + r)^n where PV = present value, FV = future value, r = periodic interest rate, n = number of periods.
• FV = PV × (1 + r)^n where FV = future value, PV = present value, r = periodic interest rate, n = number of periods.

Step-by-Step Calculation

1. Determine the expected cash flows for the project, including initial investment and subsequent cash inflows.
2. Use a financial calculator or spreadsheet to find the IRR that makes the NPV of the project equal to zero.
3. Compare the IRR to the cost of capital to determine if the project is profitable.
4. Consider the time value of money and the risk associated with the project when evaluating the IRR.

Common Mistakes

• Mistake: Confusing IRR and NPV ranking.
• Correction: IRR and NPV are different metrics that should not be used interchangeably. IRR is a rate of return, while NPV is a dollar value.
• Mistake: Using the wrong discount rate for IRR calculation.
• Correction: The discount rate used for IRR calculation should be the cost of capital, not the required rate of return.
• Mistake: Ignoring the time value of money when evaluating IRR.
• Correction: The time value of money is critical when evaluating IRR, as it takes into account the present value of future cash flows.

Exam / CFA Tips

• Tip: Be prepared to calculate IRR using a financial calculator or spreadsheet.
• Tip: Understand the difference between IRR and NPV, and be able to explain when to use each metric.
• Tip: Consider the risk associated with the project when evaluating IRR.

Quick Practice Problem

A company is considering a project with an initial investment of $50,000 and expected cash flows of $20,000 in year 1, $30,000 in year 2, and $40,000 in year 3. What is the IRR of this project?

Answer: 12.5% Explanation: Using a financial calculator or spreadsheet, we can find the IRR that makes the NPV of the project equal to zero.

Last-Minute Cram Sheet

• The IRR is sensitive to changes in the discount rate.
• The IRR is a rate of return, not a dollar value.
• The IRR should be compared to the cost of capital to determine profitability.
• The IRR is calculated using the NPV formula.
• The IRR is a measure of the project's profitability, not its risk.
• The IRR is calculated using a financial calculator or spreadsheet.
• The IRR is sensitive to changes in the expected cash flows.
• The IRR is a key metric in capital budgeting decisions.
• The IRR is not the same as the required rate of return.
• The IRR is a measure of the project's return on investment.