Intro to Finance: Capital Budgeting - Modified IRR MIRR

What This Is

Modified Internal Rate of Return (MIRR) is a financial metric used to evaluate the attractiveness of a project or investment by considering the time value of money and the cost of capital. It takes into account the initial investment, expected cash flows, and the cost of capital to provide a more accurate picture of the project's return. For example, consider a project with an initial investment of $100,000, expected cash flows of $20,000 per year for 5 years, and a cost of capital of 10%. The MIRR would provide a more accurate return on investment compared to the traditional IRR.

Key Formulas & Symbols

• MIRR = [(FV - PV) / PV] × (1 + r)^n where MIRR = modified internal rate of return, FV = future value, PV = present 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.
• PV = FV / (1 + r)^n where PV = present value, FV = future value, r = periodic interest rate, n = number of periods.
• r = (1 + (1 + g)^n - (1 + d)^n) / n where r = periodic interest rate, g = growth rate, d = discount rate, n = number of periods.
• g = (FV / PV)^(1/n) - 1 where g = growth rate, FV = future value, PV = present value, n = number of periods.
• d = (1 + r)^n - 1 where d = discount rate, r = periodic interest rate, n = number of periods.
• CF = PMT × [(1 + g)^n - 1] / g where CF = cash flow, PMT = periodic payment, g = growth rate, n = number of periods.

Step-by-Step Calculation

1. Determine the initial investment (PV) and the expected cash flows (CF).
2. Calculate the future value (FV) using the formula FV = PV × (1 + r)^n.
3. Calculate the present value of the future cash flows using the formula PV = FV / (1 + r)^n.
4. Calculate the modified internal rate of return (MIRR) using the formula MIRR = [(FV - PV) / PV] × (1 + r)^n.
5. Consider the cost of capital and the growth rate to determine the periodic interest rate (r).
6. Use the periodic interest rate (r) to calculate the modified internal rate of return (MIRR).

Common Mistakes

• Mistake: Using the traditional IRR to evaluate a project with a large initial investment and small cash flows.
• Correction: Use the modified IRR (MIRR) to account for the time value of money and the cost of capital.
• Mistake: Assuming a constant growth rate for the cash flows.
• Correction: Use a more realistic growth rate that reflects the company's historical growth and industry trends.
• Mistake: Ignoring the cost of capital when evaluating a project.
• Correction: Consider the cost of capital when calculating the modified internal rate of return (MIRR).

Exam / CFA Tips

• Tip: Be prepared to calculate the modified internal rate of return (MIRR) using different scenarios and assumptions.
• Tip: Understand the differences between the traditional IRR and the modified IRR (MIRR).
• Tip: Consider the cost of capital and the growth rate when evaluating a project using the modified IRR (MIRR).

Quick Practice Problem

A company is evaluating a project with an initial investment of $100,000 and expected cash flows of $20,000 per year for 5 years. The cost of capital is 10% and the growth rate is 5%. What is the modified internal rate of return (MIRR)?

Answer: 12.34% Explanation: Using the formula MIRR = [(FV - PV) / PV] × (1 + r)^n, we can calculate the modified internal rate of return (MIRR) as 12.34%.

Last-Minute Cram Sheet

• MIRR = [(FV - PV) / PV] × (1 + r)^n
• FV = PV × (1 + r)^n
• PV = FV / (1 + r)^n
• r = (1 + (1 + g)^n - (1 + d)^n) / n
• g = (FV / PV)^(1/n) - 1
• d = (1 + r)^n - 1
• CF = PMT × [(1 + g)^n - 1] / g
• MIRR > IRR when the project has a large initial investment and small cash flows.
• MIRR < IRR when the project has a small initial investment and large cash flows.
• The modified IRR (MIRR) assumes a constant growth rate for the cash flows.
• The modified IRR (MIRR) ignores the impact of inflation on the cash flows.