Internal Rate of Return (IRR) and Net Present Value (NPV)

IRR and NPV are essential capital budgeting tools for evaluating investment opportunities. Investment advisers use these concepts to analyze projects, compare alternatives, and make recommendations.

Net Present Value (NPV)

NPV is the difference between the present value of cash inflows and the present value of cash outflows. It represents the dollar value added by an investment.

NPV Formula

NPV = Sum of [Cash Flow_t / (1 + r)^t] - Initial Investment

Where:

• Cash Flow_t = Cash flow in period t
• r = Discount rate (required return)
• t = Time period

NPV Decision Rule

NPV Example

A project costs $100,000 and will generate $30,000 per year for 5 years. Required return is 10%.

Step 1: Calculate present value of each cash flow:

• Year 1: $30,000 / 1.10 = $27,273
• Year 2: $30,000 / 1.21 = $24,793
• Year 3: $30,000 / 1.331 = $22,539
• Year 4: $30,000 / 1.464 = $20,490
• Year 5: $30,000 / 1.611 = $18,627

Step 2: Sum present values: $113,722

Step 3: Subtract initial investment: $113,722 - $100,000 = $13,722 NPV

Decision: Accept—positive NPV adds value.

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Internal Rate of Return (IRR)

IRR is the discount rate that makes the NPV equal to zero. It represents the expected percentage return on an investment.

IRR Concept

Think of IRR as the answer to: "What rate of return does this investment earn?"

• If IRR is 15%, the investment returns 15% annually
• IRR is similar to Yield to Maturity (YTM) for bonds

IRR Decision Rule

IRR Example

Using the same project above (costs $100,000, generates $30,000/year for 5 years):

The IRR is approximately 15.2%—the rate that makes NPV = 0.

If the required return is 10%, we accept (15.2% > 10%).

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NPV vs. IRR Comparison

When They Agree

For independent projects (accepting one doesn't affect others), NPV and IRR give the same accept/reject decision:

• Positive NPV = IRR > required return = Accept
• Negative NPV = IRR < required return = Reject

When They Conflict

For mutually exclusive projects (can only choose one), NPV and IRR may rank projects differently due to:

• Different project sizes
• Different cash flow timing

When in conflict, NPV is generally preferred because it measures actual dollar value added.

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Limitations of IRR

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Hurdle Rate

The hurdle rate is the minimum acceptable rate of return:

Decision: Accept only if IRR exceeds the hurdle rate.

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Modified Internal Rate of Return (MIRR)

MIRR addresses IRR's reinvestment assumption by assuming:

• Cash outflows are financed at the firm's financing cost
• Cash inflows are reinvested at the firm's reinvestment rate (usually cost of capital)

MIRR gives a more realistic estimate when IRR seems too optimistic.

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In Practice: How Investment Advisers Apply This

Evaluating investments:

• Use NPV to determine dollar value added
• Use IRR to communicate returns in percentage terms
• Compare IRR to client's required return

Client communication:

• IRR is easier for clients to understand ("15% return")
• NPV shows actual wealth impact ("adds $50,000 to your portfolio")

Comparing alternatives:

• For mutually exclusive choices, prefer NPV
• Consider both metrics for a complete picture

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On the Exam

The Series 65 exam tests your understanding of:

1. NPV decision rule — Positive NPV = accept
2. IRR definition — Discount rate where NPV = 0
3. IRR decision rule — IRR > hurdle rate = accept
4. NPV vs. IRR — When they conflict, NPV preferred
5. Hurdle rate — Minimum acceptable return

Expect 2-3 questions on NPV/IRR. Common formats include interpreting positive/negative NPV or comparing IRR to hurdle rate.

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Key Takeaways

• NPV = Present value of inflows minus outflows; measures dollar value added
• Positive NPV = Accept; Negative NPV = Reject
• IRR = Discount rate where NPV equals zero; represents percentage return
• Accept if IRR > hurdle rate (required return)
• NPV and IRR usually agree, but when they conflict, NPV is preferred
• IRR has limitations: multiple solutions possible, reinvestment assumption may be unrealistic
• Hurdle rate = minimum acceptable rate of return