2.6 IRR and NPV

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 CF_t / (1 + r)^t, for t = 1 to n, minus Initial Investment

Where:

- CF_t = Cash flow in period t

- r = Discount rate (required return)

- t = Time period

NPV Decision Rule

Positive NPV: Accept. Investment adds value; earns more than required return

Negative NPV: Reject. Investment destroys value; earns less than required return

Zero NPV: Indifferent. Earns exactly the required return

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.

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 is the rate r where: NPV = sum of CF_t / (1 + r)^t, minus Initial Investment = 0

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 greater than Required Return (Hurdle Rate): Accept

IRR less than Required Return: Reject

IRR equal to Required Return: Indifferent

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% greater than 10%).

NPV vs. IRR Comparison

What It Measures: NPV - Dollar value added; IRR - Percentage return

Output: NPV - Dollar amount; IRR - Percentage

Assumes Reinvestment At: NPV - Discount rate; IRR - IRR itself

Preferred For: NPV - Mutually exclusive projects; IRR - Quick return comparison

Limitations: NPV - Requires discount rate selection; IRR - May have multiple solutions

When They Agree

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

- Positive NPV = IRR greater than required return = Accept

- Negative NPV = IRR less than 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.

Limitations of IRR

Multiple IRRs: Projects with unconventional cash flows (sign changes) may have multiple IRRs

Reinvestment Assumption: Assumes cash flows are reinvested at IRR, which may be unrealistic

Scale Blindness: Doesn't account for project size; 20% on $1,000 vs. $1,000,000

Timing Issues: May favor projects with faster payback even if larger project adds more value

Hurdle Rate

The hurdle rate is the minimum acceptable rate of return:

Hurdle Rate: Minimum IRR required to accept a project

Required Return: Same concept, different name

Cost of Capital: Often used as the hurdle rate

Decision: Accept only if IRR exceeds the hurdle rate.

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.

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

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 greater than hurdle rate = accept

4. NPV vs. IRR - When they conflict, NPV preferred

5. Hurdle rate - Minimum acceptable return

Common formats include interpreting positive/negative NPV or comparing IRR to hurdle rate.

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 greater than 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