Skip to main content
Back

Investment Decision Rules: NPV, IRR, and Payback Methods

NotesPracticeVideo lessons

Study Guide - Smart Notes

Tailored notes based on your materials, expanded with key definitions, examples, and context.

Chapter 7: Investment Decision Rules

Overview of Capital Investment Decision Methods

Capital investment decisions are critical for firms, as they determine which projects or assets to undertake. Several methods exist for evaluating these investments, each with its own strengths and limitations. The most commonly used methods include the Payback Period, Net Present Value (NPV), and Internal Rate of Return (IRR).

  • Payback Period: Measures how long it takes to recover the initial investment.

  • Net Present Value (NPV): Calculates the present value of all cash flows associated with a project, discounted at the project's cost of capital.

  • Internal Rate of Return (IRR): The discount rate that makes the NPV of a project zero.

Other methods, such as the profitability index and incremental IRRs, exist but are less commonly emphasized.

Payback Period Rule

The Payback Period is the amount of time required to recover the initial investment from the project's cash flows. It is a simple and intuitive method, often used for small projects or when capital is constrained.

  • Decision Rule: Accept the project if the payback period is less than a pre-specified threshold.

  • Pitfalls:

    • Ignores the time value of money (TVM) and the project's cost of capital.

    • Ignores cash flows that occur after the payback period.

Example: Payback Period Calculation

Project

Initial Cost

Annual Cash Flow

Payback Period

A

$80

$25

3.2 years

B

$120

$30

4.0 years

C

$150

$35

4.29 years

If the required payback period is 4 years, accept projects A and B, and reject C.

Net Present Value (NPV) Rule

The NPV Rule is the most comprehensive method for evaluating investments. It discounts all future cash flows to their present value using the project's cost of capital (discount rate), reflecting both the timing and risk of cash flows.

  • Formula:

  • Decision Rule: Accept the project if NPV > 0; reject if NPV < 0.

  • Merits: Considers all cash flows, TVM, and risk via the discount rate.

Example: Perpetuity Project

Project costs $250 million and generates $35 million per year forever. If the discount rate is 10%:

million

Since NPV is positive, the project should be accepted.

Internal Rate of Return (IRR) Rule

The IRR is the discount rate that makes the NPV of a project zero. It is analogous to the yield to maturity (YTM) for bonds.

  • Decision Rule: Accept the project if IRR > required rate of return (cost of capital).

  • Merits: Provides a rate of return for the project, which is easy to interpret.

  • Limitations: Can give multiple or no solutions, especially with non-conventional cash flows (i.e., cash flows that change sign more than once).

Example: CEO Book Deal

The CEO is offered $1,000,000 upfront but must forgo $500,000 per year for three years. The opportunity cost of capital is 10%.

Timeline of CEO book deal cash flows

  • IRR Calculation: IRR = 23.38% (using financial calculator or Excel).

  • Decision: Accept the deal based on IRR rule (since 23.38% > 10%).

  • NPV Calculation:

Reject the deal based on NPV rule (since NPV < 0). This illustrates a potential problem with the IRR rule when the timing of cash flows is unusual.

Multiple IRRs and Nonexistent IRR

  • When cash flows change sign more than once, there may be multiple IRRs or no IRR at all.

  • In such cases, the NPV rule should always be used.

Choosing Between Projects: Mutually Exclusive Investments

When only one project can be chosen (mutually exclusive), the NPV rule recommends selecting the project with the highest NPV. The IRR rule may not always lead to the correct choice, especially when projects differ in scale, timing, or risk.

  • Scale: NPV scales with project size; IRR does not.

  • Timing: IRR can be distorted by the timing of cash flows.

  • Risk: IRR does not account for differences in project risk.

Example: Comparing Projects

Project

Initial Investment

Year 1 Cash Flow

Growth Rate

Cost of Capital

IRR

NPV

Hair Salon

$400,000

$120,000

4%

8%

34%

$2,600,000

Clothing Store

$500,000

$125,000

8%

12%

33%

$2,625,000

NPV rule says to choose the Clothing Store, even though the Hair Salon has a slightly higher IRR.

Investments of Unequal Lives

When comparing projects with different lifespans, the NPV rule can be misleading. Two main approaches are used to adjust for unequal lives:

  • Matching Cycle: Repeat projects until they align over the same time period, then compare NPVs.

  • Equivalent Annual Cost (EAC): Converts the NPV of each project into an annualized value, allowing for direct comparison.

EAC Formula:

Where is the present value annuity factor for rate and years.

Example: Air Cleaner Comparison

  • Cheapo: $1,000 initial, $500 annual, lasts 5 years

  • Cadillac: $4,000 initial, $100 annual, lasts 10 years

  • Discount rate: 10%

Calculate NPV for each, then EAC:

For Cadillac:

For Cheapo:

Choose the option with the lower (less negative) EAC to minimize costs.

Summary of Investment Decision Rules

  • NPV is the most reliable and comprehensive method for evaluating investments.

  • Payback and IRR can be useful but have significant limitations.

  • When methods conflict, always use the NPV rule.

  • For mutually exclusive projects or projects with unequal lives, use adjustment methods to ensure valid comparisons.

Using Calculators and Excel

  • Both financial calculators and Excel have built-in NPV and IRR functions.

  • In Excel, use =NPV(rate, values) and =IRR(values).

  • Ensure the first cash flow (usually negative) is entered at t=0.

Pearson Logo

Study Prep