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Principles of Finance

16.3 Internal Rate of Return (IRR) Method

Principles of Finance16.3 Internal Rate of Return (IRR) Method

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Table of contents
  1. Preface
  2. 1 Introduction to Finance
    1. Why It Matters
    2. 1.1 What Is Finance?
    3. 1.2 The Role of Finance in an Organization
    4. 1.3 Importance of Data and Technology
    5. 1.4 Careers in Finance
    6. 1.5 Markets and Participants
    7. 1.6 Microeconomic and Macroeconomic Matters
    8. 1.7 Financial Instruments
    9. 1.8 Concepts of Time and Value
    10. Summary
    11. Key Terms
    12. Multiple Choice
    13. Review Questions
    14. Video Activity
  3. 2 Corporate Structure and Governance
    1. Why It Matters
    2. 2.1 Business Structures
    3. 2.2 Relationship between Shareholders and Company Management
    4. 2.3 Role of the Board of Directors
    5. 2.4 Agency Issues: Shareholders and Corporate Boards
    6. 2.5 Interacting with Investors, Intermediaries, and Other Market Participants
    7. 2.6 Companies in Domestic and Global Markets
    8. Summary
    9. Key Terms
    10. CFA Institute
    11. Multiple Choice
    12. Review Questions
    13. Video Activity
  4. 3 Economic Foundations: Money and Rates
    1. Why It Matters
    2. 3.1 Microeconomics
    3. 3.2 Macroeconomics
    4. 3.3 Business Cycles and Economic Activity
    5. 3.4 Interest Rates
    6. 3.5 Foreign Exchange Rates
    7. 3.6 Sources and Characteristics of Economic Data
    8. Summary
    9. Key Terms
    10. CFA Institute
    11. Multiple Choice
    12. Review Questions
    13. Problems
    14. Video Activity
  5. 4 Accrual Accounting Process
    1. Why It Matters
    2. 4.1 Cash versus Accrual Accounting
    3. 4.2 Economic Basis for Accrual Accounting
    4. 4.3 How Does a Company Recognize a Sale and an Expense?
    5. 4.4 When Should a Company Capitalize or Expense an Item?
    6. 4.5 What Is “Profit” versus “Loss” for the Company?
    7. Summary
    8. Key Terms
    9. Multiple Choice
    10. Review Questions
    11. Problems
    12. Video Activity
  6. 5 Financial Statements
    1. Why It Matters
    2. 5.1 The Income Statement
    3. 5.2 The Balance Sheet
    4. 5.3 The Relationship between the Balance Sheet and the Income Statement
    5. 5.4 The Statement of Owner’s Equity
    6. 5.5 The Statement of Cash Flows
    7. 5.6 Operating Cash Flow and Free Cash Flow to the Firm (FCFF)
    8. 5.7 Common-Size Statements
    9. 5.8 Reporting Financial Activity
    10. Summary
    11. Key Terms
    12. CFA Institute
    13. Multiple Choice
    14. Review Questions
    15. Problems
    16. Video Activity
  7. 6 Measures of Financial Health
    1. Why It Matters
    2. 6.1 Ratios: Condensing Information into Smaller Pieces
    3. 6.2 Operating Efficiency Ratios
    4. 6.3 Liquidity Ratios
    5. 6.4 Solvency Ratios
    6. 6.5 Market Value Ratios
    7. 6.6 Profitability Ratios and the DuPont Method
    8. Summary
    9. Key Terms
    10. CFA Institute
    11. Multiple Choice
    12. Review Questions
    13. Problems
    14. Video Activity
  8. 7 Time Value of Money I: Single Payment Value
    1. Why It Matters
    2. 7.1 Now versus Later Concepts
    3. 7.2 Time Value of Money (TVM) Basics
    4. 7.3 Methods for Solving Time Value of Money Problems
    5. 7.4 Applications of TVM in Finance
    6. Summary
    7. Key Terms
    8. CFA Institute
    9. Multiple Choice
    10. Review Questions
    11. Problems
    12. Video Activity
  9. 8 Time Value of Money II: Equal Multiple Payments
    1. Why It Matters
    2. 8.1 Perpetuities
    3. 8.2 Annuities
    4. 8.3 Loan Amortization
    5. 8.4 Stated versus Effective Rates
    6. 8.5 Equal Payments with a Financial Calculator and Excel
    7. Summary
    8. Key Terms
    9. CFA Institute
    10. Multiple Choice
    11. Problems
    12. Video Activity
  10. 9 Time Value of Money III: Unequal Multiple Payment Values
    1. Why It Matters
    2. 9.1 Timing of Cash Flows
    3. 9.2 Unequal Payments Using a Financial Calculator or Microsoft Excel
    4. Summary
    5. Key Terms
    6. CFA Institute
    7. Multiple Choice
    8. Review Questions
    9. Problems
    10. Video Activity
  11. 10 Bonds and Bond Valuation
    1. Why It Matters
    2. 10.1 Characteristics of Bonds
    3. 10.2 Bond Valuation
    4. 10.3 Using the Yield Curve
    5. 10.4 Risks of Interest Rates and Default
    6. 10.5 Using Spreadsheets to Solve Bond Problems
    7. Summary
    8. Key Terms
    9. CFA Institute
    10. Multiple Choice
    11. Review Questions
    12. Problems
    13. Video Activity
  12. 11 Stocks and Stock Valuation
    1. Why It Matters
    2. 11.1 Multiple Approaches to Stock Valuation
    3. 11.2 Dividend Discount Models (DDMs)
    4. 11.3 Discounted Cash Flow (DCF) Model
    5. 11.4 Preferred Stock
    6. 11.5 Efficient Markets
    7. Summary
    8. Key Terms
    9. CFA Institute
    10. Multiple Choice
    11. Review Questions
    12. Problems
    13. Video Activity
  13. 12 Historical Performance of US Markets
    1. Why It Matters
    2. 12.1 Overview of US Financial Markets
    3. 12.2 Historical Picture of Inflation
    4. 12.3 Historical Picture of Returns to Bonds
    5. 12.4 Historical Picture of Returns to Stocks
    6. Summary
    7. Key Terms
    8. Multiple Choice
    9. Review Questions
    10. Video Activity
  14. 13 Statistical Analysis in Finance
    1. Why It Matters
    2. 13.1 Measures of Center
    3. 13.2 Measures of Spread
    4. 13.3 Measures of Position
    5. 13.4 Statistical Distributions
    6. 13.5 Probability Distributions
    7. 13.6 Data Visualization and Graphical Displays
    8. 13.7 The R Statistical Analysis Tool
    9. Summary
    10. Key Terms
    11. CFA Institute
    12. Multiple Choice
    13. Review Questions
    14. Problems
    15. Video Activity
  15. 14 Regression Analysis in Finance
    1. Why It Matters
    2. 14.1 Correlation Analysis
    3. 14.2 Linear Regression Analysis
    4. 14.3 Best-Fit Linear Model
    5. 14.4 Regression Applications in Finance
    6. 14.5 Predictions and Prediction Intervals
    7. 14.6 Use of R Statistical Analysis Tool for Regression Analysis
    8. Summary
    9. Key Terms
    10. Multiple Choice
    11. Review Questions
    12. Problems
    13. Video Activity
  16. 15 How to Think about Investing
    1. Why It Matters
    2. 15.1 Risk and Return to an Individual Asset
    3. 15.2 Risk and Return to Multiple Assets
    4. 15.3 The Capital Asset Pricing Model (CAPM)
    5. 15.4 Applications in Performance Measurement
    6. 15.5 Using Excel to Make Investment Decisions
    7. Summary
    8. Key Terms
    9. CFA Institute
    10. Multiple Choice
    11. Review Questions
    12. Problems
    13. Video Activity
  17. 16 How Companies Think about Investing
    1. Why It Matters
    2. 16.1 Payback Period Method
    3. 16.2 Net Present Value (NPV) Method
    4. 16.3 Internal Rate of Return (IRR) Method
    5. 16.4 Alternative Methods
    6. 16.5 Choosing between Projects
    7. 16.6 Using Excel to Make Company Investment Decisions
    8. Summary
    9. Key Terms
    10. CFA Institute
    11. Multiple Choice
    12. Review Questions
    13. Problems
    14. Video Activity
  18. 17 How Firms Raise Capital
    1. Why It Matters
    2. 17.1 The Concept of Capital Structure
    3. 17.2 The Costs of Debt and Equity Capital
    4. 17.3 Calculating the Weighted Average Cost of Capital
    5. 17.4 Capital Structure Choices
    6. 17.5 Optimal Capital Structure
    7. 17.6 Alternative Sources of Funds
    8. Summary
    9. Key Terms
    10. CFA Institute
    11. Multiple Choice
    12. Review Questions
    13. Problems
    14. Video Activity
  19. 18 Financial Forecasting
    1. Why It Matters
    2. 18.1 The Importance of Forecasting
    3. 18.2 Forecasting Sales
    4. 18.3 Pro Forma Financials
    5. 18.4 Generating the Complete Forecast
    6. 18.5 Forecasting Cash Flow and Assessing the Value of Growth
    7. 18.6 Using Excel to Create the Long-Term Forecast
    8. Summary
    9. Key Terms
    10. Multiple Choice
    11. Review Questions
    12. Problems
    13. Video Activity
  20. 19 The Importance of Trade Credit and Working Capital in Planning
    1. Why It Matters
    2. 19.1 What Is Working Capital?
    3. 19.2 What Is Trade Credit?
    4. 19.3 Cash Management
    5. 19.4 Receivables Management
    6. 19.5 Inventory Management
    7. 19.6 Using Excel to Create the Short-Term Plan
    8. Summary
    9. Key Terms
    10. Multiple Choice
    11. Review Questions
    12. Video Activity
  21. 20 Risk Management and the Financial Manager
    1. Why It Matters
    2. 20.1 The Importance of Risk Management
    3. 20.2 Commodity Price Risk
    4. 20.3 Exchange Rates and Risk
    5. 20.4 Interest Rate Risk
    6. Summary
    7. Key Terms
    8. CFA Institute
    9. Multiple Choice
    10. Review Questions
    11. Problems
    12. Video Activity
  22. Index

Learning Outcomes

By the end of this section, you will be able to:

  • Define internal rate of return (IRR).
  • Calculate internal rate of return.
  • List advantages and disadvantages of using the internal rate of return method.

Internal Rate of Return (IRR) Calculation

The internal rate of return (IRR) is the discount rate that sets the present value of the cash inflows equal to the present value of the cash outflows. In considering whether Sam’s Sporting Goods should purchase the embroidery machine, the IRR method approaches the time value of money problem from a slightly different angle. Instead of using the company’s cost of attracting funds for the discount rate and solving for NPV, as we did in the first NPV equation, we set NPV equal to zero and solve for the discount rate to find the IRR:

NPV=$2,0001 + i1+$4,000(1 + i)2+$5,0001 + i3+$5,0001 + i4+$5,0001 + i5+$5,0001 + i6-$16,000=0NPV=$2,0001 + i1+$4,000(1 + i)2+$5,0001 + i3+$5,0001 + i4+$5,0001 + i5+$5,0001 + i6-$16,000=0

The IRR is the discount rate at which the NPV profile graph crosses the horizontal axis. If the IRR is greater than the cost of capital, a project should be accepted. If the IRR is less than the cost of capital, a project should be rejected. The NPV profile graph for the embroidery machine crossed the horizontal axis at 14%. Therefore, if Sam’s Sporting Goods can attract capital for less than 14%, the IRR exceeds the cost of capital and the embroidery machine should be purchased. However, if it costs Sam’s more than 14% to attract capital, the embroidery machine should not be purchased.

In other words, a company wants to accept projects that have an IRR that exceed the company’s cost of attracting funds. The cash flow from these projects will be great enough to cover the cost of attracting money from investors in addition to the other costs of the project. A company should reject any project that has an IRR less than the company’s cost of attracting funds; the cash flows from such a project are not enough to compensate the investors for the use of their funds.

Calculating IRR without a financial calculator is an arduous, time-consuming process that requires trial and error to find the discount rate that makes NPV exactly equal zero. Your calculator uses the same type of trial-and-error iterative process, but because it uses an automated process, it can do so much more quickly than you can. A problem that might require 30 minutes of detailed mathematical calculations by hand can be completed in a matter of seconds with the assistance of a financial calculator.

All the information your calculator needs to calculate IRR is the value of each cash flow and the time period in which it occurs. To calculate IRR, begin by entering the cash flows for the project, just as you do for the NPV calculation (see Table 16.7). After these cash flows are entered, simply compute IRR in the final step.

Step Description Enter Display
1 Select cash flow worksheet CF CF0 XXXX
2 Clear the cash flow worksheet 2ND [CLR WORK] CF0 0
3 Enter initial cash flow 16000 +/- ENTER CF0 = -16,000.00
4 Enter cash flow for the first year ↓     2000 ENTER C01 = 2,000.00
    F01 = 1.0
5 Enter cash flow for the second year ↓     4000 ENTER C02 = 4,000.00
    F02 = 1.0
6 Enter cash flow for the third year ↓     5000 ENTER C03 = 5,000.00
    F03 = 1.0
7 Enter cash flow for the fourth year ↓     5000 ENTER C04 = 5,000.00
    F04 = 1.0
8 Enter cash flow for the fifth year ↓     5000 ENTER C05 = 5,000.00
    F05 = 1.0
9 Enter cash flow for the sixth year ↓     5000 ENTER C06 = 5,000.00
    F06 = 1.0
10 Compute IRR IRR CPT IRR = 14.09
Table 16.7 Calculator Steps for IRR

Advantages

The primary advantage of using the IRR method is that it is easy to interpret and explain. Investors like to speak in terms of annual percentage returns when evaluating investment possibilities.

Disadvantages

One disadvantage of using IRR is that it can be tedious to calculate. We knew the IRR was about 14% for the embroidery machine project because we had previously calculated the NPV for several discount rates. The IRR is about, but not exactly, 14%, because NPV is not exactly equal to zero (just very close to zero) when we use 14% as the discount rate. Before the prevalence of financial calculators and spreadsheets, calculating the exact IRR was difficult and time-consuming. With today’s technology, this is no longer a major consideration. Later in this chapter, we will look at how to use a spreadsheet to do these calculations.

No Single Mathematical Solution. Another disadvantage of using the IRR method is that there may not be a single mathematical solution to an IRR problem. This can happen when negative cash flows occur in more than one period in the project. Suppose your company is considering building a facility for an upcoming Olympic competition. The construction cost would be $350 million. The facility would be used for one year and generate cash inflows of $950 million. Then, the following year, your company would be required to convert the facility into a public park area for the city, which is expected to cost $620 million. Placing these cash flows in a timeline results in the following (Table 16.8):

Year 0 1 2
Cash Flow ($Millions) (350) 950 (620)
Table 16.8

The NPV profile for this project looks like Figure 16.3. The NPV is negative at low interest rates, becomes positive at higher interest rates, and then turns negative again as the interest rate continues to rise. Because the NPV profile line crosses the horizontal axis twice, there are two IRRs. In other words, there are two interest rates at which NPV equals zero.

Net present value graph for a project with two IRRs. It shows that the NPV is negative at low-interest rates, and becomes positive at higher interest rates. The NPV then turns negative again as the interest rate continues to rise. Because the NPV profile line crosses the horizontal axis twice, there are two IRRs.
Figure 16.3 NPV Profile Graph for a Project with Two IRRs

Reinvestment Rate Assumption. The IRR assumes that the cash flows are reinvested at the internal rate of return when they are received. This is a disadvantage of the IRR method. The firm may not be able to find any other projects with returns equal to a high-IRR project, so the company may not be able to reinvest at the IRR.

The reinvestment rate assumption becomes problematic when a company has several acceptable projects and is attempting to rank the projects. We will look more closely at the issues that can arise when considering mutually exclusive projects later in this chapter. If a company is simply deciding whether to accept a single project, the reinvestment assumption limitation is not relevant.

Overlooking Differences in Scale. Another disadvantage of using the IRR method to choose among various acceptable projects is that it ignores differences in scale. The IRR converts the cash flows to percentages and ignores differences in the size or scale of projects. Issues that occur when comparing projects of different scales are covered later in this chapter.

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