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4. Defining the IRR Calculating the IRR Advantages of the IRR Method Disadvantages of the IRR Method Multiple IRRs Modified IRR Internal Rate of Return Capital Budgeting > Internal Rate of Return Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance?campaign_content=book_192_section_93&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. The IRR of an investment is the discount rate at which the net present value of costs (negative cash flows) of the investment equals the net present value of the benefits (positive cash flows) of the investment. The higher a project's IRR, the more desirable it is to undertake the project. A firm (or individual) should, in theory, undertake all projects or investments available with IRRs that exceed the cost of capital. Investment may be limited by availability of funds to the firm and/or by the firm's capacity or ability to manage numerous projects. Defining the IRR Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/capital-budgeting-11/internal-rate-of-return-93/defining-the-irr-401- 4888?campaign_content=book_192_section_93&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess IRR View on Boundless.com Capital Budgeting > Internal Rate of Return

6. Given the (period, cash flow) pairs (n, Cn) where n is a positive integer, the total number of periods N, and the net present value NPV, the internal rate of return is given by the function in which NPV = 0. Any fixed time can be used in place of the present (e.g., the end of one interval of an annuity); the value obtained is zero if and only if the NPV is zero. If the IRR is greater than the cost of capital, accept the project. If the IRR is less than the cost of capital, reject the project. Calculating the IRR Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/capital-budgeting-11/internal-rate-of-return-93/calculating-the-irr-402- 6409?campaign_content=book_192_section_93&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Calculating IRR View on Boundless.com Capital Budgeting > Internal Rate of Return

7. The IRR method is very clear and easy to understand. An investment is considered acceptable if its internal rate of return is greater than an established minimum acceptable rate of return or cost of capital. The IRR method also uses cash flows and recognizes the time value of money. The internal rate of return is a rate quantity, an indicator of the efficiency, quality, or yield of an investment. Advantages of the IRR Method Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/capital-budgeting-11/internal-rate-of-return-93/advantages-of-the-irr-method- 403- 4845?campaign_content=book_192_section_93&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Internal rate of return View on Boundless.com Capital Budgeting > Internal Rate of Return

8. The first disadvantage of IRR method is that IRR, as an investment decision tool, should not be used to rate mutually exclusive projects, but only to decide whether a single project is worth investing in. IRR overstates the annual equivalent rate of return for a project whose interim cash flows are reinvested at a rate lower than the calculated IRR. IRR does not consider cost of capital; it should not be used to compare projects of different duration. In the case of positive cash flows followed by negative ones and then by positive ones, the IRR may have multiple values. Disadvantages of the IRR Method Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/capital-budgeting-11/internal-rate-of-return-93/disadvantages-of-the-irr- method-404- 874?campaign_content=book_192_section_93&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundle ss Disadvantage of IRR View on Boundless.com Capital Budgeting > Internal Rate of Return

9. In the case of positive cash flows followed by negative ones and then by positive ones, the IRR may have multiple values. It has been shown that with multiple internal rates of return, the IRR approach can still be interpreted in a way that is consistent with the present value approach provided that the underlying investment stream is correctly identified as net investment or net borrowing. NPV remains the "more accurate" reflection of value to the business. IRR, as a measure of investment efficiency may give better insights in capital constrained situations. However, when comparing mutually exclusive projects, NPV is the appropriate measure. Multiple IRRs Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/capital-budgeting-11/internal-rate-of-return-93/multiple-irrs-405- 4847?campaign_content=book_192_section_93&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess Multiple internal rates of return View on Boundless.com Capital Budgeting > Internal Rate of Return

10. MIRR is a modification of the internal rate of return (IRR) and as such aims to resolve some problems with the IRR. More than one IRR can be found for projects with alternating positive and negative cash flows, which leads to confusion and ambiguity. MIRR finds only one value. MIRR = {[FV(positive cash flows, reinvestment rate)/-PV(negative cash flows, finance rate)]^(1/n)}-1. Modified IRR Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/finance/textbooks/boundless-finance-textbook/capital-budgeting-11/internal-rate-of-return-93/modified-irr-406- 4850?campaign_content=book_192_section_93&campaign_term=Finance&utm_campaign=powerpoint&utm_medium=direct&utm_source=boundl ess MIRR View on Boundless.com Capital Budgeting > Internal Rate of Return

11. Free to share, print, make copies and changes. Get yours at www.boundless.com Appendix

12. Key terms capital budgeting The budgeting process in which a company plans its capital expenditure (the spending on assets of long-term value). cost of capital the rate of return that capital could be expected to earn in an alternative investment of equivalent risk duration A measure of the sensitivity of the price of a financial asset to changes in interest rates, computed for a simple bond as a weighted average of the maturities of the interest and principal payments associated with it effective interest rate The effective interest rate, effective annual interest rate, annual equivalent rate (AER), or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears. Modified Internal Rate of Return The modified internal rate of return (MIRR) is a financial measure of an investment's attractiveness. It is used in capital budgeting to rank alternative investments of equal size. As the name implies, MIRR is a modification of the internal rate of return (IRR) and, as such, aims to resolve some problems with the IRR. mutually exclusive Describing multiple events or states of being such that the occurrence of any one implies the non- occurrence of all the others. net present value profile a graph of the sum of all cash inflows and outflows adjusted for the time value of money at different discount rates reinvestment rate The annual yield at which cash flows from an investment can be reinvested. Free to share, print, make copies and changes. Get yours at www.boundless.com Capital Budgeting

13. Calculating IRR Cash flows and time Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Internal rate of return." GNU FDL http://en.wikipedia.org/wiki/Internal_rate_of_return View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Internal_rate_of_returnView on Boundless.com Capital Budgeting

14. Disadvantage of IRR NPV vs discount rate comparison for two mutually exclusive projects. Project A has a higher NPV (for certain discount rates), even though its IRR (= x- axis intercept) is lower than for project B Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Internal rate of return." GNU FDL http://en.wikipedia.org/wiki/Internal_rate_of_return View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Internal_rate_of_returnView on Boundless.com Capital Budgeting

15. Calculating IRR IRR is the rate at which NPV = 0. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Internal rate of return." GNU FDL http://en.wikipedia.org/wiki/Internal_rate_of_return View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Internal_rate_of_returnView on Boundless.com Capital Budgeting

16. Internal rate of return Internal rate of return is the rate at which the NPV of an investment equals 0. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia. "Klk-IR1a." CC BY-SA http://commons.wikimedia.org/wiki/File:Klk-IR1a.png View on Boundless.comCC BY-SAhttp://commons.wikimedia.org/wiki/File:Klk-IR1a.pngView on Boundless.com Capital Budgeting

17. Multiple internal rates of return As cash flows of a project change sign more than once, there will be multiple IRRs. NPV is a preferable metric in these cases. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikimedia. "Klk-IR3l." CC BY-SA http://commons.wikimedia.org/wiki/File:Klk-IR3l.png View on Boundless.comCC BY-SAhttp://commons.wikimedia.org/wiki/File:Klk-IR3l.pngView on Boundless.com Capital Budgeting

18. IRR Showing the position of the IRR on the graph of NPV(r) (r is labelled 'i' in the graph). Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Internal rate of return." GNU FDL http://en.wikipedia.org/wiki/Internal_rate_of_return View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Internal_rate_of_returnView on Boundless.com Capital Budgeting

19. Calculating IRR NPV formula with r as IRR Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Internal rate of return." GNU FDL http://en.wikipedia.org/wiki/Internal_rate_of_return View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Internal_rate_of_returnView on Boundless.com Capital Budgeting

20. MIRR The formula for calculating MIRR. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Modified internal rate of return." GNU FDL http://en.wikipedia.org/wiki/Modified_internal_rate_of_return View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Modified_internal_rate_of_returnView on Boundless.com Capital Budgeting

21. Free to share, print, make copies and changes. Get yours at www.boundless.com Capital Budgeting Which of the following is a way the internal rate of return (IRR) is used in capital budgeting? A) To determine the average annual return of an investment. B) All of these answers. C) As a means to compare the profitability of different investments. D) As the effective interest rate for savings and loans.

22. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Capital Budgeting Which of the following is a way the internal rate of return (IRR) is used in capital budgeting? A) To determine the average annual return of an investment. B) All of these answers. C) As a means to compare the profitability of different investments. D) As the effective interest rate for savings and loans.

23. Free to share, print, make copies and changes. Get yours at www.boundless.com Capital Budgeting A project has an initial investment requirement of $100,000. In year 1, it should earn $25,000; in year two, $30,000; and in year 3, $50,000. What is the project's internal rate of return? A) 5% B) 6.5% C) 6 D) 7.5%

24. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Capital Budgeting A project has an initial investment requirement of $100,000. In year 1, it should earn $25,000; in year two, $30,000; and in year 3, $50,000. What is the project's internal rate of return? A) 5% B) 6.5% C) 6 D) 7.5%

25. Free to share, print, make copies and changes. Get yours at www.boundless.com Capital Budgeting Which of the following describes an advantage the internal rate of return has over net present value for capital budgeting purposes? A) Internal rate of return is an indicator of the efficiency, quality or yield of an investment. B) The IRR method is clear an easy to understand. C) The IRR method recognizes the time value of money. D) All of these answers.

26. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Capital Budgeting Which of the following describes an advantage the internal rate of return has over net present value for capital budgeting purposes? A) Internal rate of return is an indicator of the efficiency, quality or yield of an investment. B) The IRR method is clear an easy to understand. C) The IRR method recognizes the time value of money. D) All of these answers.

27. Free to share, print, make copies and changes. Get yours at www.boundless.com Capital Budgeting In which of the following situations would it be appropriate to use the IRR method to make an investment decision? A) To compare two investments that have different durations. B) To compare two projects that have an equal initial investment. C) To assess a project which cash flows fluctuate between positive and negative. D) All of these answers.

28. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Capital Budgeting In which of the following situations would it be appropriate to use the IRR method to make an investment decision? A) To compare two investments that have different durations. B) To compare two projects that have an equal initial investment. C) To assess a project which cash flows fluctuate between positive and negative. D) All of these answers.

29. Free to share, print, make copies and changes. Get yours at www.boundless.com Capital Budgeting You are analyzing two different investments and will present your findings to company executives. Both projects have cash flows that alternate between positive and negative. Which budgeting method should you use to evaluate the projects? A) Modified Internal Rate of Return. B) Internal Rate of Return. C) Net Present Value. D) Payback period method.

30. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Capital Budgeting You are analyzing two different investments and will present your findings to company executives. Both projects have cash flows that alternate between positive and negative. Which budgeting method should you use to evaluate the projects? A) Modified Internal Rate of Return. B) Internal Rate of Return. C) Net Present Value. D) Payback period method.

31. Free to share, print, make copies and changes. Get yours at www.boundless.com Capital Budgeting Under the internal rate of return rule in capital budgeting, which of the following statements does not apply? A) The internal rate of return can vary throughout the life of a project. B) The cash inflows can be estimates. C) The internal rate of return can be equal to the cost of capital. D) The initial investment can cover the cost from purchasing new equipment.

32. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Saylor OER. "Business Administration « Saylor.org – Free Online Courses Built by Professors." CC BY 3.0 http://www.saylor.org/majors/Business/CC BY 3.0 http://www.saylor.org/majors/Business/ Capital Budgeting Under the internal rate of return rule in capital budgeting, which of the following statements does not apply? A) The internal rate of return can vary throughout the life of a project. B) The cash inflows can be estimates. C) The internal rate of return can be equal to the cost of capital. D) The initial investment can cover the cost from purchasing new equipment.

33. Free to share, print, make copies and changes. Get yours at www.boundless.com Capital Budgeting A project has a finance rate of 8% and a reinvestment rate of 10%. The project requires an initial investment of $10,000. In year one, it will have cash flows of $12,000; year two, -$5000; year three, $8000. What is the project's MIRR? A) 7.3% B) 18.4% C) 12.1% D) 5.8%

34. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Capital Budgeting A project has a finance rate of 8% and a reinvestment rate of 10%. The project requires an initial investment of $10,000. In year one, it will have cash flows of $12,000; year two, -$5000; year three, $8000. What is the project's MIRR? A) 7.3% B) 18.4% C) 12.1% D) 5.8%

35. Attribution Wikipedia. "Internal rate of return." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Internal_rate_of_returnCC BY-SA 3.0http://en.wikipedia.org/wiki/Internal_rate_of_return Wikipedia. "duration." CC BY-SA 3.0 http://en.wikipedia.org/wiki/durationCC BY-SA 3.0http://en.wikipedia.org/wiki/duration Wiktionary. "mutually exclusive." CC BY-SA 3.0 http://en.wiktionary.org/wiki/mutually+exclusiveCC BY-SA 3.0http://en.wiktionary.org/wiki/mutually+exclusive Wikipedia. "Internal rate of return." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Internal_rate_of_returnCC BY-SA 3.0http://en.wikipedia.org/wiki/Internal_rate_of_return Wikipedia. "cost of capital." CC BY-SA 3.0 http://en.wikipedia.org/wiki/cost%20of%20capitalCC BY-SA 3.0http://en.wikipedia.org/wiki/cost%20of%20capital Wikipedia. "capital budgeting." CC BY-SA 3.0 http://en.wikipedia.org/wiki/capital%20budgetingCC BY-SA 3.0http://en.wikipedia.org/wiki/capital%20budgeting Wikipedia. "Internal rate of return." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Internal_rate_of_returnCC BY-SA 3.0http://en.wikipedia.org/wiki/Internal_rate_of_return Wiktionary. "mutually exclusive." CC BY-SA 3.0 http://en.wiktionary.org/wiki/mutually+exclusiveCC BY-SA 3.0http://en.wiktionary.org/wiki/mutually+exclusive Wikipedia. "Modified Internal Rate of Return." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Modified%20Internal%20Rate%20of%20ReturnCC BY-SA 3.0 http://en.wikipedia.org/wiki/Modified%20Internal%20Rate%20of%20Return Wikipedia. "Modified internal rate of return." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Modified_internal_rate_of_returnCC BY-SA 3.0http://en.wikipedia.org/wiki/Modified_internal_rate_of_return Wikipedia. "cost of capital." CC BY-SA 3.0 http://en.wikipedia.org/wiki/cost%20of%20capitalCC BY-SA 3.0http://en.wikipedia.org/wiki/cost%20of%20capital Wikipedia. "reinvestment rate." CC BY-SA 3.0 http://en.wikipedia.org/wiki/reinvestment%20rateCC BY-SA 3.0http://en.wikipedia.org/wiki/reinvestment%20rate Wikipedia. "Internal rate of return." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Internal_rate_of_returnCC BY-SA 3.0http://en.wikipedia.org/wiki/Internal_rate_of_return Wikipedia. "effective interest rate." CC BY-SA 3.0 http://en.wikipedia.org/wiki/effective%20interest%20rateCC BY-SA 3.0http://en.wikipedia.org/wiki/effective%20interest%20rate Wikipedia. "Internal rate of return." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Internal_rate_of_returnCC BY-SA 3.0http://en.wikipedia.org/wiki/Internal_rate_of_return Wikipedia. "Net present value." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Net_present_valueCC BY-SA 3.0http://en.wikipedia.org/wiki/Net_present_value Wikipedia. "cost of capital." CC BY-SA 3.0 http://en.wikipedia.org/wiki/cost%20of%20capitalCC BY-SA 3.0http://en.wikipedia.org/wiki/cost%20of%20capital Free to share, print, make copies and changes. Get yours at www.boundless.com Capital Budgeting