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**Chapter 2 Capital Budgeting**

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1. Introduction Capital budgeting is the allocation of funds to long-lived capital projects. A capital project is a long-term investment in tangible assets. The principles and tools of capital budgeting are applied in many different aspects of a business entity’s decision making and in security valuation and portfolio management. A company’s capital budgeting process and prowess are important in valuing a company. LOS: Describe the capital budgeting process, including the typical steps of the process, and distinguish among the various categories of capital projects. Page 48 1. Introduction The word “capital” implies long term. Capital funds are long-term sources of funds (notes, bonds, and stocks). Capital budgeting is investing in long-lived assets. Working capital are the funds necessary to support the operation of the long-lived assets. Copyright © 2013 CFA Institute

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**2. The capital budgeting process**

Generating Ideas Step 1 Generate ideas from inside or outside of the company Analyzing Individual Proposals Step 2 Collect information and analyze the profitability of alternative projects Planning the Capital Budget Step 3 Analyze the fit of the proposed projects with the company’s strategy Monitoring and Post Auditing Step 4 Compare expected and realized results and explain any deviations LOS: Describe the capital budgeting process, including the typical steps of the process, and distinguish among the various categories of capital projects. Page 49 2. The Capital Budgeting Process The capital budgeting process requires analyzing many ideas and identifying the profitable projects that fit with the company’s strategy. Copyright © 2013 CFA Institute

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**Classifying projects Replacement Projects Expansion Projects**

New Products and Services Regulatory, Safety, and Environmental Projects Other LOS: Describe the capital budgeting process, including the typical steps of the process, and distinguish among the various categories of capital projects. Pages 49–50 Classifying Projects Replacement projects: Existing assets are replaced with similar assets. Example: A manufacturing company replacing equipment on an assembly line Expansion projects: Increase the size of the business. Example: Wal-Mart opening a new retail outlet New products and services: These create greater uncertainties; hence, more attention may be required in the analysis of these projects. Example: Apple’s initial introduction of the iPhone Regulatory, safety, and environmental projects: Generally are mandatory projects, but the company may have choices in how to satisfy requirements. If sufficiently costly, shutdown is an alternative. Also referred to as mandated projects. Other: These may include projects that are difficult to analyze (e.g., research and development [R&D]). Note: R&D expenses are sunk costs, but the decision to embark on R&D for the development of a project is itself a capital project. Copyright © 2013 CFA Institute

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**3. Basic principles of Capital Budgeting**

Decisions are based on cash flows. The timing of cash flows is crucial. Cash flows are incremental. Cash flows are on an after-tax basis. Financing costs are ignored. LOS: Describe the basic principles of capital budgeting, including cash flow estimation. Pages 50–52 3. Basic Principles of Capital Budgeting Principles Decisions are based on cash flows, not accounting income. The timing of cash flows is crucial; that is, the time value of money is important. Cash flows are incremental; that is, cash flows are based on opportunity costs. Cash flows are on an after-tax basis because cash flows related to taxes (payments or benefits) are part of the cash flows that must be analyzed. Financing costs are ignored in the cash flow analysis. Financing costs enter the decision making through the required rate of return. Copyright © 2013 CFA Institute

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**Costs: include or exclude?**

A sunk cost is a cost that has already occurred, so it cannot be part of the incremental cash flows of a capital budgeting analysis. An opportunity cost is what would be earned on the next-best use of the assets. An incremental cash flow is the difference in a company’s cash flows with and without the project. An externality is an effect that the investment project has on something else, whether inside or outside of the company. Cannibalization is an externality in which the investment reduces cash flows elsewhere in the company (e.g., takes sales from an existing company project). LOS: Describe the basic principles of capital budgeting, including cash flow estimation. Pages 51–52 Costs: Include or Exclude? Examples: Sunk cost: Using a building that would otherwise be idle. The cost of the building is a sunk cost. Opportunity cost: Using a building that could otherwise be rented to another business. Incremental cash flow: Change in sales of the company from a new product. Externality: A project has the effect of reducing the unemployment rate of the town in which the company invests in this project. Cannibalization: An externality in which the investment reduces cash flows elsewhere in the company. For example, a soup producer introduces a new soup that results in lower sales of an existing soup. Discussion question: Suppose a company is investing in research and development to develop new products. Would any of the R&D costs be relevant for the capital budgeting decision pertaining to a new product that results from this R&D? Copyright © 2013 CFA Institute

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**Conventional and nonconventional cash flows**

Conventional Cash Flow (CF) Patterns Today 1 2 3 4 5 | –CF +CF LOS: Describe the basic principles of capital budgeting, including cash flow estimation. Page 51–52 Conventional and Nonconventional Cash Flows Conventional Cash Flow Patterns What is conventional? Only one sign change. No cash flow (e.g., $0) is not viewed as a sign change. Copyright © 2013 CFA Institute

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**Conventional and nonconventional cash flows**

Nonconventional Cash Flow Patterns Today 1 2 3 4 5 | –CF +CF LOS: Describe the basic principles of capital budgeting, including cash flow estimation. Pages 51–52 Conventional and Nonconventional Cash Flows Nonconventional Cash Flow Patterns Where do the negative cash flows come from? Investment Shut-down costs Environment mitigation Copyright © 2013 CFA Institute

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**Independent vs. mutually exclusive projects**

When evaluating more than one project at a time, it is important to identify whether the projects are independent or mutually exclusive This makes a difference when selecting the tools to evaluate the projects. Independent projects are projects in which the acceptance of one project does not preclude the acceptance of the other(s). Mutually exclusive projects are projects in which the acceptance of one project precludes the acceptance of another or others. LOS: Explain how the evaluation and selection of capital projects is affected by mutually exclusive projects, project sequencing, and capital rationing. Page 52 Independent vs. Mutually Exclusive Projects Mutually exclusive projects: The acceptance of one project precludes the acceptance of the other project(s). Example: An airline requires a single jet for a new route. The airline can buy a jet from Boeing or Airbus, but cannot buy one from each. Independent projects: The acceptance of one project does not affect the acceptance of another project. Example: A large conglomerate is introducing a new soup and a new peanut butter substitute. Discussion question: A company is evaluating the purchase of a new drying system for its production line. One system uses gas heat, whereas the other uses electric lamps. Are these systems mutually exclusive or independent projects? Why? Copyright © 2013 CFA Institute

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Project sequencing Capital projects may be sequenced, which means a project contains an option to invest in another project. Projects often have real options associated with them; so the company can choose to expand or abandon the project, for example, after reviewing the performance of the initial capital project. LOS: Explain how the evaluation and selection of capital projects is affected by mutually exclusive projects, project sequencing, and capital rationing. Page 52 Project Sequencing Capital sequencing is a situation in which one project’s acceptance is conditional on another project’s success. Capital sequencing is, essentially, when a project includes an option on future, related projects. Example: An entertainment company may release a children’s movie, but wait to introduce the related toy line until the performance of the movie is assessed. Copyright © 2013 CFA Institute

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Capital rationing Capital rationing is when the amount of expenditure for capital projects in a given period is limited. If the company has so many profitable projects that the initial expenditures in total would exceed the budget for capital projects for the period, the company’s management must determine which of the projects to select. The objective is to maximize owners’ wealth, subject to the constraint on the capital budget. Capital rationing may result in the rejection of profitable projects. LOS: Explain how the evaluation and selection of capital projects is affected by mutually exclusive projects, project sequencing, and capital rationing. Page 52 Capital Rationing Capital rationing exists when there is a limit on how much can be spent on capital projects. Capital rationing is not consistent with owners’ wealth maximization. Capital rationing may be imposed artificially (e.g., a company’s board permits only $100 million on capital projects per period) or be due to capital constraints (e.g., credit crunch). Copyright © 2013 CFA Institute

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**4. Investment decision criteria**

Net Present Value (NPV) Internal Rate of Return (IRR) Payback Period Discounted Payback Period Average Accounting Rate of Return (AAR) Profitability Index (PI) LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Investment Decision Criteria Net present value (NPV) Internal rate of return (IRR) Payback period Discounted payback period Average accounting rate of return (AAR) Profitability index (PI) Copyright © 2013 CFA Institute

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**Net present Value If NPV > 0: Invest: Capital project adds value**

The net present value is the present value of all incremental cash flows, discounted to the present, less the initial outlay: NPV = t=1 n CF t (1+r) t − Outlay (2-1) Or, reflecting the outlay as CF0, NPV = t=0 n CF t (1+r) t (2-2) where CFt = After-tax cash flow at time t r = Required rate of return for the investment Outlay = Investment cash flow at time zero If NPV > 0: Invest: Capital project adds value If NPV < 0: Do not invest: Capital project destroys value LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Pages 52–53 Net Present Value The net present value is the difference between the present value of the inflows and the present value of the outflows (hence, net). If the outlays occur over more than one period, they are discounted to the present and then this present value is used in Equation 2-1. The net present value is the estimate of how much the value of the firm changes with the adoption of the project. NPV is the estimate of the value added (or destroyed if negative). Note: When NPV = 0, we are indifferent between accepting and rejecting the project. Advantages Easy to understand (i.e., value added) Considers the time value of money Considers all project cash flows Disadvantages Result is a monetary amount, not a return Copyright © 2013 CFA Institute

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Example: NPV Consider the Hoofdstad Project, which requires an investment of $1 billion initially, with subsequent cash flows of $200 million, $300 million, $400 million, and $500 million. We can characterize the project with the following end-of-year cash flows: What is the net present value of the Hoofdstad Project if the required rate of return of this project is 5%? Period Cash Flow (millions) –$1,000 1 200 2 300 3 400 4 500 LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Pages 52–53 Example: NPV Copyright © 2013 CFA Institute

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**Example: NPV Time Line Solving for the NPV:**

NPV = $ million 1 2 3 4 | –$1,000 $200 $300 $400 $500 LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Pages 52–53 Example: NPV Copyright © 2013 CFA Institute

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**Internal rate of return**

The internal rate of return is the rate of return on a project. The internal rate of return is the rate of return that results in NPV = 0. t=1 n CF t (1 + IRR) t − Outlay = 0 (2-3) Or, reflecting the outlay as CF0, t=0 n CF t (1 + IRR) t = 0 (2-4) If IRR > r (required rate of return): Invest: Capital project adds value If IRR < r: Do not invest: Capital project destroys value LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Pages 53–55 Internal Rate of Return The internal rate of return is the geometric average return on a project. Advantages Easy to understand (i.e., return) Considers the time value of money Considers all project cash flows Disadvantages Solved iteratively Copyright © 2013 CFA Institute

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Example: IRR Consider the Hoofdstad Project that we used to demonstrate the NPV calculation: The IRR is the rate that solves the following: Period Cash Flow (millions) –$1,000 1 200 2 300 3 400 4 500 LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Pages 53–55 Example: IRR $0 = −$1, $ IRR $ IRR $ IRR $ IRR 4 Copyright © 2013 CFA Institute

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**A note on solving for IRR**

The IRR is the rate that causes the NPV to be equal to zero. The problem is that we cannot solve directly for IRR, but rather must either iterate (trying different values of IRR until the NPV is zero) or use a financial calculator or spreadsheet program to solve for IRR. In this example, IRR = %: $0 = −$1, $ $ $ $ LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Pages 53–55 A Note on Solving for IRR If using iteration, at 12%, NPV = $20.20 at 13%, NPV = ($4.19) Therefore, we know that the IRR is between 12% and 13% and likely closest to 13%. Using a financial calculator (e.g., HP 12c): 1000 +/– CF0 200 CFt 300 CFt 400 CFt 500 CFt IRR Using Excel: =IRR(B3:B7) where B3 through B7 contain the cash flows in time order (–1000 in B3, 200 in B4, etc.). Copyright © 2013 CFA Institute

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Payback Period The payback period is the length of time it takes to recover the initial cash outlay of a project from future incremental cash flows. In the Hoofdstad Project example, the payback occurs in the last year, Year 4: Period Cash Flow (millions) Accumulated Cash flows –$1,000 1 200 –$800 2 300 –$500 3 400 –$100 4 500 +400 LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Payback Period The payback period is how long it takes to get the original investment back, in terms of undiscounted cash flows. Advantages Easy to calculate Easy to understand Disadvantages Ignores the time value of money Ignores the cash flows beyond the payback period Copyright © 2013 CFA Institute

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**Payback Period: Ignoring Cash Flows**

For example, the payback period for both Project X and Project Y is three years, even through Project X provides more value through its Year 4 cash flow: Year Project X Cash Flows Project Y –£100 1 £20 2 £50 3 £45 4 £60 £0 LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Payback Period: Ignoring Cash Flows The payback period does not consider projects’ cash flows beyond the payback period. Discussion question: Is the payback period method consistent with shareholder wealth maximization? Why or why not? Copyright © 2013 CFA Institute

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**Discounted Payback Period**

The discounted payback period is the length of time it takes for the cumulative discounted cash flows to equal the initial outlay. In other words, it is the length of time for the project to reach NPV = 0. LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Page 57 Discounted Payback Period The discounted payback period is how long it takes to recover the initial investment in terms of discounted cash flows. If a project does not payback in terms of the discounted cash flows, then its NPV is negative. Advantages Easy to understand Considers the time value of money Disadvantages Ignores cash flows beyond the payback period No criteria for making a decision other than whether a project pays back Copyright © 2013 CFA Institute

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**Example: Discounted Payback Period**

Consider the example of Projects X and Y. Both projects have a discounted payback period close to three years. Project X actually adds more value but is not distinguished from Project Y using this approach. Cash Flows Discounted Accumulated Discounted Year Project X Project Y –£100.00 1 20.00 19.05 –80.95 2 50.00 45.35 –35.60 3 45.00 38.87 3.27 4 60.00 0.00 49.36 52.63 LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Example: Discounted Payback Period Copyright © 2013 CFA Institute

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**Average Accounting rate of return**

The average accounting rate of return (AAR) is the ratio of the average net income from the project to the average book value of assets in the project: AAR = Average net income Average book value LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Page 58 Average Accounting Rate of Return The average accounting rate of return is the return on equity for the project. Advantages Easy to calculate Easy to understand Disadvantages Not based on cash flows Ignores the time value of money No objective decision criteria Calculated different ways Copyright © 2013 CFA Institute

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Profitability index The profitability index (PI) is the ratio of the present value of future cash flows to the initial outlay: PI = Present value of future cash flows Initial investment = 1 + NPV Initial investment (2-5) If PI > 1.0: Invest Capital project adds value If PI < 0: Do not invest Capital project destroys value LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Pages 58–59 Profitability Index The profitability index is the ratio of the present value of the future cash inflows to the present value of the cash outlays. In a simple project, all outlays are completed in the initial period, so no discounting is necessary. Copyright © 2013 CFA Institute

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Example: PI In the Hoofdstad Project, with a required rate of return of 5%, the present value of the future cash flows is $1, Therefore, the PI is: PI = $1, $1, = 1.219 Period Cash Flow (millions) -$1,000 1 200 2 300 3 400 4 500 LOS: Calculate and interpret the results using each of the following methods to evaluate a single capital project: net present value (NPV), internal rate of return (IRR), payback period, discounted payback period, average accounting rate of return (AAR), and profitability index (PI). Pages 58–59 Example: PI Note: The sum of the present value of future cash flows = $ = $1, Discussion question: What is the relationship between the NPV and the PI in terms of decision making? Copyright © 2013 CFA Institute

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**Net present value profile**

The net present value profile is the graphical illustration of the NPV of a project at different required rates of return. LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. Page 59–61 Net Present Value Profile The NPV profile is an illustration of the NPV at different required rates of return. Copyright © 2013 CFA Institute

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**NPV Profile: Hoofdstad Capital project**

LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. Page 59–61 NPV Profile: Hoofdstad Capital Project Copyright © 2013 CFA Institute

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**NPV Profile: Hoofdstad Capital project**

LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. Page 59–61 NPV Profile: Hoofdstad Capital Project Items to note: Sum of all cash flows = $400 (intersection of profile with vertical axis). Internal rate of return is % (NPV = 0 at this rate). Relationship between NPV and required rate of return is curvilinear, reflecting compound interest (i.e., not a straight line). Copyright © 2013 CFA Institute

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**Ranking conflicts: NPV vs. IRR**

The NPV and IRR methods may rank projects differently. If projects are independent, accept if NPV > 0 produces the same result as when IRR > r. If projects are mutually exclusive, accept if NPV > 0 may produce a different result than when IRR > r. The source of the problem is different reinvestment rate assumptions Net present value: Reinvest cash flows at the required rate of return Internal rate of return: Reinvest cash flows at the internal rate of return The problem is evident when there are different patterns of cash flows or different scales of cash flows. LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. Pages 61–65 Ranking conflicts: NPV vs. IRR Ranking conflicts arise when comparing mutually exclusive projects (not an issue for independent projects). Copyright © 2013 CFA Institute

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**Example: Ranking conflicts**

Consider two mutually exclusive projects, Project P and Project Q: Which project is preferred and why? Hint: It depends on the projects’ required rates of return. End of Year Cash Flows Year Project P Project Q –100 1 33 2 3 4 142 LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. Pages 61–65 Example: Ranking Conflicts Copyright © 2013 CFA Institute

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**Decision at various required rates of return**

Project P Project Q Decision 0% $42 $32 Accept P, Reject Q 4% $21 $20 6% $12 $14 Reject P, Accept Q 10% –$3 $5 14% –$16 –$4 Reject P, Reject Q IRR 9.16% 12.11% LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. Page 64, Similar to Exhibits 2-12 and 2-13 Decision at Various Required Rates of Return This example demonstrates how the decision changes, depending on the project’s cost of capital, and how choosing on the basis of the IRR may not be optimal. Copyright © 2013 CFA Institute

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**NPV Profiles: Project P and Project Q**

LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. Pages 61–65 NPV Profiles: Project P and Project Q Issue: For required rates of return less than 4.89%, Project P is preferred (that is, higher NPV). For required rates of return between 4.89% and 12.11%, Project Q is preferred. For required rates of return above 12.11%, both projects are rejected. Copyright © 2013 CFA Institute

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**The multiple IRR problem**

If cash flows change sign more than once during the life of the project, there may be more than one rate that can force the present value of the cash flows to be equal to zero. This scenario is called the “multiple IRR problem.” In other words, there is no unique IRR if the cash flows are nonconventional. LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. Pages 65–68 The Multiple IRR Problem When there is more than one sign change, there may be more than one rate that results in NPV = 0. When there are multiple IRRs, each one is meaningless. Copyright © 2013 CFA Institute

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**Example: The multiple IRR problem**

Consider the fluctuating capital project with the following end of year cash flows, in millions: What is the IRR of this project? Year Cash Flow –€550 1 €490 2 3 4 –€940 LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. Pages 65–68 Example: The Multiple IRR Problem Copyright © 2013 CFA Institute

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**Example: The Multiple IRR Problem**

LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. Pages 65–68 Example: The Multiple IRR Problem The multiple IRR problem: There are two rates that solve the problem NPV = 0. There is no unique IRR, so the IRR is not useful as a decision criteria. Copyright © 2013 CFA Institute

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**Popularity and usage of capital budgeting methods**

In terms of consistency with owners’ wealth maximization, NPV and IRR are preferred over other methods. Larger companies tend to prefer NPV and IRR over the payback period method. The payback period is still used, despite its failings. The NPV is the estimated added value from investing in the project; therefore, this added value should be reflected in the company’s stock price. LOS: Explain the NPV profile, compare NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods. LOS: Describe the relative popularity of the various capital budgeting methods and explain the relation between NPV and company value and stock price. Pages 68–70 Popularity and Usage of Capital Budgeting Methods The NPV and IRR methods are used most often (from survey evidence). The payback period’s popularity may be because it is often used as a first-pass method, screening out projects that obviously will not be profitable. Copyright © 2013 CFA Institute

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5. Cash flow projections The goal is to estimate the incremental cash flows of the firm for each year in the project’s useful life. 1 2 3 4 5 | Investment Outlay After-Tax Operating Cash Flow + Terminal Nonoperating Cash Flow = Total After-Tax Cash Flow LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Pages 70–71 Cash Flow Projections This slide is the basic structure of the cash flows for a “normal” project, although actual cash flows for a project may have a different pattern (e.g., two years of outlay for a project). This structure is similar to Exhibit 2-19. Copyright © 2013 CFA Institute

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**Investment outlay Start with Capital expenditure Subtract**

Increase in working capital Equals Initial outlay LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Pages 72–74 Investment Outlay The initial outlay is the net cash flows for acquiring and setting up/installing the assets, as well as any working capital adjustments. Increases in working capital asset accounts are negative cash flows (e.g., increase investment in raw materials). Decreases in working capital asset accounts are positive cash flows (e.g., more efficient operation and thus less raw material on hand). Increases in working capital liability accounts are positive cash flows (e.g., taking advantage of trade credit will free up cash flows). Decreases in working capital liability accounts are negative cash flows. (e.g., less favorable credit terms would encourage the company to pay sooner). Copyright © 2013 CFA Institute

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**After-tax operating cash flow**

Start with Sales Subtract Cash operating expenses Depreciation Equals Operating income before taxes Taxes on operating income Operating income after taxes Plus After-tax operating cash flow LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Pages 72–74 After-Tax Operating Cash Flow The after-tax operating cash flow is similar to an income statement, but with depreciation added back in. The after-tax operating cash flow is often simply referred to as the operating cash flow. Copyright © 2013 CFA Institute

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**Terminal year after-tax nonoperating cash flow**

Start with After-tax salvage value Add Return of net working capital Equals Nonoperating cash flow LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Pages 72–74 Terminal Year After-Tax Nonoperating Cash Flow Terminal cash flows are those related to the disposition of the assets and return on working capital to pre-project levels. They are separate from any operating cash flows that occur in the same year. Copyright © 2013 CFA Institute

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**Formula approach Initial outlay**

Outlay = FCInv + NWCInv – Sal0 + T(Sal0 – B0) (6) After-tax operating cash flow CF = (S – C – D)(1 – T) + D CF = (S – C)(1 – T) + TD (7) (8) Terminal year after-tax nonoperating cash flow (TNOCF) TNOCF = SalT + NWCInv – T(SalT – BT) (9) LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Pages 72–74 Formula Approach If using formulas, the key is to consider all relevant incremental cash flows, whether related to making the investment, operating the project, or closing out the project. FCINV = Investment in new fixed capital S = Sales NWCInv = Investment in working capital C = Cash operating expenses Sal0 = Cash proceeds D = Depreciation B0 = Book value of capital T = Tax rate Copyright © 2013 CFA Institute

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**Example: Cash Flow analysis**

Suppose a company has the opportunity to bring out a new product, the Vitamin- Burger. The initial cost of the assets is $100 million, and the company’s working capital would increase by $10 million during the life of the new product. The new product is estimated to have a useful life of four years, at which time the assets would be sold for $5 million. Management expects company sales to increase by $120 million the first year, $160 million the second year, $140 million the third year, and then trailing to $50 million by the fourth year because competitors have fully launched competitive products. Operating expenses are expected to be 70% of sales, and depreciation is based on an asset life of three years under MACRS (modified accelerated cost recovery system). If the required rate of return on the Vitamin-Burger project is 8% and the company’s tax rate is 35%, should the company invest in this new product? Why or why not? LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Example: Cash Flow Analysis Copyright © 2013 CFA Institute

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**Example: Cash Flow Analysis**

Pieces: Investment outlay = –$100 – $10 = –$110 million. Book value of assets at end of four years = $0. Therefore, the $5 salvage represents a taxable gain of $5 million. Cash flow upon salvage = $5 – ($5 × 0.35) = $5 – 1.75 = $3.25 million. LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Example: Cash Flow Analysis Copyright © 2013 CFA Institute

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**Example: Cash Flow analysis**

Year Investment outlays Fixed capital –$100.00 Net working capital –10.00 Total –$110.00 LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Example: Cash Flow Analysis Common errors: Wrong sign on working capital investment Ignoring working capital investment Copyright © 2013 CFA Institute

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**Example: Cash Flow analysis**

Year 1 2 3 4 Annual after-tax operating cash flows Sales $120.00 $160.00 $140.00 $50.00 Cash operating expenses 84.00 112.00 98.00 35.00 Depreciation 33.33 44.45 14.81 7.41 Operating income before taxes $2.67 $3.55 $27.19 $7.59 Taxes on operating income 0.93 1.24 9.52 2.66 Operating income after taxes $1.74 $2.31 $17.67 $4.93 Add back depreciation After-tax operating cash flow $35.07 $46.76 $32.48 $12.34 LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Example: Cash Flow Analysis Common errors: Not adding back depreciation. Copyright © 2013 CFA Institute

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**Example: Cash Flow analysis**

Year 4 Terminal year after-tax nonoperating cash flows After-tax salvage value $3.25 Return of net working capital 10.00 Total terminal after-tax non-operating cash flows $13.25 LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Example: Cash Flow Analysis Common errors: Forgetting that the salvage value is an estimate of the cash flow from the sale of the assets Forgetting the tax on the sale: Sale is for more than book value ($0 in this case), so there is a cash outflow for taxes. Copyright © 2013 CFA Institute

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**Example: Cash Flow Analysis**

Year 1 2 3 4 Total after-tax cash flow –$110.00 $35.07 $46.76 $32.48 $25.59 Discounted value, at 8% $32.47 $40.09 $25.79 $18.81 Net present value $7.15 Internal rate of return 11.068% LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Example: Cash Flow Analysis Common errors: Not summing the relevant cash flows in the terminal year (terminal year nonoperating cash flows plus terminal year operating cash flows). Copyright © 2013 CFA Institute

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**6. More on cash flow projections**

Depreciation Issues Replacement Decisions Inflation LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Pages 74–81 6. More on Cash Flow Projections Issues: Depreciation Replacement decisions Inflation Copyright © 2013 CFA Institute

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**Relevant depreciation**

The relevant depreciation expense to use is the expense allowed for tax purposes. In the United States, the relevant depreciation is MACRS, which is a set of prescribed rates for prescribed classes (e.g., 3-year, 5-year, 7-year, and 10- year). MACRS is based on the declining balance method, with an optimal switch to straight-line and half of a year of depreciation in the first year. LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Pages 74–76 Relevant Depreciation The relevant depreciation is that for taxes because that is what affects cash flows (that is, reduce taxes by permitting a deduction for depreciation). United States Most of the depreciation under MACRS is based on the double-declining balance method (200DB), with a built-in switch to straight-line when it is optimal to do so. The assets with longer lives in MACRS use straight-line depreciation (i.e., for real estate). It would not usually be rational to depreciate at less than MACRS; exceptions may relate to financial distress situation whereby not all depreciation under MACRS can be used immediately. Because of the half-year convention (that is, half of a year’s worth of depreciation in the first year), there is always one more year of depreciation (four years for a three-year asset, six years for a five-year asset, etc.). Copyright © 2013 CFA Institute

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Example: MACRS Suppose a U.S. company is investing in an asset that costs $200 million and is depreciated for tax purposes as a five-year asset. The depreciation for tax purposes is (in millions): Year MACRS Rate Depreciation 1 20.00% $40.00 2 32.00% 64.00 3 19.20% 38.40 4 11.52% 23.04 5 6 5.76% 11.52 Total 100.00% $200.00 LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Pages 74–76 Example: MACRS To apply the rates, simply multiply the MACRS rate for the appropriate life and year by the cost of the asset. Note: A five-year asset has six years of depreciation under MACRS. This means that the book value of the asset for tax purposes is not equal to $0 until the end of Year 6. Copyright © 2013 CFA Institute

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**Present value of depreciation tax savings**

The cash flow generated from the deductibility of depreciation (which itself is a noncash expense) is the product of the tax rate and the depreciation expense. If the depreciation expense is $40 million, the cash flow from this expense is $40 million × Tax rate. The present value of these cash flows over the life of the project is the present value of tax savings from depreciation. LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Pages 74–77 Present Value of Depreciation Tax Savings The product of depreciation and the tax rate is often referred to as the “depreciation tax shield” because it is the amount of tax shielded by the deductibility of the noncash expense of depreciation. The present value of the depreciation tax savings is the value added from permitting depreciation. Copyright © 2013 CFA Institute

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**Present value of depreciation tax savings**

Continuing the example with the five-year asset, the company’s tax rate is 35% and the appropriate required rate of return is 10%.Therefore, the present value of the tax savings is $55.89 million. (in millions) Year MACRS Rate Depreciation Tax Savings Present Value of Depreciation 1 20.00% $40.00 $14.00 $12.73 2 32.00% 64.00 22.40 18.51 3 19.20% 38.40 13.44 10.10 4 11.52% 23.04 8.06 5.51 5 5.01 6 5.76% 11.52 4.03 $200.00 $69.99 $55.89 LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Page 77 Present Value of Depreciation Tax Savings This is similar to Exhibit 2-23. Present value of depreciation for one year = Cost of asset × MACRS rate × Tax rate × Discount factor. Copyright © 2013 CFA Institute

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**Cash flows for a replacement project**

When there is a replacement decision, the relevant cash flows expand to consider the disposition of the replaced assets: Incremental depreciation expense (old versus new depreciation) Other incremental operating expenses Nonoperating expenses Key: The relevant cash flows are those that change with the replacement. LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Pages 77–79 Cash Flows for a Replacement Project A replacement project requires determining incremental cash flows and considering the depreciation, salvage value, and so on for the replaced asset. Copyright © 2013 CFA Institute

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Spreadsheet modeling We can use spreadsheets (e.g., Microsoft Excel) to model the capital budgeting problem. Useful Excel functions: Data tables NPV IRR A spreadsheet makes it easier for the user to perform sensitivity and simulation analyses. LOS: Calculate the yearly cash flows of an expansion capital project and a replacement capital project, and evaluate how the choice of depreciation method affects those cash flows. Page 79 Spreadsheet Modeling Copyright © 2013 CFA Institute

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**Effects of inflation on capital budgeting analysis**

Issue: Although the nominal required rate of return reflects inflation expectations and sales and operating expenses are affected by inflation, The effect of inflation may not be the same for sales as operating expenses. Depreciation is not affected by inflation. The fixed cost nature of payments to bondholders may result in a benefit or a cost to the company, depending on inflation relative to expected inflation. LOS: Explain the effects of inflation on capital budgeting analysis. Page 81 Effects of Inflation on Capital Budgeting Analysis Fixed charges (e.g., depreciation) remain constant, but variable elements (e.g., sales price, operating costs) likely change with inflation. Inflation may not affect all variable elements in the same way; for example, the input and output prices may be affected differently by inflation. It is possible to analyze the project using all nominal flows or all real (that is, inflation-adjusted cash flows), but consistency is important (that is, cannot mix real and nominal). Discussion question: Why not simply use real interest rates and real cash flows? Copyright © 2013 CFA Institute

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**7. Project analysis and evaluation**

What if we are choosing among mutually exclusive projects that have different useful lives? What happens under capital rationing? How do we deal with risk? LOS: Evaluate and select the optimal capital project in situations of (1) mutually exclusive projects with unequal lives, using either the least common multiple of lives approach or the equivalent annual annuity approach, and (2) capital rationing. Page 82 Project Analysis and Evaluation What if we are choosing among mutually exclusive projects that have different useful lives? What happens under capital rationing? How do we deal with risk? Copyright © 2013 CFA Institute

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**Mutually exclusive projects with unequal lives**

When comparing projects that have different useful lives, we cannot simply compare NPVs because the timing of replacing the projects would be different, and hence, the number of replacements between the projects would be different in order to accomplish the same function. Approaches Determine the least common life for a finite number of replacements and calculate NPV for each project. Determine the annual annuity that is equivalent to investing in each project ad infinitum (that is, calculate the equivalent annual annuity, or EAA). LOS: Evaluate and select the optimal capital project in situations of (1) mutually exclusive projects with unequal lives, using either the least common multiple of lives approach or the equivalent annual annuity approach, and (2) capital rationing. Pages 82–84 Mutually Exclusive Projects with Unequal Lives Both the least common multiple life and the equivalent annual annuity methods will result in the same decision. Examples of least common multiple life: One project has a four-year life, the other has a five-year life. Least common multiple life is 20 years (three and four replacements, respectively). One project has a three-year life, the other has a five-year life. Least common multiple life is 15 years (four and two replacements, respectively). One project has a six-year life, the other has an eight-year life. Least common multiple life is 24 years (three and two replacements, respectively). The equivalent annuity approach requires calculating the payment that is equivalent to the NPV of the project, considering the useful life of the project. Example: If a four-year project has a NPV of $1,000 and a cost of capital of 10%, the EAA is $ (PV = $1,000; I = 10%; N = 4; solve for annuity PMT). Copyright © 2013 CFA Institute

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**Example: Unequal lives**

Consider two projects, Project G and Project H, both with a required rate of return of 5%: Which project should be selected, and why? End-of-Year Cash Flows Year Project G Project H –$100 1 30 38 2 39 3 40 4 NPV $6.38 $6.12 LOS: Evaluate and select the optimal capital project in situations of (1) mutually exclusive projects with unequal lives, using either the least common multiple of lives approach or the equivalent annual annuity approach, and (2) capital rationing. Page 82 Example: Unequal Lives Cannot make a decision based on the NPVs that are calculated using different lives: The projects are not on the same basis. Copyright © 2013 CFA Institute

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**Example: Unequal lives NPV with a Finite number of replacements**

Project G: Two replacements Project H: Three replacements 1 2 3 4 5 6 7 8 9 10 11 12 | Project G $6.38 Project H $6.12 LOS: Evaluate and select the optimal capital project in situations of (1) mutually exclusive projects with unequal lives, using either the least common multiple of lives approach or the equivalent annual annuity approach, and (2) capital rationing. Page 82 Example: Unequal Lives NPV with a Finite Number of Replacements Conclusion: Project H is preferred over Project G because it has a larger NPV considering a finite number of replacements. NPV of Project G: original, plus two replacements = $17.37 NPV of Project H: original, plus three replacements = $21.69 Copyright © 2013 CFA Institute

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**Example: Unequal lives Equivalent annual annuity**

Project G PV = $6.38 N = 4 I = 5% Solve for PMT PMT = $1.80 Project H PV = $6.12 N = 3 I = 5% Solve for PMT PMT = $2.25 LOS: Evaluate and select the optimal capital project in situations of (1) mutually exclusive projects with unequal lives, using either the least common multiple of lives approach or the equivalent annual annuity approach, and (2) capital rationing. Page 82 Example: Unequal Lives Equivalent Annual Annuity Therefore, Project H is preferred (higher equivalent annual annuity). Copyright © 2013 CFA Institute

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**Decision making under Capital rationing**

When there is capital rationing, the company may not be able to invest in all profitable projects. The key to decision making under capital rationing is to select those projects that maximize the total net present value given the limit on the capital budget. LOS: Evaluate and select the optimal capital project in situations of (1) mutually exclusive projects with unequal lives, using either the least common multiple of lives approach or the equivalent annual annuity approach, and (2) capital rationing. Pages 84–86 Decision Making under Capital Rationing Goal: Maximize the NPV from the set of projects, given the funds constraint. The capital rationing affects the total initial outlay for projects. Copyright © 2013 CFA Institute

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**Example: Capital rationing**

Consider the following projects, all with a required rate of return of 4%: Which projects, if any, should be selected if the capital budget is: $100? $200? $300? $400? $500? Project Initial Outlay NPV PI IRR One –$100 $20 1.20 15% Two –$300 $30 1.10 10% Three –$400 $40 8% Four –$500 $45 1.09 5% Five –$200 $15 1.08 LOS: Evaluate and select the optimal capital project in situations of (1) mutually exclusive projects with unequal lives, using either the least common multiple of lives approach or the equivalent annual annuity approach, and (2) capital rationing. Pages 84–86 Example: Capital Rationing Copyright © 2013 CFA Institute

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**Example: Capital rationing**

Possible decisions: Budget Choices NPV $100 One $20 $200 Two $15 $300 One + Five $35 $400 One + Two $50 Three $40 $500 One + Three $60 Four $45 Two + Five Optimal choices LOS: Evaluate and select the optimal capital project in situations of (1) mutually exclusive projects with unequal lives, using either the least common multiple of lives approach or the equivalent annual annuity approach, and (2) capital rationing. Pages 84–86 Example: Capital Rationing The first set of choices would be optimal because they result in the highest sum of NPV for the given budget. Key: Maximize the total net present value for any given budget. Copyright © 2013 CFA Institute

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**Risk analysis: Stand-alone methods**

Sensitivity analysis involves examining the effect on NPV of changes in one input variable at a time. Scenario analysis involves examining the effect on NPV of a set of changes that reflect a scenario (e.g., recession, normal, or boom economic environments). Simulation analysis (Monte Carlo analysis) involves examining the effect on NPV when all uncertain inputs follow their respective probability distributions. With a large number of simulations, we can determine the distribution of NPVs. LOS: Explain how sensitivity analysis, scenario analysis, and Monte Carlo simulation can be used to estimate the stand-alone risk of a capital project. Pages 86–92 Risk Analysis: Stand-Alone Methods Stand-alone risk is the risk of a project considered apart from all other projects of the same firm (as if this is a single-project firm). The distinction among sensitivity, scenario, and simulation analyses relates to how many of the uncertain inputs are allowed to vary. Sensitivity analysis: One variable Scenario analysis: Sets of variables that create a scenario Simulation analysis: All uncertain inputs whose distributions can be estimated All of this analysis presumes that possible variations of inputs can be estimated in some way. For example, with simulation analysis, we would need to know the probability distribution (e.g., mean, standard deviation, type of distribution) of all input variables that are specified to vary. Discussion question: There is a school of thought that the distributions analyzed should be of IRRs not NPV because the NPV assumes a risk-adjusted discount rate. What is the reasoning for arguing that we should be analyzing IRRs? What is the reasoning for arguing for analyzing NPVs? Copyright © 2013 CFA Institute

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**Risk analysis: Market risk methods**

The required rate of return, when using a market risk method, is the return that a diversified investor would require for the project’s risk. Therefore, the required rate of return is a risk-adjusted rate. We can use models, such as the CAPM or the arbitrage pricing theory, to estimate the required return. Using CAPM, ri = RF + βi [E(RM) – RF] (10) where ri = required return for project or asset i RF = risk-free rate of return βi = beta of project or asset i [E(RM) – RF] = market risk premium, the difference between the expected market return and the risk-free rate of return LOS: Explain the procedure for determining the discount rate to be used in valuing a capital project and calculate a project’s required rate of return using the capital asset pricing model (CAPM). Pages 92–95 Risk Analysis: Market Risk Methods We can use the CAPM to estimate the required rate of return (that is, cost of capital) of a project by using an estimate of the market risk of the project along with an estimated risk-free rate of interest and market risk premium. Example: If the risk-free rate is 3%, the market risk premium is 5%, and a project’s beta is estimated as 1.5, the risk-adjusted return is r = (1.2 × 0.05) = 0.09 or 9%. Note that the required rate of return is specific for a project and should reflect the market risk of the project. Using one rate for all projects, the firm’s cost of capital will result in: Rejecting profitable projects that are less risky than the average project and Accepting unprofitable projects that are more risky than the average project. Copyright © 2013 CFA Institute

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Real options A real option is an option associated with a real asset that allows the company to enhance or alter the project’s value with decisions some time in the future. Real option examples: Timing option: Allow the company to delay the investment Sizing option: Allow the company to expand, grow, or abandon a project Flexibility option: Allow the company to alter operations, such as changing prices or substituting inputs Fundamental option: Allow the company to alter its decisions based on future events (e.g., drill based on price of oil, continued R&D depending on initial results) LOS: Describe the types of real options and evaluate the profitability of investments with real options. Pages 95–99 Real Options A real option is an option embedded in a real asset (as differentiated from a financial asset). List of real options (nonexhaustive, but useful for discussion purposes): Abandon project Grow the project Expand the project Contract the project Shut down temporarily Delay investment Switch inputs Alter distribution systems Rainbow option (alter project based on both output price and demand uncertainties) Note: Most real options are complex options (i.e., more than one option); hence valuation is difficult. Copyright © 2013 CFA Institute

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**Alternative treatments for analyzing projects with real options**

Use NPV without considering real options; if positive, the real options would not change the decision. Estimate NPV = NPV – Cost of real options + Value of real options. Use decision trees to value the options at different decision junctures. Use option-pricing models, although the valuation of real options becomes complex quite easily. LOS: Describe the types of real options and evaluate the profitability of investments with real options. Pages 95–99 Alternative Treatments For Analyzing Projects With Real Options Key: Real options add value to a capital project (otherwise they would not be exercised). Copyright © 2013 CFA Institute

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**Common capital budgeting pitfalls**

Not incorporating economic responses into the investment analysis Misusing capital budgeting templates Pet projects Basing investment decisions on EPS, net income, or return on equity Using IRR to make investment decisions Bad accounting for cash flows Overhead costs Not using the appropriate risk-adjusted discount rate Spending all of the investment budget just because it is available Failure to consider investment alternatives Handling sunk costs and opportunity costs incorrectly LOS: Explain capital budgeting pitfalls. Pages 99–101 Common Capital Budgeting Pitfalls The pitfalls listed in Exhibit 2-34 are not all possible pitfalls, but illustrate the commonly mentioned problems. Key: Any time a company’s management deviates from methods that are consistent with owners’ wealth maximization, there is an issue. Many of the pitfalls arise from the agency relationship between managers and owners. Discussion question: Some companies have been noted for overpaying in acquisitions. Viewing the acquisition of another company as a capital budgeting problem, what pitfalls may apply in the case of mergers and acquisitions? Copyright © 2013 CFA Institute

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**8. Other income measures and valuation models**

In the basic capital budgeting model, we estimate the incremental cash flows associated with acquiring the assets, operating the project, and terminating the project. Once we have the incremental cash flows for each period of the capital project’s useful life, including the initial outlay, we apply the net present value or internal rate of return methods to evaluate the project. Other income measures are variations on the basic capital budgeting model. LOS: Calculate and interpret accounting income and economic income in the context of capital budgeting. Page 101 Other Income Measures and Valuation Models Income: Accounting income Economic income Models: Economic profit Residual income Claims valuation Copyright © 2013 CFA Institute

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**Economic and accounting income**

Focus on income Depreciation based on original cost Economic Income Focus on cash flow and change in market value Depreciation based on loss of market value Cash Flows for Capital Budgeting Focus on cash flow Depreciation based on tax basis LOS: Calculate and interpret accounting income and economic income in the context of capital budgeting. Page 101 Economic and Accounting Income Copyright © 2013 CFA Institute

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**Economic profit, residual income, and claims valuation**

Economic profit (EP) is the difference between net operating profit after tax (NOPAT) and the cost of capital (in monetary terms). EP = NOPAT – $WACC (12) Residual income (RI) is the difference between accounting net income and an equity charge. The equity charge reflects the required rate of return on equity (re) multiplied by the book value of equity (Bt-1). RIt = NIt – reBt–1 (15) Claims valuation is the division of the value of assets among security holders based on claims (e.g., interest and principal payments to bondholders). LOS: Distinguish among and evaluate a capital project using the economic profit, residual income, and claims valuation models. Pages 106–110 Economic Profit, Residual Income, and Claims Valuation There are many different valuation approaches available, and they will likely produce different valuations. The key is to use methods in decision making that are consistent with owners’ wealth maximization. Copyright © 2013 CFA Institute

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**Example: Economic vs. Accounting income**

Consider the Hoofdstad Project again, with the after-tax cash flows as before, plus additional information: What is this project’s economic and accounting income? Year 1 2 3 4 After-tax operating cash flow $35.07 $46.76 $32.48 $12.34 Beginning market value (project) $10.00 $15.00 $17.00 $19.00 Ending market value (project) $20.00 Debt $50.00 Book equity $47.74 $46.04 $59.72 $60.65 Market value of equity $55.00 $49.74 $48.04 $60.72 LOS: Calculate and interpret accounting income and economic income in the context of capital budgeting. Pages 102–105 Example: Economic vs. Accounting Income This analysis assumes an 8% before-tax cost of debt. Copyright © 2013 CFA Institute

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**Example: Economic vs. Accounting income**

Solution: Year 1 2 3 4 Economic income $40.07 $48.76 $34.48 $13.34 Accounting income –$2.26 –$1.69 $13.67 $0.93 LOS: Calculate and interpret accounting income and economic income in the context of capital budgeting. Pages 102–105 Example: Economic vs. Accounting Income Copyright © 2013 CFA Institute

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**Residual income method**

The residual income method requires: Estimating the return on equity; Estimating the equity charge, which is the product of the return on equity and the book value of equity; and Subtracting the equity charge from the net income. RIt = NIt – reBt–1 (15) where RIt = Residual income during period t NIt = Net income during period t reBt–1 = Equity charge for period t, which is the required rate of return on equity, re, times the beginning-of-period book value of equity, Bt–1 LOS: Distinguish among and evaluate a capital project using the economic profit, residual income, and claims valuation models. Pages 107–108 Residual Income Method The residual income is the difference between net income and the income expected by investors based on the required rate of return and the book value of equity. Discussion question: Why is the return on equity used in the calculation of the equity charge in the residual income method? Copyright © 2013 CFA Institute

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**Example: Residual Income Method**

Suppose the Boat Company has the following estimates, in millions: The residual income for each year, in millions: Year 1 2 3 4 Net income $46 $49 $56 Book value of equity $78 $81 $84 $85 Required rate of return on equity 12% Year 1 2 3 4 Step 1 Start with Book value of equity $78 $81 $84 $85 Multiply by Required rate of return on equity 12% Equals Required earnings on equity $9 $10 Step 2 Net income $46 $49 $56 Subtract 9 10 Residual income $37 $39 LOS: Distinguish among and evaluate a capital project using the economic profit, residual income, and claims valuation models. Pages 107–108 Example: Residual Income Method Copyright © 2013 CFA Institute

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**Example: Residual Method**

The present value of the residual income, discounted using the 12% required rate of return, is $126 million. This is an estimate of how much value a project will add (or subtract, if negative). LOS: Distinguish among and evaluate a capital project using the economic profit, residual income, and claims valuation models. Pages 107–108 Example: Residual Method Copyright © 2013 CFA Institute

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Claims Valuation The claims valuation method simply divides the “claims” of the suppliers of capital (creditors and owners) and then values the equity distributions. The claims of creditors are the interest and principal payments on the debt. The claims of the owners are the anticipated dividends. LOS: Distinguish among and evaluate a capital project using the economic profit, residual income, and claims valuation models. Pages 109–110 Claims Valuation The claims valuation method divides the cash flows of the company into those going to debtholders and those going to owners. We then value the claims going to owners. Copyright © 2013 CFA Institute

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**Example: Claims Valuation**

Suppose the Portfolio Company has the following estimates, in millions: What are the distributions to owners if dividends are 50% of earnings after principal payments? What is the value of the distributions to owners if the required rate of return is 12% and the before-tax cost of debt is 8%? Year 1 2 3 4 Cash flow before interest and taxes $80 $85 $95 Interest expense Cash flow before taxes $76 $82 $93 $94 Taxes 30 33 37 38 Operating cash flow $46 $49 $56 Principal payments $11 $12 $13 $14 LOS: Distinguish among and evaluate a capital project using the economic profit, residual income, and claims valuation models. Pages 109–110 Example: Claims Valuation The claims to debtholders: interest and principal repayments The claims to owners: the assumed equity distribution after principal payments are made Copyright © 2013 CFA Institute

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**Example: Claims Valuation**

1. Distributions to Owners: Year 1 2 3 4 Start with Interest expense $4 $3 $2 $1 Add Principal payments 11 12 13 14 Equals Total payments to bondholders $15 Operating cash flow $46 $49 $56 Subtract Principal payments to bondholders Cash flow after principal payments $35 $37 $43 $42 Multiply by Portion of cash flow distributed 50% Equity distribution $17 $19 $21 LOS: Distinguish among and evaluate a capital project using the economic profit, residual income, and claims valuation models. Pages 109–110 Example: Claims Valuation Copyright © 2013 CFA Institute

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**Example: Claims Valuation**

2. Value of Claims Present value of debt claims = $50 Present value of equity claims = $59 Therefore, the value of the firm = $109 LOS: Distinguish among and evaluate a capital project using the economic profit, residual income, and claims valuation models. Pages 109–110 Example: Claims Valuation For the present value of debt claims: PMT = $15; N = 4; I = 8%; Solve for PV. For the present value of equity claims: Cash flows: $17, $19, $21, $21; I = 12%; Solve for NPV. Copyright © 2013 CFA Institute

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**Traditional Capital Budgeting**

Comparison of methods Issue Traditional Capital Budgeting Economic Profit Residual Income Claims Valuation Uses net income or cash flow? Cash flow Net income Is there an equity charge? In the cost of capital In the cost of capital in dollar terms Using the required rate of return No Based on actual distributions to debtholders and owners? Yes LOS: Distinguish among and evaluate a capital project using the economic profit, residual income, and claims valuation models. Pages 106–110 Comparison of Methods Possible issue: Is claims valuation the same as contingent claims valuation? No. Contingent claims valuation (CCV) is the valuation of assets today based on a future event or events occurring. CCV uses option pricing to estimate the real options associated with a project. Copyright © 2013 CFA Institute

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9. Summary Capital budgeting is used by most large companies to select among available long-term investments. The process involves generating ideas, analyzing proposed projects, planning the budget, and monitoring and evaluating the results. Projects may be of many different types (e.g., replacement, new product), but the principles of analysis are the same: Identify incremental cash flows for each relevant period. Incremental cash flows do not explicitly include financing costs, but are discounted at a risk-adjusted rate that reflects what owners require. Methods of evaluating a project’s cash flows include the net present value, the internal rate of return, the payback period, the discounted payback period, the accounting rate of return, and the profitability index. Summary Copyright © 2013 CFA Institute

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Summary (continued) The preferred capital budgeting methods are the net present value, internal rate of return, and the profitability index. In the case of selecting among mutually exclusive projects, analysts should use the NPV method. The IRR method may be problematic when a project has a nonconventional cash flow pattern. The NPV is the expected added value from a project. We can look at the sensitivity of the NPV of a project using the NPV profile, which illustrates the NPV for different required rates of return. We can identify cash flows relating to the initial outlay, operating cash flows, and terminal, nonoperating cash flows. Inflation may affect the various cash flows differently, so this should be explicitly included in the analysis. 9. Summary Copyright © 2013 CFA Institute

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Summary (continued) When comparing projects that have different useful lives, we can either assume a finite number of replacements of each so that the projects have a common life or we can use the equivalent annual annuity approach. We can use sensitivity analysis, scenario analysis, or simulation to examine a project’s attractiveness under different conditions. The discount rate applied to cash flows or used as a hurdle in the internal rate of return method should reflect the project’s risk. We can use different methods, such as the capital asset pricing model, to estimate a project’s required rate of return. Most projects have some form of real options built in, and the value of a real option may affect the project’s attractiveness. There are valuation alternatives to traditional capital budgeting methods, including economic profit, residual income, and claims valuation. 9. Summary Copyright © 2013 CFA Institute

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