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2005, Pearson Prentice Hall CHAPTER 11 Capital Budgeting Decision Criteria

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CHAPTER 11 The Basics of Capital Budgeting Should we build this plant?

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What is capital budgeting? The process of planning for purchases of long-term assets. Analysis of potential additions to fixed assets. Long-term decisions; involve large expenditures, therefore irreversible once made. Very important to firm’s future.

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Capital Budgeting For example: Suppose our firm must decide whether to purchase a new plastic molding machine for $125,000. How do we decide? Will the machine be profitable? Will our firm earn a high rate of return on the investment?

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Decision-making Criteria in Capital Budgeting How do we decide if a capital investment project should be accepted or rejected?

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The ideal evaluation method should: a) include all cash flows that occur during the life of the project, b) consider the time value of money, and c) incorporate the required rate of return on the project. Decision-making Criteria in Capital Budgeting

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Steps to capital budgeting 1. Estimate CFs (inflows & outflows). 2. Assess riskiness of CFs. 3. Determine the appropriate cost of capital. 4. Find NPV and/or IRR. 5. Accept if NPV > 0 and/or IRR > WACC.

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What is the difference between independent and mutually exclusive projects? Independent projects – if the cash flows of one project are unaffected by the acceptance of the other projects. Mutually exclusive projects – if the cash flows of one project can be adversely impacted by the acceptance of the other project. These are a set of projects that perform essentially the same task, so that acceptance of one will necessarily mean rejection of the others.

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What is the difference between normal and nonnormal cash flow streams? Normal cash flow stream – Cost (negative CF) followed by a series of positive cash inflows. One change of signs. (- + + + + +) (- + + + + +) CF($)(500) 150 150 150 150 150 Year 0 1 2 3 4 5 Non-normal cash flow stream – Two or more changes of signs. Most common: Cost (negative CF), then string of positive CFs, then cost to close project.. (- + + - + +). Examples: Nuclear power plant, strip mine, etc. CF ($)(500) 200 100 (200) 400 300 Year 0 1 2 3 4 5

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Payback Period How long will it take for the project to generate enough cash to pay for itself? 012345 8 6 7 (500) 150 150 150 150 150 150 150 150

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Payback Period How long will it take for the project to generate enough cash to pay for itself? Payback period = 3.33 years (50/150 =0.33) 012345 8 6 7 (500) 150 150 150 150 150 150 150 150

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Is a 3.33 year payback period good? Is it acceptable? Firms that use this method will compare the payback calculation to some standard set by the firm. If our senior management had set a cut- off of 5 years for projects like ours, what would be our decision? Accept the project. Payback Period

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Further Example: Calculating payback Payback L = 2 + / = 2.375 years CF t -100 10 60 100 Cumulative -100 -90 0 50 012 3 = 2.4 3080 -30 Project L Payback S = 1 + / = 1.6 years CF t -100 70 100 20 Cumulative -100 0 20 40 012 3 = 1.6 3050 -30 Project S

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Strengths of payback Provides an indication of a project’s risk and liquidity. Easy to calculate and understand.

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Drawbacks of Payback Period Firm cutoffs are subjective. Does not consider time value of money. Does not consider any required rate of return. Ignores cash flows occurring after the payback period.

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Drawbacks of Payback Period Does not consider all of the project’s cash flows. Consider this cash flow stream! 012345 8 6 7 (500) 150 150 150 150 150 150 150 150

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Drawbacks of Payback Period Does not consider all of the project’s cash flows. This project is clearly unprofitable, but we would accept it based on a 4-year payback criterion! 012345 8 6 7 (500) 150 150 150 150 150 150 150 150

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Discounted Payback Uses discounted cash flows rather than raw cash flows. Discounts the cash flows at the firm’s required rate of return. Payback period is calculated using these discounted net cash flows. Problems: Cutoffs are still subjective. Still does not examine all cash flows.

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Discounted Payback 0 123 45 (500) 250 250 250 250 250 Discounted Discounted Year Cash FlowCF (14%) 0-500-500.00 0-500-500.00 1 250 219.30 1 year 1 250 219.30 1 year 280.70 280.70 2 250 192.37 2 years 2 250 192.37 2 years 88.33 88.33 3 250 168.74 3 250 168.74

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Discounted Payback 0 123 45 (500) 250 250 250 250 250 Discounted Discounted Year Cash FlowCF (14%) 0-500-500.00 0-500-500.00 1 250 219.30 1 year 1 250 219.30 1 year 280.70 280.70 2 250 192.37 2 years 2 250 192.37 2 years 88.33 (88.33/168.74)= 88.33 (88.33/168.74)= 3 250 168.74.52 years 3 250 168.74.52 years

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Discounted Payback 0 123 45 (500) 250 250 250 250 250 Discounted Discounted Year Cash FlowCF (14%) 0-500-500.00 0-500-500.00 1 250 219.30 1 year 1 250 219.30 1 year 280.70 280.70 2 250 192.37 2 years 2 250 192.37 2 years 88.33 88.33 3 250 168.74.52 years 3 250 168.74.52 years The Discounted Payback is 2.52 years

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Further Example: Discounted payback period Disc Payback L = 2 + / = 2.7 years CF t -100 10 60 80 Cumulative -100 -90.91 18.79 012 3 = 2.7 60.11 -41.32 PV of CF t -100 9.09 49.59 41.3260.11 10%

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Other Methods (Discounted Cash Flow Methods) 1) Net Present Value (NPV) 2) Profitability Index (PI) 3) Internal Rate of Return (IRR) Consider each of these decision-making criteria: All net cash flows. The time value of money. The required rate of return.

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NPV = the total PV of the annual net cash flows - the initial outlay. NPV = - IO FCF t FCF t (1 + k) t nt=1 Net Present Value

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Decision Rule: If NPV is positive, accept. If NPV is negative, reject.

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NPV Example Suppose we are considering a capital investment that costs $250,000 and provides annual net cash flows of $100,000 for five years. The firm’s required rate of return is 15%.

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NPV Example 0 1 2 3 4 5 (250,000) 100,000 100,000 100,000 100,000 100,000 Suppose we are considering a capital investment that costs $250,000 and provides annual net cash flows of $100,000 for five years. The firm’s required rate of return is 15%.

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Net Present Value NPV is just the PV of the annual cash flows minus the initial outflow. Mathematical Solution: PV of cash flows = $100,000(PVIFA15%,5) = $100,000(3.352) = $100,000(3.352) PV of cash flows = $335,216 PV of cash flows = $335,216 - Initial outflow ($250,000) - Initial outflow ($250,000) = Net PV $85,216 = Net PV $85,216

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EXAMPLE: What is Project S’s and L’s NPVs? Year CFs PVs CF L PV L 0-100-100 -$100.00 1 70 10 9.09 2 50 60 49.59 3 20 80 60.11 NPVs = $19.98NPV L = $ 18.79 (k = 10%)

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Rationale for the NPV method NPV= PV of inflows – Cost = Net gain in wealth If projects are independent, accept if the project NPV > 0. If projects are mutually exclusive, accept projects with the highest positive NPV, those that add the most value. In this example, we would accept S if the 2 projects are mutually exclusive (NPV s > NPV L ), and would accept both if they are independent projects.

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Profitability Index NPV = - IO FCF t (1 + k) t n t=1

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Profitability Index PI = IO FCF t (1 + k) n t=1 t NPV = - IO FCF t (1 + k) t n t=1

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Decision Rule: If PI is greater than or equal to 1, accept. If PI is less than 1, reject. Profitability Index

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Mathematical Solution PI = $335,216/$250,000 = 1.34 = 1.34 PI = IO FCF t (1 + k) n t=1 t

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Internal Rate of Return (IRR) IRR: The return on the firm’s invested capital. IRR is simply the rate of return that the firm earns on its capital budgeting projects.

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Internal Rate of Return (IRR) NPV = - IO FCF t (1 + k) t n t=1

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Internal Rate of Return (IRR) NPV = - IO FCF t (1 + k) t n t=1 n t=1 IRR: = IO FCF t (1 + IRR) t

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Internal Rate of Return (IRR) IRR is the rate of return that makes the PV of the cash flows equal to the initial outlay. This looks very similar to our Yield to Maturity formula for bonds. In fact, YTM is the IRR of a bond. n t=1 IRR: = IO FCF t (1 + IRR) t

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Calculating IRR Looking again at our problem: The IRR is the discount rate that makes the PV of the projected cash flows equal to the initial outlay. 0 1 2 3 4 5 (250,000) 100,000 100,000 100,000 100,000 100,000

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IRR with your Calculator IRR is easy to find with your financial calculator. Just enter the cash flows as you did with the NPV problem and solve for IRR. You should get IRR = 28.65%!

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IRR Decision Rule: If IRR is greater than or equal to the required rate of return, accept. If IRR is less than the required rate of return, reject.

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IRR Acceptance Criteria If IRR > k, accept project. If IRR < k, reject project. If projects are independent, accept both projects, if both projects’ IRR > k. If projects are mutually exclusive, accept the project with the higher IRR.

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IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +) Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +) 0 1 2 3 4 5 (500) 200 100 (200) 400 300 1 2 3

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Rationale for the IRR method If IRR > WACC, the project’s rate of return is greater than its costs. There is some return left over to boost stockholders’ returns.

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Summary Problem Enter the cash flows only once. Find the IRR. Using a discount rate of 15%, find NPV. Add back IO and divide by IO to get PI. 0 1 2 3 4 5 (900) 300 400 400 500 600

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Summary Problem IRR = 34.37%. Using a discount rate of 15%, NPV = $510.52. NPV = $510.52. PI = 1.57. 0 1 2 3 4 5 (900) 300 400 400 500 600

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NPV Profiles A graphical representation of project NPVs at various different costs of capital. k NPV L NPV S k NPV L NPV S 0$50$40 0$50$40 5 33 29 5 33 29 10 19 20 15 7 12 20 (4) 5

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Drawing NPV profiles -10 0 10 20 30 40 50 60 5 10 152023.6 NPV ($) Discount Rate (%) IRR L = 18.1% IRR S = 23.6% Crossover Point = 8.7% S L...........

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Comparing the NPV and IRR methods If projects are independent, the two methods always lead to the same accept/reject decisions. If projects are mutually exclusive … If k > crossover point, the two methods lead to the same decision and there is no conflict. If k < crossover point, the two methods lead to different accept/reject decisions.

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Finding the crossover point (using financial calculator) 1. Find cash flow differences between the projects for each year. 2. Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68%, rounded to 8.7%. 3. Can subtract S from L or vice versa, but better to have first CF negative. 4. If profiles don’t cross, one project dominates the other.

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Reasons why NPV profiles cross Size (scale) differences – the smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high k favors small projects (Project S with higher NPV). Timing differences – the project with faster payback provides more CFs in early years for reinvestment. If k is high, early CF especially good, NPV S > NPV L. (CF L =-100, +10, +60, +80; NPV=18.79) (CFs = -100, +70, +50, +20; NPV = $19.98)

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Reinvestment rate assumptions NPV method assumes CFs are reinvested at k, the opportunity cost of capital. IRR method assumes CFs are reinvested at IRR. Assuming CFs are reinvested at the opportunity cost of capital is more realistic, so NPV method is the best. NPV method should be used to choose between mutually exclusive projects. Perhaps a hybrid of the IRR that assumes cost of capital reinvestment is needed.

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Since managers prefer the IRR to the NPV method, is there a better IRR measure? Yes, Modified Internal Rate of Return (MIRR). IRR assumes that all cash flows are reinvested at the IRR. MIRR provides a rate of return measure that assumes cash flows are reinvested at the required rate of return (or WACC). MIRR is the discount rate that causes the PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by compounding inflows at WACC.

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MIRR Steps: Calculate the PV of the cash outflows. Using the required rate of return. Calculate the FV of the cash inflows at the last year of the project’s time line. This is called the terminal value (TV). Using the required rate of return. MIRR: the discount rate that equates the PV of the cash outflows with the PV of the terminal value, ie, that makes: PV outflows = PV inflows

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MIRR Using our time line and a 15% rate: PV outflows = (900). FV inflows (at the end of year 5) = 2,837. MIRR: FV = 2837, PV = (900), N = 5. Solve: I = 25.81%. 0 1 2 3 4 5 (900) 300 400 400 500 600

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Using our time line and a 15% rate: PV outflows = (900). FV inflows (at the end of year 5) = 2,837. MIRR: FV = 2837, PV = (900), N = 5. Solve: I = 25.81%. Conclusion: The project’s IRR of 34.37% assumes that cash flows are reinvested at 34.37%. Assuming a reinvestment rate of 15%, the project’s MIRR is 25.81%. MIRR

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