You are comparing two potential mutually exclusive investment projects. You have calculated the expected NPV of project A to be $3758 and that of project B to be $3114. Can you be certain that you should recommend to your management to implement project
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Should we build this plant? CHAPTER 11 The Basics of Capital Budgeting
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What is capital budgeting? <ul><li>Analysis of potential additions to fixed assets. </li></ul><ul><li>Long-term decisions; involve large expenditures. </li></ul><ul><li>Very important to firm’s future. </li></ul>
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What is the difference between independent and mutually exclusive projects? <ul><li>Projects are: </li></ul><ul><li>independent , if the cash flows of one are unaffected by the acceptance of the other. </li></ul><ul><li>mutually exclusive , if the cash flows of one can be adversely impacted by the acceptance of the other. </li></ul>
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An Example of Mutually Exclusive Projects BRIDGE vs. BOAT to get products across a river.
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Normal Cash Flow Project: Cost (negative CF) followed by a series of positive cash inflows. One change of signs. Nonnormal Cash Flow Project: Two or more changes of signs. Most common: Cost (negative CF), then string of positive CFs, then cost to close project. Nuclear power plant, strip mine.
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Inflow (+) or Outflow (-) in Year 0 1 2 3 4 5 N NN - + + + + + N - + + + + - NN - - - + + + N + + + - - - N - + + - + - NN
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What is the payback period? The number of years required to recover a project’s cost, or how long does it take to get our money back?
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Payback for Project L (Long: Large CFs in later years) 10 60 0 1 2 3 -100 = CF t Cumulative -100 -90 -30 50 Payback L 2 + 30/80 = 2.375 years 0 100 2.4 80
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Project S (Short: CFs come quickly) 70 20 50 0 1 2 3 -100 CF t Cumulative -100 -30 20 40 Payback L 1 + 30/ 50 = 1.6 years 100 0 1.6 =
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Strengths of Payback: 1. Provides an indication of a project’s risk and liquidity. 2. Easy to calculate and understand. Weaknesses of Payback: 1. Ignores the TVM. 2. Ignores CFs occurring after the payback period.
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Discounted Payback: Uses discounted rather than raw CFs. 10 80 60 0 1 2 3 CF t Cumulative -100 -90.91 -41.32 18.79 Discounted payback 2 + 41.32/ 60.11 = 2.7 years PVCF t -100 -100 10% 9.09 49.59 60.11 = Recover invest. + cap. costs in 2.7 years.
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Calculator Solution Enter in CFLO for L: -100 10 60 80 10 CF 0 CF 1 NPV CF 2 CF 3 I = 18.78 = NPV L
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Rationale for the NPV Method NPV = PV inflows – Cost = Net gain in wealth. Accept project if NPV > 0. Choose between mutually exclusive projects on basis of higher NPV. Adds most value.
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Using NPV method, which project(s) should be accepted? <ul><li>If Projects S and L are mutually exclusive, accept S because NPV s > NPV L . </li></ul><ul><li>If S & L are independent, accept both; NPV > 0. </li></ul>
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Internal Rate of Return: IRR 0 1 2 3 CF 0 CF 1 CF 2 CF 3 Cost Inflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0.
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NPV: Enter k, solve for NPV. IRR: Enter NPV = 0, solve for IRR.
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What’s Project L’s IRR? 10 80 60 0 1 2 3 IRR = ? -100.00 PV 3 PV 2 PV 1 0 = NPV Enter CFs in CFLO, then press IRR: IRR L = 18.13%. IRR S = 23.56%.
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40 40 40 0 1 2 3 IRR = ? Find IRR if CFs are constant: -100 Or, with CFLO, enter CFs and press IRR = 9.70%. 3 -100 40 0 9.70% INPUTS OUTPUT N I/YR PV PMT FV
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90 1090 90 0 1 2 10 IRR = ? Q. How is a project’s IRR related to a bond’s YTM? A. They are the same thing. A bond’s YTM is the IRR if you invest in the bond. -1134.2 IRR = 7.08% (use TVM or CFLO). ...
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Rationale for the IRR Method If IRR > WACC, then the project’s rate of return is greater than its cost--some return is left over to boost stockholders’ returns. Example : WACC = 10%, IRR = 15%. Profitable.
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Decisions on Projects S and L per IRR <ul><li>If S and L are independent, accept both. IRRs > k = 10%. </li></ul><ul><li>If S and L are mutually exclusive, accept S because IRR S > IRR L . </li></ul>
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Construct NPV Profiles Enter CFs in CFLO and find NPV L and NPV S at different discount rates: k 0 5 10 15 20 NPV L 50 33 19 7 (4 NPV S 40 29 20 12 5 (4)
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-10 0 10 20 30 40 50 60 5 10 15 20 23.6 NPV ($) Discount Rate (%) IRR L = 18.1% IRR S = 23.6% Crossover Point = 8.7% k 0 5 10 15 20 NPV L 50 33 19 7 (4) NPV S 40 29 20 12 5 S L . . . . . . . . . . .
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NPV and IRR always lead to the same accept/reject decision for independent projects: k > IRR and NPV < 0. Reject. NPV ($) k (%) IRR IRR > k and NPV > 0 Accept.
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Mutually Exclusive Projects k 8.7 k NPV % IRR S IRR L L S k < 8.7: NPV L > NPV S , IRR S > IRR L CONFLICT k > 8.7: NPV S > NPV L , IRR S > IRR L NO CONFLICT
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To Find the Crossover Rate 1. Find cash flow differences between the projects. See data at beginning of the case. 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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Two Reasons NPV Profiles Cross 1. Size (scale) differences. 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. 2. Timing differences. Project with faster payback provides more CF in early years for reinvestment. If k is high, early CF especially good, NPV S > NPV L .
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Reinvestment Rate Assumptions <ul><li>NPV assumes reinvest at k (opportunity cost of capital). </li></ul><ul><li>IRR assumes reinvest at IRR. </li></ul><ul><li>Reinvest at opportunity cost, k, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects. </li></ul>
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Managers like rates--prefer IRR to NPV comparisons. Can we give them a better IRR? Yes, 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. Thus, MIRR assumes cash inflows are reinvested at WACC.
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MIRR = 16.5% 10.0 80.0 60.0 0 1 2 3 10% 66.0 12.1 158.1 MIRR for Project L (k = 10%) -100.0 10% 10% TV inflows - 100.0 PV outflows MIRR L = 16.5% $100 = $158.1 (1 + MIRR L ) 3
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To find TV with HP 10B, enter in CFLO: I = 10 NPV = 118.78 = PV of inflows. Enter PV = -118.78, N = 3, I = 10, PMT = 0. Press FV = 158.10 = FV of inflows. Enter FV = 158.10, PV = -100, PMT = 0, N = 3. Press I = 16.50% = MIRR. CF 0 = 0, CF 1 = 10, CF 2 = 60, CF 3 = 80
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Why use MIRR versus IRR? MIRR correctly assumes reinvestment at opportunity cost = WACC. MIRR also avoids the problem of multiple IRRs. Managers like rate of return comparisons, and MIRR is better for this than IRR.
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Pavilion Project: NPV and IRR? 5,000 -5,000 0 1 2 k = 10% -800 Enter CFs in CFLO, enter I = 10. NPV = -386.78 IRR = ERROR. Why?
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We got IRR = ERROR because there are 2 IRRs. Nonnormal CFs--two sign changes. Here’s a picture: NPV Profile 450 -800 0 400 100 IRR 2 = 400% IRR 1 = 25% k NPV
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Logic of Multiple IRRs 1. At very low discount rates, the PV of CF 2 is large & negative, so NPV < 0. 2. At very high discount rates, the PV of both CF 1 and CF 2 are low, so CF 0 dominates and again NPV < 0. 3. In between, the discount rate hits CF 2 harder than CF 1 , so NPV > 0. 4. Result: 2 IRRs.
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Could find IRR with calculator: 1. Enter CFs as before. 2. Enter a “guess” as to IRR by storing the guess. Try 10%: 10 STO IRR = 25% = lower IRR Now guess large IRR, say, 200: 200 STO IRR = 400% = upper IRR
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When there are nonnormal CFs and more than one IRR, use MIRR: 0 1 2 -800,000 5,000,000 -5,000,000 PV outflows @ 10% = -4,932,231.40. TV inflows @ 10% = 5,500,000.00. MIRR = 5.6%
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Accept Project P? NO . Reject because MIRR = 5.6% < k = 10%. Also, if MIRR < k, NPV will be negative: NPV = -$386,777.
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