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Dr. Nguyen Hai Quan Email: Quan_nh@yahoo.com Phone: 0934221978

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Overview and “vocabulary” Methods ◦ Payback, discounted payback ◦ NPV ◦ IRR, MIRR ◦ Profitability Index Unequal lives Economic life

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Analysis of potential projects. Long-term decisions; involve large expenditures. Very important to firm’s future.

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Estimate cash flows (inflows & outflows). Assess risk of cash flows. Determine r = WACC for project. Evaluate cash flows.

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Projects are: independent, if the cash flows of one are unaffected by the acceptance of the other. mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.

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The number of years required to recover a project’s cost, or how long does it take to get the business’s money back?

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108060 0123 -100 = CF t Cumulative-100-90-3050 Payback L 2+30/80 = 2.375 years 0 100 2.4

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702050 0123 -100CF t Cumulative-100-302040 Payback S 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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108060 0123 CF t Cumulative-100-90.91-41.3218.79 Discounted payback 2 + 41.32/60.11 = 2.7 yrs Discounted Payback: Uses discounted rather than raw CFs. PVCF t -100 10% 9.0949.5960.11 = Recover invest. + cap. costs in 2.7 yrs.

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NPV:Sum of the PVs of inflows and outflows. Cost often is CF 0 and is negative.

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108060 0123 10% Project L: -100.00 9.09 49.59 60.11 18.79 = NPV L NPV S = $19.98.

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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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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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If Franchise S and L are mutually exclusive, accept S because NPV s > NPV L. If S & L are independent, accept both; NPV > 0.

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0123 CF 0 CF 1 CF 2 CF 3 CostInflows IRR is the discount rate that forces PV inflows = cost. This is the same as forcing NPV = 0.

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NPV: Enter r, solve for NPV. IRR: Enter NPV = 0, solve for IRR.

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108060 0123 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 0123 IRR = ? Find IRR if CFs are constant: -100 Or, with CFLO, enter CFs and press IRR = 9.70%. 3 -100 40 0 9.70% NI/YRPVPMTFV INPUTS OUTPUT

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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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If S and L are independent, accept both. IRRs > r = 10%. If S and L are mutually exclusive, accept S because IRR S > IRR L.

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Enter CFs in CFLO and find NPV L and NPV S at different discount rates: r 0 5 10 15 20 NPV L 50 33 19 7 NPV S 40 29 20 12 5 (4)

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NPV ($) Discount Rate (%) IRR L = 18.1% IRR S = 23.6% Crossover Point = 8.7% r 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: r > IRR and NPV < 0. Reject. NPV ($) r (%) IRR IRR > r and NPV > 0 Accept.

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Mutually Exclusive Projects r 8.7 r NPV % IRR S IRR L L S r NPV S, IRR S > IRR L CONFLICT r > 8.7: NPV S > NPV L, IRR S > IRR L NO CONFLICT

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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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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 r favors small projects. 2.Timing differences. Project with faster payback provides more CF in early years for reinvestment. If r is high, early CF especially good, NPV S > NPV L.

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NPV assumes reinvest at r (opportunity cost of capital). IRR assumes reinvest at IRR. Reinvest at opportunity cost, r, is more realistic, so NPV method is best. NPV should be used to choose between mutually exclusive projects.

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Yes, MIRR is the discount rate which 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% 10.080.060.0 0123 10% 66.0 12.1 158.1 MIRR for Franchise L (r = 10%) -100.0 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 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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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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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 012345NNN -+++++N -++++- ---+++N +++---N -++-+-

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5,000-5,000 012 r = 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 400100 IRR 2 = 400% IRR 1 = 25% r NPV

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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%: 10STO IRR = 25% = lower IRR Now guess large IRR, say, 200: 200STO IRR = 400% = upper IRR

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When there are nonnormal CFs and more than one IRR, use MIRR: 012 -800,0005,000,000-5,000,000 PV outflows @ 10% = -4,932,231.40. TV inflows @ 10% = 5,500,000.00. MIRR = 5.6%

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NO. Reject because MIRR = 5.6% < r = 10%. Also, if MIRR < r, NPV will be negative: NPV = -$386,777.

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S and L are mutually exclusive and will be repeated. r = 10%. Which is better? (000s) 01234 Project S: (100) Project L: (100) 60 33.5 60 33.5

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S L CF 0 -100,000 -100,000 CF 1 60,000 33,500 N j 2 4 I 10 10 NPV 4,132 6,190 NPV L > NPV S. But is L better? Can’t say yet. Need to perform common life analysis.

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Note that Project S could be repeated after 2 years to generate additional profits. Can use either replacement chain or equivalent annual annuity analysis to make decision.

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NPV = $7,547. Replacement Chain Approach (000s) 01234 Franchise S: (100) (100) 60 60 (100) (40) 60

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Compare to Franchise L NPV = $6,190. Or, use NPVs: 01234 4,132 3,415 7,547 4,132 10%

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If the cost to repeat S in two years rises to $105,000, which is best? (000s) NPV S = $3,415 < NPV L = $6,190. Now choose L. NPV S = $3,415 < NPV L = $6,190. Now choose L. 01234 Franchise S: (100) 60 (105) (45) 60

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Year 0 1 2 3 CF ($5,000) 2,100 2,000 1,750 Salvage Value $5,000 3,100 2,000 0 Consider another project with a 3-year life. If terminated prior to Year 3, the machinery will have positive salvage value.

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1.751. No termination 2. Terminate 2 years 3. Terminate 1 year (5) 2.1 5.2 2424 0123 CFs Under Each Alternative (000s)

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NPV (no) = -$123. NPV (2) = $215. NPV (1) = -$273. Assuming a 10% cost of capital, what is the project’s optimal, or economic life?

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The project is acceptable only if operated for 2 years. A project’s engineering life does not always equal its economic life. Conclusions

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Finance theory says to accept all positive NPV projects. Two problems can occur when there is not enough internally generated cash to fund all positive NPV projects: ◦ An increasing marginal cost of capital. ◦ Capital rationing

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Externally raised capital can have large flotation costs, which increase the cost of capital. Investors often perceive large capital budgets as being risky, which drives up the cost of capital. (More...)

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If external funds will be raised, then the NPV of all projects should be estimated using this higher marginal cost of capital.

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Capital rationing occurs when a company chooses not to fund all positive NPV projects. The company typically sets an upper limit on the total amount of capital expenditures that it will make in the upcoming year. (More...)

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Reason: Companies want to avoid the direct costs (i.e., flotation costs) and the indirect costs of issuing new capital. Solution: Increase the cost of capital by enough to reflect all of these costs, and then accept all projects that still have a positive NPV with the higher cost of capital. (More...)

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Reason: Companies don’t have enough managerial, marketing, or engineering staff to implement all positive NPV projects. Solution: Use linear programming to maximize NPV subject to not exceeding the constraints on staffing. (More...)

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Reason: Companies believe that the project’s managers forecast unreasonably high cash flow estimates, so companies “filter” out the worst projects by limiting the total amount of projects that can be accepted. Solution: Implement a post-audit process and tie the managers’ compensation to the subsequent performance of the project.

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