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Capital Budgeting Rules for Sensible Investment Decisions!!

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Cost vs. Benefits Investment typically has two components:Investment typically has two components: –Outflow of cash (cost) –Inflow of cash (benefits) TVM requires all cash flows to be compared at the same point in timeTVM requires all cash flows to be compared at the same point in time –Most convenient is time 0

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Recall Forbes Example Tax savings: $500,000 foreverTax savings: $500,000 forever Campaign Costs: $40 millionCampaign Costs: $40 million r = 10%r = 10% PV of Benefits:.5 mill /.10 = $5 millionPV of Benefits:.5 mill /.10 = $5 million Cost: $40 millionCost: $40 million Benefit - Cost = 5- 40 = -$35 millionBenefit - Cost = 5- 40 = -$35 million

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Forbes example... Obviously this is a lousy investmentObviously this is a lousy investment What you just used in analyzing this ‘investment’ proposal is NPV rule!What you just used in analyzing this ‘investment’ proposal is NPV rule! It turns out the NPV rule is the most sensible rule to use for evaluating projectsIt turns out the NPV rule is the most sensible rule to use for evaluating projects

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Examples of Capital Budgeting Projects To open a corner latte standTo open a corner latte stand To replace replace a 486 computer used in business with a Pentium computerTo replace replace a 486 computer used in business with a Pentium computer To decide between a coal-fired and a nuclear fuel power plant costing $1 billionTo decide between a coal-fired and a nuclear fuel power plant costing $1 billion To add 5 stories to an existing office towerTo add 5 stories to an existing office tower To shut down an aging factory making ball bearingsTo shut down an aging factory making ball bearings

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Evaluating Investments There are many ways to evaluate investmentsThere are many ways to evaluate investments Among all the investment rules we will consider, NPV rule is the only rule that always gives correct answer in all situations!!Among all the investment rules we will consider, NPV rule is the only rule that always gives correct answer in all situations!! Other rules may or may not give an answer consistent with NPV ruleOther rules may or may not give an answer consistent with NPV rule

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Net Present Value NPV = PV of Benefits - PV of CostsNPV = PV of Benefits - PV of Costs Accept project if NPV > 0Accept project if NPV > 0 Reject project if NPV < 0Reject project if NPV < 0

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Another Example... 0 1 2 Initial outlay ($1,100) Revenues$1,000 Expenses500 Cash flow$500 Revenues$2,000 Expenses1,000 Cash flow$1,000 – $1,100.00 +454.54 +826.45 +$180.99 1 $500 x 1.10 1 $1,000 x 1.10 2 NPV

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NPV Formula ‘r’ has many names:‘r’ has many names: –‘r’ is called the discount rate or –‘r’ is called the required return or –‘r’ is called the cost of capital

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Computing NPV on calculator Use the CF j keyUse the CF j key –First entry is at time 0 –Subsequent entries are time 1, 2, 3,... and so on –make sure the cash flows have the proper signs Enter ‘r’ as the I/YREnter ‘r’ as the I/YR Use the keys That’s it!!Use the keys That’s it!! NPV

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Another Example.. NPV = $ _______ Accept / Reject Project ?

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The cash flows areThe cash flows are Year Cash flow Year Cash flow 0-$252 0-$252 1 1431 1 1431 2-3035 2-3035 3 2850 3 2850 4-1000 4-1000 r = 10% NPV = _______ Accept / Reject ?? Another Example...

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Example continued... This was an example of unconventional cash flowsThis was an example of unconventional cash flows Conventional Cash Flows: Only one change in sign (from + to - or vice versa) e.g. -++++Conventional Cash Flows: Only one change in sign (from + to - or vice versa) e.g. -++++ Unconventional Cash Flows: More than one change in sign e.g.-++-+-Unconventional Cash Flows: More than one change in sign e.g.-++-+-

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Importance of NPV NPV is the dollar value added to the enterpriseNPV is the dollar value added to the enterprise –it’s the amount by which the enterprise is richer! For public companies, NPV is the increase in total market value of equityFor public companies, NPV is the increase in total market value of equity Managers should not take negative NPV projects since it reduces the firm valueManagers should not take negative NPV projects since it reduces the firm value

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Other Rules Alternative rules of evaluating investments are:Alternative rules of evaluating investments are: –Internal Rate of Return (IRR) –Payback –Discounted Payback –Profitability Index –Accounting Rate of Return

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IRR Rule IRR: the discount rate that makes NPV = 0IRR: the discount rate that makes NPV = 0 Rule: Accept if IRR > required return Reject if IRR required return Reject if IRR < required return

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IRR and Required Return Required return also called the ‘Hurdle Rate’Required return also called the ‘Hurdle Rate’ Required return is the cost of investment fundsRequired return is the cost of investment funds –i.e. what it costs to borrow money or raise equity capital for investments –it is the same cost of capital ‘r’ used in NPV calculations

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IRR on Calculator Enter the cash flows as beforeEnter the cash flows as before Use the keysUse the keys That’s it!That’s it! Without financial calculator, IRR is computed by trial and errorWithout financial calculator, IRR is computed by trial and error IRR/YR

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IRR Example Year Cash flow Year Cash flow 0-200 150 150 2100 2100 3150 3150 50 100 150 50 100 150 0 = -200 + + + 0 = -200 + + + (1+IRR) 1 (1+IRR) 2 (1+IRR) 3 (1+IRR) 1 (1+IRR) 2 (1+IRR) 3 IRR = ______% Hurdle rate = 9% Accept / reject?

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Another Example What is the IRR?Ans: _____What is the IRR?Ans: _____ What is the NPV if r = 16%Ans: _____What is the NPV if r = 16%Ans: _____ Do IRR and NPV give the same answer?Do IRR and NPV give the same answer? 0 2345 6 1 -256+31+128+194+61+55+108

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Year Cash flow 0– $275 1100 2100 3100 4100 Net Present Value Profile Discount rate 2% 6% 10% 14% 18% 120 100 80 60 40 20 Net present value 0 – 20 – 40 22% IRR NPV>0 NPV < 0

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IRR and Unconventional Cash Flows l The cash flows are Year Cash flow 0-$252 11431 2-3035 32850 4-1000 IRR = ?

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Example continued.... What’s the IRR?What’s the IRR? at 25.00%:NPV = _______ at 25.00%:NPV = _______ at 33.33%:NPV = _______ at 33.33%:NPV = _______ at 42.86%:NPV = _______ at 42.86%:NPV = _______ at 66.66%:NPV = _______ at 66.66%:NPV = _______ Two questions:Two questions: –1.What’s going on here? –2.How many IRRs can there be?

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NPV Profile - Multiple IRR Problem $0.06 $0.04 $0.02 $0.00 ($0.02) NPV ($0.04) ($0.06) ($0.08) 0.20.280.360.440.520.60.68 IRR = 25% IRR = 33.3% IRR = 42.8% IRR = 66.6% Discount rate

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Problem 1 with IRR Rule IRR Rule does not always give a clear answer with unconventional cash flowsIRR Rule does not always give a clear answer with unconventional cash flows In the above example, there are multiple IRRsIn the above example, there are multiple IRRs The accept/reject decision in the example depends on required rate of returnThe accept/reject decision in the example depends on required rate of return

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Another Problem with IRR Year 01234 Project A:– $35050100150200 Project B:– $2501251007550 If the projects are mutually exclusive (i.e. can take one or the other, but not both), which project to take?

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Example Continued...

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Decision with mutually exclusive projects l IRR Rule does not always give a correct answer with mutually exclusive projects l In the above example, it seems we would prefer Project ________ (higher IRR)

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Mutually Exclusive… (contd.) But always take the project with higher NPV!!But always take the project with higher NPV!! If r = 5%, then accept project AIf r = 5%, then accept project A If r = 14%, then accept project BIf r = 14%, then accept project B

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IRR, NPV, and Mutually Exclusive Projects Discount rate % 2% 6% 10% 16%20% 60 40 20 0 – 20 – 40 Net present value $ – 60 – 80 – 100 24% IRR A < IRR B 0 140 120 100 80 160 NPV B >NPV A NPV A >NPV B Project A Project B Crossover rate

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Cross-over Rate the discount rate that makes NPV of two projects equalthe discount rate that makes NPV of two projects equal the interest rate at which you are indifferent between two mutually exclusive projectsthe interest rate at which you are indifferent between two mutually exclusive projects

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Finding Crossover Rate Take difference between cash flows of two projects and find IRR (of these incremental cash flows)Take difference between cash flows of two projects and find IRR (of these incremental cash flows) Year 01234 Project A:– $350150120150200 Project B:– $25012510075165 Difference:–$10025207535 IRR (difference) = _______ %

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Another example Find the crossover rate of these two projectsFind the crossover rate of these two projects Answer: _________Answer: _________

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IRR - Criticisms Not a measure of dollar value addedNot a measure of dollar value added Does not consider the scale of the projectDoes not consider the scale of the project Interim cash flows are assumed to be reinvested at the IRR which is unrealisticInterim cash flows are assumed to be reinvested at the IRR which is unrealistic Does not give correct answer whenDoes not give correct answer when –you have mutually exclusive project –unconventional cash flows

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Payback Rule Measure of the length of time until the sum of future cash flows equals the initial investmentMeasure of the length of time until the sum of future cash flows equals the initial investment –Time it takes to get you money back Accept: if payback period is less than some pre- specified benchmarkAccept: if payback period is less than some pre- specified benchmark

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Payback Example l The cash flows are YearProj. AProj. B 0-$100-$100 19015 21590 31010 41020 Payback = 2 yrs

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Problem with Payback YearProj. AProj. B 0-$100-$100 19015 21590 310100 4102000 Payback rule ignores these cash flows Although both projects have the same payback, Proj. B is clearly superior

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Payback Rule - Criticisms It does not take into account time value of money (i.e. no discounting of cash flows)It does not take into account time value of money (i.e. no discounting of cash flows) Payback rule ignores all the cash flows that occur after the payback periodPayback rule ignores all the cash flows that occur after the payback period Required payback benchmark is arbitraryRequired payback benchmark is arbitrary

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Discounted Payback Length of time until present value of future cash flows equals the intial investmentLength of time until present value of future cash flows equals the intial investment –avoids the time value criticism of simple payback rule Accept if discounted payback less than pre- specified benchmarkAccept if discounted payback less than pre- specified benchmark Does not avoid other criticisms of payback ruleDoes not avoid other criticisms of payback rule

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Disc. Payback Example l The cash flows are YearProj. APV (r=10%) 0-$100-$100 19081.82 21512.40 3107.51 4106.83 discounted payback = 3 years

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Discounted Payback - criticism Incorporates time value in decision in contrast with simple payback,Incorporates time value in decision in contrast with simple payback, It still ignores all cash flows occuring after the required payback periodIt still ignores all cash flows occuring after the required payback period Benchmark is still arbitraryBenchmark is still arbitrary BUT

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Profitability Index Ratio of PV of benefits to PV of costsRatio of PV of benefits to PV of costs –“Bang for the buck” Rule: Accept Project if PI > 1 Reject project if PI 1 Reject project if PI < 1

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P. I. Example P. I. = ______=________ 200P. I. = ______=________ 200 Interpretation: NPV of $0.204 is added for each $1 of investiment.Interpretation: NPV of $0.204 is added for each $1 of investiment.

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Problems with P. I. As with IRR, it does not consider the scale of the project.As with IRR, it does not consider the scale of the project. –Not a measure of total $ value added to firm With mutually exclusive projects, P. I. can give wrong rankingsWith mutually exclusive projects, P. I. can give wrong rankings

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Another Example Although Proj. A has higher P. I., Proj. B should be accepted because NPV is higherAlthough Proj. A has higher P. I., Proj. B should be accepted because NPV is higher

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Average Accounting Return Measure of avg. accounting profit divided by avg. accounting value of investment: A. A. R. = avg. net income avg. book value of invest.Measure of avg. accounting profit divided by avg. accounting value of investment: A. A. R. = avg. net income avg. book value of invest. Accept ifAAR > benchmark return Reject ifAAR benchmark return Reject ifAAR < benchmark return

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A. A. R. Example Average net income: Year 1 2 3 Sales$440$240$160 Costs22012080 Gross profit22012080 Depreciation808080 Earnings before taxes140400 Taxes (25%)35100 Net income$105$30$0 Average net income = (105 + 30 + 0)/3 = $45

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Example continued Average book value: Initial investment = $240 Average investment = ($240 + 160 + 80 + 0)/4 = $120 (or) = $240/2 = $120 Average accounting return (AAR): Average net income $45 AAR = = = 37.5% Average book value $120

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Problems with AAR Does not use cash flowsDoes not use cash flows Ignores timing of incomeIgnores timing of income Pre-specified benchmark is arbitraryPre-specified benchmark is arbitrary

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Summary Of all the rules considered, NPV consistently gives the correct answersOf all the rules considered, NPV consistently gives the correct answers Other rules may or may not give the same answer as NPVOther rules may or may not give the same answer as NPV Decisions based on NPV rule are always correct!Decisions based on NPV rule are always correct!

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Summary Why study other rules?Why study other rules? Corporations often use more than one ruleCorporations often use more than one rule However, most corporations have adopted the NPV ruleHowever, most corporations have adopted the NPV rule In practice, IRR is the strongest challenge to the NPV ruleIn practice, IRR is the strongest challenge to the NPV rule managers seem to prefer talking about investment ‘returns’ rather than NPVmanagers seem to prefer talking about investment ‘returns’ rather than NPV

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Major remaining issues So far we have ignored from where we got the cash flows and ‘r’:So far we have ignored from where we got the cash flows and ‘r’: How do you compute the correct cash flows to use in NPV?How do you compute the correct cash flows to use in NPV? –accounting income vs. relevant cash flows How do you determine the correct cost of capital ‘r’?How do you determine the correct cost of capital ‘r’? –risk and return

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