# Calculating the crossover rate compute the irr for

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Calculating the Crossover RateCompute the IRR for either project “A-B” or “B-A”YearProject AProject B Project A-B Project B-A 0(\$10,000) (\$10,000)\$0\$01\$10,000\$1,000\$9,000(\$9,000)2\$1,000\$1,000\$0\$03\$1,000\$12,000(\$11,000)\$11,00010.55% = IRR
Mutually Exclusive ProjectsIf the required return is less than the crossover point of 10.55%, then you should choose BIf the required return is greater than the crossover point of 10.55%, then you should choose A
NPV versus IRRNPV and IRR will generally give the same decision.Exceptions:Non-conventional cash flows – cash flow signs change more than onceMutually exclusive projectsInitial investments are substantially differentTiming of cash flows is substantially different
9-53NPV directly measures the increase in value to the firm.Whenever there is a conflict between NPV and another decision rule, you should alwaysuse NPV!Conflicts Between NPV and IRR
PeriodProject AProject B0-500-40013253252325200IRRNPVIf the required rate of return for the firm is 10% and Projects A and B are both of equal risk, which project would you select?Mutually Exclusive Projects
PeriodProject AProject B0-500-40013253252325200IRR19.43%22.17%NPV\$64.05\$60.74If the required rate of return for the firm is 10% and Projects A and B are both of equal risk, which project would you select?Mutually Exclusive Projects
IRR for A = 19.43%IRR for B = 22.17%Crossover Point = 11.8%NPV ProfilesRequired rate of return<cross-over rate10%<11.8% so choose A
6.7 The Profitability Index (PI)Minimum Acceptance Criteria: Accept if PI > 1Ranking Criteria: Select alternative with highest PIInvestentInitialFlowsCash FutureofPVTotalPI
9-58PI = PV of Future Cash FlowsPV of Outflows (Initial Investment)\$177,627= 1.0765\$165,000A Profitability Index of 1.076 implies that for every \$1 of investment, we create an additional \$0.0765 in value. A PI >1 means the firm is increasing in value.Profitability Index Example
The Profitability IndexDisadvantages:Problems with mutually exclusive investmentsAdvantages:May be useful when available investment funds are limitedEasy to understand and communicateCorrect decision when evaluating independent projects
9-60TechniqueUnitsAccept if:PaybackTimePayback < Mgt’s #Discounted PaybackTimePayback < Mgt’s #Net Present Value \$NPV > \$0Profitability Index (PI)NonePI > 1.0Average Acct. Return %AAR > Mgt’s #Internal Rate of Return %IRR > RCapital Budgeting Decision Criteria Comparison
6.8 The Practice of Capital BudgetingVaries by industry:Some firms use payback, others use accounting rate of return.The most frequently used technique for large corporations is IRR or NPV.
Example of Investment RulesCompute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 10%. YearProject AProject B0 -\$200 -\$1501 \$200\$502 \$800\$1003 -\$800 \$150
Example of Investment RulesProject AProject BCF0-\$200.00-\$150.00PV0of CF1-3\$241.92 \$240.80NPV = \$41.92\$90.80IRR =0%, 100%36.19%PI = 1.20961.6053
Example of Investment RulesPayback Period:Project AProject BTime CFCum. CFCFCum. CF0-200 -200 -150 -1501200050-100280080010003-800 0150150Payback period for project B = 2 years.