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Capital Budgeting Criteria for Investments Projects Mutually Exclusive versus Independent Project

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## Capital Budgeting Criteria for Investments Projects Mutually Exclusive versus Independent Project

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**Chapter 6**Capital Budgeting Criteria for Investments ProjectsMutually Exclusive versus Independent Project • Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system. • RANK all alternatives and select the best one. • Independent Projects: accepting or rejecting one project does not affect the decision of the other projects. • Must exceed a MINIMUM acceptance criteria. Jacoby, Stangeland and Wajeeh, 2000**The Net Present Value (NPV) Rule**• Net Present Value (NPV) = Total PV of future CF’s - Initial Investment • Estimating NPV: • 1. Estimate future cash flows: how much? and when? • 2. Estimate discount rate • 3. Estimate initial costs • Minimum Acceptance Criteria: Accept if: NPV > 0 • Ranking Criteria: Choose the highest NPV Jacoby, Stangeland and Wajeeh, 2000**NPV - An Example**• Assume you have the following information on Project X: Initial outlay -$1,100 Required return = 10% Annual cash revenues and expenses are as follows: Year Revenues Expenses 1 $1,000 $500 2 2,000 1,300 3 2,200 2,700 4 2,600 1,400 • Draw a time line and compute the NPV of project X. Jacoby, Stangeland and Wajeeh, 2000**The Time Line & NPV of Project X**0 1 2 3 4 Initial outlay ($1,100) Revenues $2,000 Expenses 1,300 Cash flow $700 Revenues $1,000 Expenses 500 Cash flow $500 Revenues $2,200 Expenses 2,700 Cash flow (500) Revenues $2,600 Expenses 1,400 Cash flow $1,200 – $1,100.00 +454.54 +578.51 -375.66 +819.62 1 $500 x 1.10 1 $700 x 1.102 1 - $500 x 1.103 1 $1,200 x 1.104 NPV = -C0 + PV0(Future CFs) = -C0 + C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)4 = - + + + + = $377.02 > 0**NPV in your HP 10B Calculator**First, clear previous data, and check that your calculator is set to 1 P/YR: The display should show: 1 P_Yr Input data (based on above NPV example) Yellow C C ALL Display should show: CF 0 +/- CFj 1,100 Key in CF0 Display should show: CF 1 500 CFj Key in CF1 Display should show: CF 2 700 CFj Key in CF2 Display should show: CF 3 Key in CF3 +/- CFj 500 Display should show: CF 4 1,200 CFj Key in CF4 Key in r I/YR 10 Display should show: 377.01659723 Compute NPV Yellow PRC NPV**The Payback Period Rule**• How long does it take the project to “pay back” its initial investment? • Payback Period = # of years to recover costs of project • Minimum Acceptance Criteria: set by management • Ranking Criteria: set by management Jacoby, Stangeland and Wajeeh, 2000**Discounted Payback - An Example**Initial outlay -$1,000 r = 10% PV of Year Cash flow Cash flow 1 $ 200 $ 182 2 400 331 3 700 526 4 300 205 Accumulated Year discounted cash flow 1 $ 182 2 513 3 1,039 4 1,244 Discounted payback period is just under 3 years Jacoby, Stangeland and Wajeeh, 2000**Average Accounting Return (AAR)**• You want to invest in a machine that produces squash balls. • The machine costs $90,000. • The machine will ‘die’ after 3 years (assume straight line depreciation, the annual depreciation is $30,000). • You estimate for the life of the project: Year 1Year 2Year 3 Sales 140 160 200 Expenses 12010090 EBD 20 60 110 Jacoby, Stangeland and Wajeeh, 2000**Calculating Projected NI**Year 1 Year 2 Year 3 Sales 140 160 200 Expenses 120 100 90 E.B.D. Depreciation E.B.T. Taxes (40%) NI: Jacoby, Stangeland and Wajeeh, 2000**We calculate:**(i) Average NI = (ii) Average book value (BV) of the investment (machine): time-0time-1time-2time-3 BV of investment: 90 60 30 0 => Average BV = (divide by 4 - not 3) (iii) The Average Accounting Return: AAR = = 44.44% Conclusion: If target AAR < 44.44% => accept If target AAR > 44.44% => reject Jacoby, Stangeland and Wajeeh, 2000**The Internal Rate of Return (IRR) Rule**• IRR: the discount rate that sets the NPV to zero • Minimum Acceptance Criteria: Accept if: IRR > required return • Ranking Criteria: Select alternative with the highest IRR • Reinvestment assumption: the IRR calculation assumes that all future cash flows are reinvested at the IRR • Disadvantages: • Does not distinguish between investing and financing • IRR may not exist or there may be multiple IRR • Problems with mutually exclusive investments • Advantages: • Easy to understand and communicate Jacoby, Stangeland and Wajeeh, 2000**Internal Rate of Return - An Example**Initial outlay = -$2,200 Year Cash flow 1 800 2 900 3 500 4 1,600 Find the IRR such that NPV = 0 0 = - + + + + (1+IRR)1 (1+IRR)2 (1+IRR)3 (1+IRR)4 Or: 800 900 500 1,600 2,200 = + + + (1+IRR)1 (1+IRR)2 (1+IRR)3 (1+IRR)4 Jacoby, Stangeland and Wajeeh, 2000**IRR in your HP 10B Calculator**First, clear previous data, and check that your calculator is set to 1 P/YR: The display should show: 1 P_Yr Input data (based on above NPV example) Yellow C C ALL Display should show: CF 0 +/- CFj Key in CF0 2,200 Display should show: CF 1 800 CFj Key in CF1 Display should show: CF 2 900 CFj Key in CF2 Display should show: CF 3 CFj Key in CF3 500 Display should show: CF 4 Key in CF4 1,600 CFj Display should show: 23.29565668% Compute IRR Yellow CST IRR/YR Jacoby, Stangeland and Wajeeh, 2000**Internal Rate of Return and the NPV Profile**The NPV Profile Discount rates NPV 0% $1,600.00 5% 1,126.47 10% 739.55 15% 419.74 20% 152.62 25% -72.64 • IRR is between 20% and 25% -- about 23.30% • If required rate of return (r) is lower than IRR => accept the project (e.g. r = 15%) • If required rate of return (r) is higher than IRR => reject the project (e.g. r = 25%) Jacoby, Stangeland and Wajeeh, 2000**The Net Present Value Profile**Net present value Year Cash flow 0 – $2,200 1 800 2 900 3 500 4 1,600 1,600.00 1,126.47 739.55 419.74 159.62 Discount rate 0 – 72.64 2% 6% 10% 14% 18% 22% IRR=23.30% Jacoby, Stangeland and Wajeeh, 2000**IRR: Investment vs. Financing Project**Initial outlay = $4,000 Year Cash flow 1 -1,200 2 -800 3 -3,500 Find the IRR such that NPV = 0 0 = + + + (1+IRR)1 (1+IRR)2 (1+IRR)3 Or: -1,200 -800 -3,500 - 4,000 = + + (1+IRR)1 (1+IRR)2 (1+IRR)3 Jacoby, Stangeland and Wajeeh, 2000**Internal Rate of Return and the NPV Profile for a Financing**Project The NPV Profile of a Financing Project: Discount rates NPV 0% -$1,500.00 5% -891.91 10% -381.67 15% 50.2 20% 418.98 • IRR is between 10% and 15% -- about 14.37% For a Financing Project, the required rate of return is the cost of financing, thus • If required rate of return (r) is lower than IRR => reject the project (e.g. r = 10%) • If required rate of return (r) is higher than IRR => accept the project (e.g. r = 15%) Jacoby, Stangeland and Wajeeh, 2000**Multiple Internal Rates of Return**Example 1 Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 -$900 1 1,200 2 1,300 3 -1,200 Jacoby, Stangeland and Wajeeh, 2000**Multiple IRRs and the NPV Profile - Example 1**IRR2=72.25% IRR1=-29.35%**Multiple IRRs in your HP 10B Calculator**First, clear previous data, and check that your calculator is set to 1 P/YR: The display should show: 1 P_Yr Input data (based on above NPV example) Yellow C C ALL Display should show: CF 0 +/- CFj Key in CF0 900 Display should show: CF 1 1,200 CFj Key in CF1 Display should show: CF 2 1,300 CFj Key in CF2 Display should show: CF 3 +/- CFj Key in CF3 1,200 Display should show: 72.252175% Yellow CST IRR/YR Compute 1st IRR +/- Yellow RCL STO Yellow CST IRR/YR 30 Compute 2nd IRR by guessing it first Display should show: -29.352494%**Multiple Internal Rates of Return**Example 2 Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 -$260 1 250 2 300 3 20 4 -340 Jacoby, Stangeland and Wajeeh, 2000**Multiple IRRs and the NPV Profile - Example 2**IRR2=29.84% IRR1=11.52%**Multiple Internal Rates of Return**Example 3 Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 $660 1 -650 2 -750 3 -50 4 850 Jacoby, Stangeland and Wajeeh, 2000**Multiple IRRs and the NPV Profile - Example 3**IRR1=8.05% IRR2=33.96% Jacoby, Stangeland and Wajeeh, 2000**IRR, NPV, and Mutually Exclusive Projects**Year 0 1 2 3 4 Project A: – $350 50 100 150 200 Project B: – $250 125 100 75 50 Jacoby, Stangeland and Wajeeh, 2000**IRR, NPV, and the Incremental Project**Year 0 1 2 3 4 Project A: – $350 50 100 150 200 Project B: – $250 125 100 75 50 (A-B): The Crossover Rate = IRRA-B = 8.07% Jacoby, Stangeland and Wajeeh, 2000**The Profitability Index (PI) Rule**• PI = Total Present Value of future CF’s / Initial Investment • Minimum Acceptance Criteria: Accept if PI > 1 • Ranking Criteria: Select alternative with highest PI • Disadvantages: • Problems with mutually exclusive investments • Advantages: • May be useful when available investment funds are limited • Easy to understand and communicate • Correct decision when evaluating independent projects Jacoby, Stangeland and Wajeeh, 2000**Profitability Index - An Example**• Consider the following information on Project Y: Initial outlay -$1,100 Required return = 10% Annual cash benefits: Year Cash flows 1 $ 500 2 1,000 • What’s the NPV? • What’s the Profitability Index (PI)? Jacoby, Stangeland and Wajeeh, 2000**The NPV of Project Y is equal to:**NPV = (500/1.1) + (1,000/1.12) - 1,100 = ($454.54 + 826.45) - 1,100 = $1,280.99 - 1,100 = $180.99. • PI = PV Cashflows/Initial Investment = • This is a good project according to the PI rule. Can you explain why? Jacoby, Stangeland and Wajeeh, 2000