Jacoby, Stangeland and Wajeeh, Capital Budgeting Criteria for Investments Projects Mutually Exclusive versus Independent Project uMutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system. u RANK all alternatives and select the best one. uIndependent Projects: accepting or rejecting one project does not affect the decision of the other projects. u Must exceed a MINIMUM acceptance criteria. Chapter 6

Jacoby, Stangeland and Wajeeh, The Net Present Value (NPV) Rule uNet Present Value (NPV) = Total PV of future CF’s - Initial Investment uEstimating NPV: u 1. Estimate future cash flows: how much? and when? u 2. Estimate discount rate u 3. Estimate initial costs uMinimum Acceptance Criteria: Accept if: NPV > 0 uRanking Criteria: Choose the highest NPV

Jacoby, Stangeland and Wajeeh, NPV - An Example uAssume 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 $ ,000 1, ,200 2, ,600 1,400 uDraw a time line and compute the NPV of project X.

4 The Time Line & NPV of Project X Initial outlay ($1,100) Revenues$1,000 Expenses500 Cash flow$500 Revenues$2,000 Expenses1,300 Cash flow $700 – $1, $500 x $700 x Revenues$2,200 Expenses2,700 Cash flow(500) 1 - $500 x Revenues$2,600 Expenses1,400 Cash flow$1,200 1 $1,200 x NPV = -C 0 + PV 0 (Future CFs) = -C 0 + C 1 /(1+r) + C 2 /(1+r) 2 + C 3 /(1+r) 3 + C 4 /(1+r) 4 = = $ > 0

5 First, clear previous data, and check that your calculator is set to 1 P/YR: NPV in your HP 10B Calculator CF j I/YR Key in CF 0 Key in CF 4 Key in r Key in CF 3 +/-CF j 500 1,200 CF j Key in CF CF j Key in CF /-CF j 1,100 The display should show: 1 P_Yr Input data (based on above NPV example) Display should show: CF 0 Display should show: CF 1 Display should show: CF 2 Display should show: CF 3 Display should show: CF 4 PRC NPV Compute NPV Display should show: Yellow C C ALL

Jacoby, Stangeland and Wajeeh, The Payback Period Rule uHow long does it take the project to “pay back” its initial investment? uPayback Period = # of years to recover costs of project uMinimum Acceptance Criteria: set by management uRanking Criteria: set by management

Jacoby, Stangeland and Wajeeh, Discounted Payback - An Example Initial outlay -$1,000 r = 10% PV of Year Cash flow Cash flow 1$ 200$ Accumulated Year discounted cash flow 1$ ,039 41,244 Discounted payback period is just under 3 years

Jacoby, Stangeland and Wajeeh, Average Accounting Return (AAR) uYou want to invest in a machine that produces squash balls. uThe machine costs $90,000. uThe machine will ‘die’ after 3 years (assume straight line depreciation, the annual depreciation is $30,000). uYou estimate for the life of the project: Year 1Year 2Year 3 Sales Expenses EBD

Jacoby, Stangeland and Wajeeh, Year 1Year 2Year 3 Sales Expenses E.B.D. Depreciation E.B.T. Taxes (40%) NI: Calculating Projected NI

Jacoby, Stangeland and Wajeeh, We calculate: (i)Average NI = (ii)Average book value (BV) of the investment (machine): time-0time-1time-2time-3 BV of investment: => Average BV = (divide by 4 - not 3) (iii)The Average Accounting Return: AAR = = 44.44% Conclusion:If target AAR accept If target AAR > 44.44% => reject

Jacoby, Stangeland and Wajeeh, The Internal Rate of Return (IRR) Rule uIRR: the discount rate that sets the NPV to zero uMinimum Acceptance Criteria: Accept if: IRR > required return uRanking Criteria: Select alternative with the highest IRR uReinvestment assumption: the IRR calculation assumes that all future cash flows are reinvested at the IRR uDisadvantages: u Does not distinguish between investing and financing u IRR may not exist or there may be multiple IRR u Problems with mutually exclusive investments uAdvantages: u Easy to understand and communicate

Jacoby, Stangeland and Wajeeh, Internal Rate of Return - An Example Initial outlay = -$2,200 Year Cash flow ,600 Find the IRR such that NPV = 0 0 = (1+IRR) 1 (1+IRR) 2 (1+IRR) 3 (1+IRR) 4 Or: ,600 2,200 = (1+IRR) 1 (1+IRR) 2 (1+IRR) 3 (1+IRR) 4

Jacoby, Stangeland and Wajeeh, First, clear previous data, and check that your calculator is set to 1 P/YR: IRR in your HP 10B Calculator CF j 500 1,600 CF j 800 CF j 900 +/- CF j 2,200 The display should show: 1 P_Yr Input data (based on above NPV example) Display should show: CF 0 Display should show: CF 1 Display should show: CF 2 Display should show: CF 3 Display should show: CF 4 CST IRR/YR Compute IRR Display should show: % Yellow Key in CF 0 Key in CF 4 Key in CF 3 Key in CF 1 Key in CF 2 Yellow C C ALL

Jacoby, Stangeland and Wajeeh, The NPV Profile Discount ratesNPV 0%$1, %1, % % % % l IRR is between 20% and 25% -- about 23.30% l If required rate of return (r) is lower than IRR => accept the project (e.g. r = 15%) l If required rate of return (r) is higher than IRR => reject the project (e.g. r = 25%) Internal Rate of Return and the NPV Profile

Jacoby, Stangeland and Wajeeh, Year Cash flow 0– $2, ,600 The Net Present Value Profile Discount rate 2% 6% 10% 14% 18% 1, , Net present value – % IRR=23.30% 0

Jacoby, Stangeland and Wajeeh, IRR: Investment vs. Financing Project Initial outlay = $4,000 Year Cash flow 1-1, ,500 Find the IRR such that NPV = 0 0 = (1+IRR) 1 (1+IRR) 2 (1+IRR) 3 Or: -1, , ,000 = + + (1+IRR) 1 (1+IRR) 2 (1+IRR) 3

Jacoby, Stangeland and Wajeeh, The NPV Profile of a Financing Project: Discount ratesNPV 0%-$1, % % % % l IRR is between 10% and 15% -- about 14.37% For a Financing Project, the required rate of return is the cost of financing, thus l If required rate of return (r) is lower than IRR => reject the project (e.g. r = 10%) l If required rate of return (r) is higher than IRR => accept the project (e.g. r = 15%) Internal Rate of Return and the NPV Profile for a Financing Project

18 The NPV Profile for a Financing Project

Jacoby, Stangeland and Wajeeh, Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 -$ , , ,200 Multiple Internal Rates of Return Example 1

20 Multiple IRRs and the NPV Profile - Example 1 IRR 2 =72.25% IRR 1 =-29.35%

21 First, clear previous data, and check that your calculator is set to 1 P/YR: Multiple IRRs in your HP 10B Calculator CF j 1,200 CF j 1,200 CF j 1,300 +/- CF j 900 The display should show: 1 P_Yr Input data (based on above NPV example) Display should show: CF 0 Display should show: CF 1 Display should show: CF 2 Display should show: CF 3 CST IRR/YR Compute 1 st IRR Display should show: % Yellow +/- CST IRR/YR Compute 2 nd IRR by guessing it first Display should show: % Yellow 30 +/- RCL STO Yellow Key in CF 0 Key in CF 3 Key in CF 1 Key in CF 2 Yellow C C ALL

Jacoby, Stangeland and Wajeeh, Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 -$ Multiple Internal Rates of Return Example 2

23 Multiple IRRs and the NPV Profile - Example 2 IRR 1 =11.52% IRR 2 =29.84%

Jacoby, Stangeland and Wajeeh, Assume you are considering a project for which the cash flows are as follows: Year Cash flows 0 $ Multiple Internal Rates of Return Example 3

Jacoby, Stangeland and Wajeeh, Multiple IRRs and the NPV Profile - Example 3 IRR 1 =8.05% IRR 2 =33.96%

Jacoby, Stangeland and Wajeeh, IRR, NPV, and Mutually Exclusive Projects Year Project A: – $ Project B: – $

Jacoby, Stangeland and Wajeeh, IRR, NPV, and the Incremental Project Year Project A: – $ Project B: – $ (A-B): The Crossover Rate = IRR A-B = 8.07%

Jacoby, Stangeland and Wajeeh, The Profitability Index (PI) Rule uPI = Total Present Value of future CF’s / Initial Investment uMinimum Acceptance Criteria: Accept if PI > 1 uRanking Criteria: Select alternative with highest PI uDisadvantages: u Problems with mutually exclusive investments uAdvantages: u May be useful when available investment funds are limited u Easy to understand and communicate u Correct decision when evaluating independent projects

Jacoby, Stangeland and Wajeeh, Profitability Index - An Example uConsider the following information on Project Y: Initial outlay -$1,100 Required return = 10% Annual cash benefits: YearCash flows 1 $ ,000 uWhat’s the NPV? uWhat’s the Profitability Index (PI)?

Jacoby, Stangeland and Wajeeh, uThe NPV of Project Y is equal to: NPV = (500/1.1) + (1,000/1.1 2 ) - 1,100 = ($ ) - 1,100 = $1, ,100 = $ uPI = PV Cashflows/Initial Investment = uThis is a good project according to the PI rule. Can you explain why?