Capital Budgeting Rules for Sensible Investment Decisions!! Cost vs. Benefits • 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 time – Most convenient is time 0 Recall Forbes Example • Tax savings: $500,000 forever • Campaign Costs: $40 million • r = 10% • PV of Benefits: .5 mill / .10 = $5 million • Cost: $40 million • Benefit - Cost = 5- 40 = -$35 million Forbes example... • Obviously this is a lousy investment • 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 projects Examples of Capital Budgeting Projects • To open a corner latte stand • To 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 billion • To add 5 stories to an existing office tower • To shut down an aging factory making ball bearings Evaluating Investments • There 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!! • Other rules may or may not give an answer consistent with NPV rule Net Present Value • NPV = PV of Benefits - PV of Costs • Accept project if NPV > 0 • Reject project if NPV < 0 Another Example... 0 1 Initial outlay ($1,100) 2 Revenues $1,000 Expenses 500 Revenues $2,000 Expenses 1,000 Cash flow Cash flow $1,000 – $1,100.00 $500 x $500 1 1.10 +454.54 $1,000 x 1.10 2 +826.45 +$180.99 1 NPV NPV Formula CF1 CF2 CF3 CFn NPV CF0 .... 2 3 n 1 r (1 r ) (1 r ) (1 r ) • ‘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 Computing NPV on calculator • Use the CFj 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/YR NPV • Use the That’s it!! keys Another Example.. Time Cash Flow 0 -$718 1 $250 2 $575 3 $100 r = 12% 4 NPV = $ _______ Accept / Reject Project ? Another Example... • The cash flows are Year 0 Cash flow -$252 1 1431 2 -3035 3 2850 4 -1000 r = 10% NPV = _______ Accept / Reject ?? Example continued... • This was an example of unconventional cash flows • 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. + + + - Importance of NPV • NPV 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 equity • Managers should not take negative NPV projects since it reduces the firm value Other Rules • Alternative rules of evaluating investments are: – – – – – Internal Rate of Return (IRR) Payback Discounted Payback Profitability Index Accounting Rate of Return IRR Rule • IRR: the discount rate that makes NPV = 0 CF3 CFn CF1 CF2 0 CF0 .... 2 3 1 IRR (1 IRR) (1 IRR) (1 IRR) n • Rule: Accept if IRR > required return Reject if IRR < required return IRR and Required Return • Required return also called the ‘Hurdle Rate’ • Required 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 IRR on Calculator • Enter the cash flows as before • Use the IRR/YR keys • That’s it! • Without financial calculator, IRR is computed by trial and error IRR Example Year Cash flow 0 -200 1 2 3 50 100 150 50 Hurdle rate = 9% 100 150 0 = -200 + (1+IRR)1 + (1+IRR)2 + (1+IRR)3 IRR = ______% Accept / reject? Another Example 0 1 2 3 4 5 6 -256 +31 +128 +194 +61 +55 +108 • What is the IRR? Ans: _____ • What is the NPV if r = 16% Ans: _____ • Do IRR and NPV give the same answer? Net Present Value Profile Net present value 120 Year 100 0 1 2 3 4 80 60 40 Cash flow – $275 100 100 100 100 NPV>0 20 0 NPV < 0 – 20 – 40 Discount rate 2% 6% 10% 14% 18% IRR 22% IRR and Unconventional Cash Flows The cash flows are Year Cash flow 0 -$252 1 2 3 4 1431 -3035 2850 -1000 IRR = ? Example continued.... • What’s the IRR? at 25.00%: NPV = _______ at 33.33%: NPV = _______ at 42.86%: NPV = _______ at 66.66%: NPV = _______ • Two questions: – 1. What’s going on here? – 2. How many IRRs can there be? NPV Profile - Multiple IRR Problem NPV $0.06 $0.04 $0.02 IRR = 25% $0.00 ($0.02) IRR = 33.3% IRR = 42.8% ($0.04) IRR = 66.6% ($0.06) ($0.08) 0.2 0.28 0.36 0.44 0.52 Discount rate 0.6 0.68 Problem 1 with IRR Rule • IRR Rule does not always give a clear answer with unconventional cash flows • In the above example, there are multiple IRRs • The accept/reject decision in the example depends on required rate of return Another Problem with IRR Year 0 1 2 3 4 Project A: – $350 50 100 150 200 Project B: – $250 125 100 75 50 If the projects are mutually exclusive (i.e. can take one or the other, but not both), which project to take? Example Continued... Project A Project B IRR 12.9% 17.8% NPV @ 5% $82.44 $65.67 NPV @ 14% -$9.53 $16.82 Decision with mutually exclusive projects IRR Rule does not always give a correct answer with mutually exclusive projects In the above example, it seems we would prefer Project ________ (higher IRR) Mutually Exclusive… (contd.) • But always take the project with higher NPV!! • If r = 5%, then accept project A • If r = 14%, then accept project B IRR, NPV, and Mutually Exclusive Projects Net present value $ 160 140 Project A 120 100 80 Project B 60 40 20 NPV A >NPV B 0 – 20 – 40 – 60 NPV B >NPV A – 80 – 100 0 2% Crossover rate 6% 10% 16% IRR A < IRR B 20% 24% Discount rate % Cross-over Rate • the discount rate that makes NPV of two projects equal • the interest rate at which you are indifferent between two mutually exclusive projects Finding Crossover Rate • Take difference between cash flows of two projects and find IRR (of these incremental cash flows) Year 0 1 2 3 4 Project A: – $350 150 120 150 200 Project B: – $250 125 100 75 165 Difference: –$100 25 20 75 35 IRR (difference) = _______ % Another example Year Project A Project B 0 -$400 -$500 1 250 320 2 280 340 • Find the crossover rate of these two projects • Answer: _________ IRR - Criticisms • Not a measure of dollar value added • Does not consider the scale of the project • Interim cash flows are assumed to be reinvested at the IRR which is unrealistic • Does not give correct answer when – you have mutually exclusive project – unconventional cash flows Payback Rule • Measure 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 prespecified benchmark Payback Example The Payback = 2 yrs cash flows are Year Proj. A Proj. B 0 -$100 -$100 1 2 3 4 90 15 10 10 15 90 10 20 Problem with Payback Payback rule ignores these cash flows Year Proj. A Proj. B 0 -$100 -$100 1 2 3 4 90 15 10 10 15 90 100 2000 Although both projects have the same payback, Proj. B is clearly superior Payback Rule - Criticisms • 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 period • Required payback benchmark is arbitrary Discounted Payback • Length 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 prespecified benchmark • Does not avoid other criticisms of payback rule Disc. Payback Example The cash flows are Year Proj. A discounted payback = 3 years PV (r=10%) 0 -$100 -$100 1 2 3 4 90 15 10 10 81.82 12.40 7.51 6.83 Discounted Payback - criticism • Incorporates time value in decision in contrast with simple payback, BUT • It still ignores all cash flows occuring after the required payback period • Benchmark is still arbitrary Profitability Index PV ( Benefits) PV ( Inflows) P. I . PV (Costs) PV (Outflows) • Ratio of PV of benefits to PV of costs – “Bang for the buck” • Rule: Accept Project if Reject project if PI > 1 PI < 1 P. I. Example Year 0 CashFlow -200 r = 10% 1 50 2 100 3 150 • P. I. = ______ =________ 200 • Interpretation: NPV of $0.204 is added for each $1 of investiment. Problems with P. I. • 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 rankings Another Example Project A Project B -$100 -$200 NPV $50 $80 P. I. 1.5 1.4 Cost (t=0) • Although Proj. A has higher P. I., Proj. B should be accepted because NPV is higher 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. • Accept if AAR > benchmark return Reject if AAR < benchmark return A. A. R. Example Average net income: Year 1 2 3 Sales $440 $240 $160 Costs 220 120 80 Gross profit 220 120 80 Depreciation 80 80 80 140 40 0 35 10 0 $105 $30 $0 Earnings before taxes Taxes (25%) Net income Average net income = (105 + 30 + 0)/3 = $45 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 AAR = Average book value $45 = $120 = 37.5% Problems with AAR • Does not use cash flows • Ignores timing of income • Pre-specified benchmark is arbitrary Summary • Of all the rules considered, NPV consistently gives the correct answers • Other rules may or may not give the same answer as NPV • Decisions based on NPV rule are always correct! Summary • Why study other rules? • Corporations often use more than one rule • However, most corporations have adopted the NPV rule • In practice, IRR is the strongest challenge to the NPV rule • managers seem to prefer talking about investment ‘returns’ rather than NPV Major remaining issues • 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? – accounting income vs. relevant cash flows • How do you determine the correct cost of capital ‘r’? – risk and return