Capital Budgeting Techniques and NPV Analysis for Financial Decision Making

Investment Decisions and Capital Budgeting Global Financial Management Campbell R. Harvey Fuqua School of Business Duke University charvey@mail.duke.edu http://www.duke.edu/~charvey 1

Overview Capital Budgeting Techniques Net Present Value (NPV) Criterion for capital budgeting decisions Special cases: Repeated projects Optimal replacement rules Alternative criteria Internal Rates of Return (IRR) Payback period Profitability Index l l l 2

Net Present Value 1) Identify base case and alternative 2) Identify all incremental cash flows (Be comprehensive!) 3) Where uncertain use expected values Don t bias your expectations to be conservative 4) Discount cash flow and sum to find net present value (NPV) 5) If NPV > 0, go ahead 6) Sensitivity Analysis 3

NPV - The Two-Period Case Suppose you have a project which has: An investment outlay of $100 in 1997 (period 0) A safe return of $110 in 1998 (period 1) Should you take it? l What is your alternative? Put your money into a bank account at 6%, receive $106 Gain 4$ in terms of 1998 money l The project has a positive value! l 4

Formal Analysis - The Idea Denote the 1997 and 1998 cash flows as follows: CF0= - 100 CF1= 110 Cash outflow in period 0 Cash return in period 1 Your comparison is a rate of return r of 6% or r=0.06. You invest only if: + + ( 1 ) 0 100 106 * . -100+110 - + 110 0 CF r CF 0 1 CF 1 + + = 1 0 38 . CF NPV 0 1.06 r The NPV expresses the gain from the investment in 1998 dollars. 5

Calculating NPVs You have incremental cash flows: l CF0 , CF1 , CF2 , ... , CFT NPV in year 0 is: CF + 1 ( CF + 1 ( CF + 1 ( = + + + + 1 2 T .... NPV CF 0 2 T ) ) ) r r r CFt T = = rt ) + ( 1 0 t 6

Computing NPVs Example Step 1: Year CF Step 2: Determine the PVs of cash flows: DF 1.000 DCF -100.0 -45.5 1997 -100 1998 -50 1999 30 2000 200 0.909 0.826 24.8 0.751 150.3 = 29.6 Total Step 3: Sum! -100.00 - 45.5 + 24.8 + 150.3 = 29.6 7

Why Use the NPV Rule? We showed that a project with a cash flow: -100 -50 had an NPV of 29.6 @ 10%. So what? Suppose the only shareholder has a bank account where she can borrow or deposit at 10%. Take on the project, draw out 29.6 and spend: l 30 200 l l Year Project Cash Flow Loan Cash Flow Interest Balance of account Payment to shareholder 1997 -100.00 129.60 0.00 -129.60 29.60 1998 -50.00 50.00 12.96 -192.56 0.00 1999 30.00 -30.00 19.26 -181.82 0.00 2000 200.00 -200.00 18.18 0.00 0.00 8

What if NPV is negative? Suppose you accept a negative NPV project: l Year Project Cash Flow Loan Cash Flow Interest Balance of account Payment to shareholder 1997 -100.00 92.04 0.00 -92.04 -7.96 1998 -50.00 50.00 9.20 -151.24 0.00 1999 30.00 -30.00 15.12 -136.36 0.00 2000 150.00 -150.00 13.64 0.00 0.00 Negative NPV means that you have to spend money today to be able to undertake the project! 9

Replicate the Project with Bonds Recall argument about zero coupon bonds Replicate project with 3 bonds: Invest in a 1-year bond with face value 50 Sell a 2 year bond with face value 30 Sell a 3 year bond with face value 200 Include project in your portfolio Year Project Cash Flow Bond 1 (1 Year) Bond 2 (2 Year) Bond 3 (3 Year) Portfolio l l 1997 -100.00 -45.45 24.79 150.26 29.60 1998 -50.00 50.00 1999 30.00 2000 200.00 -30.00 -200.00 0.00 0.00 0.00 Portfolio has zero cash flows in the future (perfect replication) * Value today = NPV! 10

Net Present Value (NPV) The NPV measures the amount by which the value of the firm s stock will increase if the project is accepted. NPV Rule: Accept all projects for which NPV > 0. Reject all projects for which NPV < 0. For mutually exclusive projects, choose the project with the highest NPV. l l 11

NPV Example Consider a drug company with the opportunity to invest $100 million in the development of a new drug. expected to generate $20 million in after-tax cash flows for the next 15 years. the required return is 10% What is the NPV of this investment project? What if the required return is 20%? l 12

NPV Example (cont.) 15 rp= 10% $20[ 1 1 110 / ( . 10 ) ] = $100 NPV . = $52. 12 NPV million rp= 20% 15 $20[ 1 1 120 / ( . 20 ) ] = $100 NPV . = $6. 49 NPV million What do you conclude? 13

Special Topics: Comparing Projects with Different Lives Your firm must decide which of two machines it should use to produce its output. Machine A costs $100,000, has a useful life of 4 years, and generates after-tax cash flows of $40,000 per year. Machine B costs $65,000, has a useful life of 3 years, and generates after-tax cash flows of $35,000 per year. The machine is needed indefinitely and the discount rate is rp= 10%. l Year Machine A Machine B -100 40 40 40 -60 40 40 40 -60 40 40 0 1 2 3 4 5 6 7 8 9 -65 35 35 -30 35 35 -30 35 35 -30 35 l l 10 l 14

Comparing Projects with Different Lives Step 1: Calculate the NPV for each project. NPVA=$26,795 NPVB=$22,040 The NPV of A is received every 4 years The NPV of B is received every 3 years Year Machine A Machine B 26795 0 0 0 26795 0 0 0 26795 0 0 l 0 1 2 3 4 5 6 7 8 9 22040 0 0 22040 0 0 22040 0 0 22040 10 0 15

Comparing Projects with Different Lives Year Machine A Machine B 0 8453 8453 8453 8453 8453 8453 8453 8453 8453 8453 Step 2: Convert the NPVs for each project into an equivalent annual annuity. l 0 1 2 3 4 5 6 7 8 9 0 8863 8863 8863 8863 8863 8863 8863 8863 8863 8863 $26, 795 EAA= = $8, 453 ( . ) 4 1 1 110 / . 01 $22, 1 1 110 01 040 EAB= = $8, 863 ( . ) 3 / . 10 16

Comparing Projects with Different Lives The firm is indifferent between the project and the equivalent annual annuity. Since the project is rolled over forever, the equivalent annual annuity lasts forever. The project with the highest equivalent annual annuity offers the highest aggregate NPV over time. Aggregate NPVA = $8,453/.10 = $84,530 Aggregate NPVB= $8,863/.10 = $88,630 l l l 17

Special Topics: Replacing an Old Machine The cost of the new machine is $20,000 (including delivery and installation costs) and its economic useful life is 3 years. The existing machine will last at most 2 more years. The annual after-tax cash flows from each machine are given in the following table. The discount rate is rp= 10%. Annual After-Tax Cash Flows l l l l Machine Year 1 Year 2 Year 3 Old $8,000 $6,000 - New $18,000 $15,000 $10,000 18

Replacing an Old Machine Step 1: Calculate the NPV of the new machine. l $18, 110 000 $15, ( . ) 110 000 $10, ( . ) 110 000 NPVNew= + + = $20, 000 $16, 273 2 3 . Step 2: Convert the NPV for the new machine into an equivalent annual annuity. $16, [ /( . ) ] . 10 l 273 EANew= = $6, 544 3 1 1 110 The NPV of the new machine is equivalent to receiving $6,544 per year for 3 years. l 19

Replacing an Old Machine (2) Step 3: Decide to reinvest machine if EANew>CFOld: l Old New 8000 6000 6544 6544 6544 0 Operate the old machine as long as its after-tax cash flows are greater than EANew= $6,544. Old machine should be replaced after one more year of operation. How did we know that the new machine itself would not be replaced early? l l l 20

Eurotunnel NPV One of the largest commercial investment project s in recent years is Eurotunnel s construction of the Channel Tunnel linking France with the U.K. The cash flows on the following page are based on the forecasts of construction costs and revenues that the company provided to investors in 1986. Given the risk of the project, we assume a 13% discount rate. l l l 21

Eurotunnels NPV Year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 Cash Flow -GBP457 -476 -497 -522 -551 -584 -619 211 489 455 502 530 544 PV (k=13%) -457 -421 -389 -362 -338 -317 -297 90 184 152 148 138 126 Year 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 NPV Cash Flow 636 594 689 729 796 859 923 983 1,050 1,113 1,177 17,781 PV (k=13%) 130 107 110 103 100 95 90 86 81 76 71 946 GBP251 22

Alternatives to NPV Internal Rate of Return (IRR) Payback Profitability Index l l l 23

Internal Rate of Return Method Calculate the discount rate which makes the NPV zero Question: How high could the cost of capital be, so that the NPV of a project is still positive? The higher the IRR the better the project l l Advantages Calculation does not demand knowledge of the cost of capital Many people find it a more intuitive measure than NPV Usually gives the same signal as NPV l l l 24

Internal Rate of Return (IRR) The IRR is the discount rate, IRR, that makes NPV = 0. CF IRR t + 1 l T = 1 = = t 0 NPV I ( ) t IRR Rule for investment projects: Accept project if IRR > rp. Reject project if IRR < rp. l 25

IRR Example Consider, once again, the drug company that has the opportunity to invest $100 million in the development of a new drug that will generate after-tax cash flows of $20 million per year for the next 15 years. What is the IRR of this investment? The IRR makes NPV = 0. l l + 15 1 ( 1 ) IRR IRR = = 20 100 0 NPV This gives IRR = 18.4%. Accept the project if rp< 18.4%. l l 26

IRR Example (2) Consider again the example above l Time 0 1 2 3 -100.00 -50.00 30.00 200.00 Then the IRR solves: l 50 30 200 = + + = 100 0 NPV ( ( ) ) 2 3 + + + 1 IRR 1 1 IRR IRR IRR=18.29% Accept project if rp<18.29% 27

IRR Problems I: Borrowing or Lending? Consider the following two investment projects faced by a firm with rp= 10%. l Project B C 0 -5000 5000 1 2 IRR 40% 40% 0 9800 -9800 Both projects have an IRR = 40%, but only project A is acceptable. What is happening here? How can you modify the IRR rule so that it works? l 28

NPV Profiles 5000 4000 3000 2000 1000 B NPV 0 C 0% 10% 20% 30% 40% 50% 60% 70% -1000 -2000 -3000 -4000 -5000 Discount Rate 29

IRR Problems II: Multiple IRRs Consider a firm with the following investment project and a discount rate of rp= 25%. l Project E 0 1 2 IRR NPV @ 10% NPV @ 20% -372 -5000 16000 -12000 100%, 20% 0 Typical if investment at the end: Repair environmental damage Dismantling of machine Nuclear power plants This project has two IRRs: one above rpand the other below rp. Which should be compared to rp? Should the firm take this project? NPV@25%=120 l l 30

NPV Profile General rule: IRR works only if sign of CFs changes once: If negative first, then investment, positive NPV: IRR>Cutoff If positive first, then financing, positive NPV: IRR<Cutoff If pattern changes signs n times, there will be n different IRRs! l 400 200 0 0% 20% 40% 60% 80% 100% -200 NPV -400 -600 -800 l -1000 Discount rate 31

IRR Problems III: Mutually Exclusive Projects with different time horizon Consider the following two mutually exclusive projects. The discount rate is rp= 20%. l Project 0 1 2 IRR NPV (k=20%) 1,667 A -5,000 8,000 0 60% B -5,000 0 9,800 40% 1,806 Despite having a higher IRR, project A is less valuable than project B. l 32

NPV Profiles IRR does not take into account: Capital outlay: project with higher IRR has lower NPV (scale effect) Time horizon: Project A achieves higher return over 1 period Project B achieves mediocre return over 2 periods Implicit reinvestment assumption l 5000 4000 Project A Project B 3000 2000 1000 NPV 0 0 0.2 0.4 0.6 0.8 1 -1000 Discount Rate, k -2000 -3000 l 33

IRR Problems IV: Mutually Exclusive Projects with different scale Consider the following two mutually exclusive projects: l Project A D 0 -5000 -10000 1 2 IRR 60% 50% NPV @ 10% NPV @ 20% 2273 3636 8000 15000 0 0 1667 2500 Project A has higher IRR Project D has higher NPV at discount rates of 10% or 20% 34

NPV Profiles 5000 A 4000 D 3000 2000 NPV 1000 0 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% -1000 -2000 -3000 Discount Rate 35

Payback Method Calculate the time for cumulative cash flows to become positive The shorter the payback the better l l Advantages Does not demand input cost of capital Don t need to be able to multiply Gives a feel for time at risk l l l 36

Drawbacks Arbitrary Ranking. The following projects: l (A) -100 (B) -100 (C) -100 +90 +10 +10 +10 +90 +90 +100 +200 0 0 0 0 all look equally good Better ways of coping with risk if worried about eg confiscation, adjust cash flows (makes you think about consequences) if worried about risk, use higher discount factor recognize time profile of risks l Not additive, hence combining projects gives different results. l 37

Payback Example Consider the following two investment projects. Assume that rp = 20%. l Project 0 1 2 3 Payback NPV (k=20%) A -1,000 200 800 300 2.0 yrs. -104 B -1,000 200 200 2,000 2.3 yrs. 463 Which project is accepted if the payback period criteria is 2 years? l 38

Payback and Money at Risk Payback realizes that for duration of project, money is at risk More distant cash flows less certain NPV approach to Money at Risk : Discount rate = Risk free rate + Risk Premium Example: Risk free rate = 10% Risk premium = 5% l l Discount factor\Period @ 10% @ 15% Difference % Difference 1 2 3 4 0.91 0.87 3.95 4.35% 0.83 0.76 7.03 8.51% 0.75 0.66 9.38 0.68 0.57 11.13 16.29% 12.48% Much better than payback period! 39

Problems with Payback Ignores the Time Value of Money Ignores Cash Flows Beyond the Payback Period Ignores the Scale of the Investment Decision Criteria is Arbitrary l l l l 40

Profitability Index Profitability Index NPV I l = PI Used when the firm (or division) has a limited amount of capital to invest. Rank projects based upon their PIs. Invest in the projects with the highest PIs until all capital is exhausted (provided PI > 1). l l 41

Profitability Index Example Suppose your division has been given a capital budget of $6,000. Which projects do you choose? l Project I NPV PI A 1,000 600 0.6 B 4,000 2,000 0.5 C 6,000 2,400 0.4 D 3,000 600 0.2 E 5,000 500 0.1 42

Profitability Index Example Suppose your budget increases to $7,000. Choosing projects in descending order of PIs no longer maximizes the aggregate NPV. Projects A and C provide the highest aggregate NPV = $3,000 and stay within budget. Linear programming techniques can be used to solve large capital allocation problems. l l l l 43

Conclusions NPV has strong attractions: based on cash flows - so does not depend on accounting conventions fully reflects time value of money takes into account riskiness of project gives clear go/no go answer l 44