# 1 Investment Decisions and Capital Budgeting Global Financial Management Campbell R. Harvey Fuqua School of Business Duke University

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1 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

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

3 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

4 NPV - The Two-Period Case l 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!

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

6 Calculating NPVs l You have incremental cash flows: CF 0, CF 1, CF 2,..., CF T NPV in year 0 is:

7 Computing NPVs Example Step 1: Year1997199819992000 CF-100 -50 30 200 Step 2: Determine the PVs of cash flows: DF1.0000.9090.8260.751Total DCF-100.0-45.5 24.8150.3 = 29.6 Step 3: Sum! -100.00 - 45.5 + 24.8 + 150.3 = 29.6

8 l We showed that a project with a cash flow: -100-5030200 had an NPV of 29.6 @ 10%. So what? l Suppose the only shareholder has a bank account where she can borrow or deposit at 10%. l Take on the project, draw out 29.6 and spend: Why Use the NPV Rule?

9 What if NPV is negative? l Suppose you accept a negative NPV project: »Negative NPV means that you have to spend money today to be able to undertake the project!

10 Replicate the Project with Bonds l Recall argument about zero coupon bonds l 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 ” »Portfolio has zero cash flows in the future (perfect replication) * Value today = NPV!

11 Net Present Value (NPV) l The NPV measures the amount by which the value of the firm ’ s stock will increase if the project is accepted. l 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.

12 NPV Example l 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%?

13 NPV Example (cont.) r p = 10% r p = 20% What do you conclude?

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

15 Comparing Projects with Different Lives l Step 1: Calculate the NPV for each project. »NPV A =\$26,795 »NPV B =\$22,040 »The NPV of A is received every 4 years »The NPV of B is received every 3 years

16 Comparing Projects with Different Lives l Step 2: Convert the NPVs for each project into an equivalent annual annuity.

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

18 Special Topics: Replacing an Old Machine l The cost of the new machine is \$20,000 (including delivery and installation costs) and its economic useful life is 3 years. l The existing machine will last at most 2 more years. l The annual after-tax cash flows from each machine are given in the following table. l The discount rate is r p = 10%.

19 Replacing an Old Machine l Step 1: Calculate the NPV of the new machine. l Step 2: Convert the NPV for the new machine into an equivalent annual annuity. l The NPV of the new machine is equivalent to receiving \$6,544 per year for 3 years.

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

21 Eurotunnel NPV l 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. l 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. l Given the risk of the project, we assume a 13% discount rate.

22 Eurotunnel ’ s NPV

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

24 Internal Rate of Return Method l 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? l The higher the IRR the better the project Advantages l Calculation does not demand knowledge of the cost of capital l Many people find it a more intuitive measure than NPV l Usually gives the same signal as NPV

25 Internal Rate of Return (IRR) l The IRR is the discount rate, IRR, that makes NPV = 0. l IRR Rule for investment projects: »Accept project if IRR > r p. »Reject project if IRR < r p.

26 IRR Example l 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? l The IRR makes NPV = 0. l This gives IRR = 18.4%. l Accept the project if r p < 18.4%.

27 IRR Example (2) l Consider again the example above l Then the IRR solves: »IRR=18.29% »Accept project if r p <18.29%

28 IRR Problems I: Borrowing or Lending? l Consider the following two investment projects faced by a firm with r p = 10%. l 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?

29 NPV Profiles

30 IRR Problems II: Multiple IRRs l Consider a firm with the following investment project and a discount rate of r p = 25%. l Typical if investment at the end: »Repair environmental damage »Dismantling of machine –Nuclear power plants l This project has two IRRs: one above r p and the other below r p. Which should be compared to r p ? »Should the firm take this project? –NPV@25%=120

31 NPV Profile l 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 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/14/4349867/slides/slide_31.jpg", "name": "31 NPV Profile l 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: IRRCutoff »If positive first, then financing, positive NPV: IRR

32 IRR Problems III: Mutually Exclusive Projects with different time horizon l Consider the following two mutually exclusive projects. The discount rate is r p = 20%. l Despite having a higher IRR, project A is less valuable than project B.

33 NPV Profiles l 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 l Implicit reinvestment assumption

34 l Consider the following two mutually exclusive projects: »Project A has higher IRR »Project D has higher NPV at discount rates of 10% or 20% IRR Problems IV: Mutually Exclusive Projects with different scale

35 NPV Profiles

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

37 Drawbacks l Arbitrary Ranking. The following projects: (A)-100+90+10 0 0 (B)-100+10+90 0 0 (C)-100+10+90 +100 +200 all look equally good l 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.

38 Payback Example l Consider the following two investment projects. Assume that r p = 20%. l Which project is accepted if the payback period criteria is 2 years?

39 Payback and Money at Risk l Payback realizes that for duration of project, money is at risk »More distant cash flows less certain l NPV approach to “ Money at Risk ” : Discount rate = Risk free rate + Risk Premium Example: Risk free rate = 10% Risk premium = 5% »Much better than payback period!

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

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

42 Profitability Index Example l Suppose your division has been given a capital budget of \$6,000. Which projects do you choose?

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

44 Conclusions l 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

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