Capital Budgeting. Net Present Value and Other Investment Criteria. Professor: Burcu Esmer

Transcription

1 Capital Budgeting Net Present Value and Other Investment Criteria Professor: Burcu Esmer 1

2 Firm Objective Maximize Value Capital Budgeting Decision Invest in projects that add value to the firm Financing Decision Maximize firm value through optimal capital structure Payout Decision Return excess cash to investors to maximize shareholder wealth 2

3 Capital Budgeting Decision Invest in projects that add value to the firm Value projects using cash flows, reflecting the timing and magnitude of cash flows and all side effects Discount cash flows using a discount rate that reflects the risk of the project and cost of capital 3

4 Capital Budgeting 1. Estimate project cash flows (CFs) 2. Estimate a discount rate (r), if needed. 3. Apply a decision rule. Possible decision rules: Rules of thumb payback rule, discounted payback rule NPV IRR, Modified IRR 4. Make a decision! 4

5 Typical Project Initial cost or outlay Cf i s : cash flows net of additional costs. C 0 CF 1 CF 2 CF 3 + CF N Terminal CF r =? N Appropriate discount rate Opportunity Cost of Capital - Expected rate of return given up by investing in a project Terminal cash flow includes Salvage Value + other cash flows resulting from the termination of the project. 5

6 Net Present Value (NPV) estimate CFs, use DCF valuation NPV = PV inflows Pv outflows Present value of cash flows minus initial investments. Net Present Value Rule Find and accept projects with a positive NPV (NPV > 0) (Reject if NPV < 0!! ) NPV is additive Value of firm is sum of NPVs of all of its (past, present, and future) projects Accepting a project with a positive NPV increases the value of the firm by the NPV 6

7 Net Present Value Example Q: Suppose we can invest $50 today & receive $60 later today. What is our increase in value? A: Profit = - $50 + $60 = $10 $10 $50 Added Value Initial Investment 7

8 Net Present Value Example Suppose we can invest $50 today and receive $60 in one year. What is our increase in value given a 10% expected return? Profit = This is the definition of NPV 1.10 $4.55 $4.55 Added Value $50 Initial Investment 8

9 Valuing an Office Building Step 1: Forecast cash flows Cost of building = C 0 = 350,000 Sale price in Year 1 = C 1 = 400,000 Step 2: Estimate opportunity cost of capital If equally risky investments in the capital market offer a return of 7%, then Cost of capital = r = 7% 9

10 Valuing an Office Building Step 3: Discount future cash flows PV C (1 r ) 400,000 (1.07) 1 373,832 Step 4: Go ahead if PV of payoff exceeds investment NPV 350, ,832 23,832 10

11 Risk and Present Value Higher risk projects require a higher rate of return Higher required rates of return cause lower PVs PV of C1 $400,000 at 7% 400,000 PV 373,

12 Risk and Present Value PV of C1 $400,000 at 12% 400,000 PV 357, PV of C1 $400,000 at 7% 400,000 PV 373,

13 Net Present Value NPV = PV - required investment NPV C 0 Ct ( 1 r) t NPV C 0 C1 C2 Ct ( 1 r) ( 1 r) ( 1 r) t 13

14 Net Present Value Terminology C = Cash Flow t = time period of the investment r = opportunity cost of capital The Cash Flow could be positive or negative at any time period. 14

15 Net Present Value Net Present Value Rule Managers increase shareholders wealth by accepting all projects that are worth more than they cost. Therefore, they should accept all projects with a positive net present value. 15

16 Net Present Value Example You have the opportunity to purchase an office building. You have a tenant lined up that will generate $16,000 per year in cash flows for three years. At the end of three years you anticipate selling the building for $450,000. How much would you be willing to pay for the building? Assume a 7% opportunity cost of capital 16

17 Net Present Value Example - continued $16,000 $16,000 $466,000 $450,000 $16,000 Present Value ,953 13, ,395 $409,323 17

18 Net Present Value Example - continued If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building? 18

19 Net Present Value Example - continued If the building is being offered for sale at a price of $350,000, would you buy the building and what is the added value generated by your purchase and management of the building? NPV NPV 16, , , 000 ( 1. 07) ( 1. 07) $59, , 000 ( 1. 07)

20 Why does the NPV Rule work? The NPV Rule works properly for three reasons: NPV uses cash flows Cash flows can t be manipulated like earnings NPV uses all cash flows of a project Some approaches ignore cash flows beyond a certain date NPV discounts the cash flows properly Cash flows discounted at the opportunity cost of capital, an economically-meaningful rate, unlike many other methods 20

21 Other Methods Many other methods of project valuation are used in practice Easier to calculate Overemphasis on short-term results Simplicity of communication Comparability across firms (or subsidiaries) Managers accustomed to certain rules Difficult for junior-level analyst to change environment Each alternative method has its own problems 21

22 Methods at Work in Actual Companies NPV IRR Payback Book Rate of Return Profitability Index 0% 10% 20% 30% 40% 50% 60% 70% 80% Source: Graham and Harvey (2001) 22 % of CFOs Using Method

23 Which Methods Will We Consider? NPV, Payback, IRR, MIRR Why not look at other methods? Most other methods are pretty bad calculations, ignoring important finance principles Don t want to create a habit of calculating these other measures because they are so bad Most are pretty easy to calculate so you can figure them out quickly if needed in the future 23

24 Other Investment Criteria 1. Payback Method Payback Period - Time until cash flows recover the initial investment of the project. The payback rule specifies that a project be accepted if its payback period is less than the specified cutoff period. The following example will demonstrate the absurdity of this statement. 24

25 Payback Method Example The three project below are available. The company accepts all projects with a 2 year or less payback period. Show how this decision will impact our decision. Cash Flows Project C 0 C 1 C 2 C 3 Payback NPV@10% A -2,000 +1,000 +1, , ,249 B -2,000 +1,000 +1, C -2, ,

26 Problems with payback: Payback does not consider any cash flows that arrive after the payback. The Payback Rule ignores the time value of money. It equally weights all the cash flows before the cutoff. Accept too many short-lived projects! Why do people use it then? IT IS EASY TO COMMUNICATE! 26

27 Other Investment Criteria 2. Discounted Payback Method Discounted-payback period: Number of periods before the present value of cash flows equals or exceeds the initial investment. Advantage : You will never accept a negative NPV project. Disadvantage: It does not account the cash flows after the cutoff date. e.g. If a project costs $5,000 and will generate annual cash flows of $660 for 20 years, what is the payback period? If the interest rate is 6, what is the discounted payback period? 27

28 Other Investment Criteria 3. Internal Rate of Return The most popular alternative to NPV IRR is the discount rate that causes the NPV of a project to equal zero NPV C C1 1 IRR C2 (1 IRR) CT (1 IRR) 0 2 T 0 Only real way to calculate IRR: trial and error N-period problem gives N-degree polynomial Calculators or computers do it much quicker than we can 28

29 NPV Profile plot of an investment s NPV at various discount rates shows ranges of r where you would accept, reject, or be indifferent Managers increase shareholders wealth by accepting all projects which offer a rate of return that is higher than the opportunity cost of capital. 29

30 Internal Rate of Return Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment? 30

31 Internal Rate of Return Example You can purchase a building for $350,000. The investment will generate $16,000 in cash flows (i.e. rent) during the first three years. At the end of three years you will sell the building for $450,000. What is the IRR on this investment? 0 350, , , , 000 ( 1 IRR) ( 1 IRR) ( 1 IRR) IRR = 12.96% 31

32 Internal Rate of Return Calculating IRR by using a spreadsheet Year Cash Flow Formula 0 ( ,00) IRR = 12,96% =IRR(B4:B7) , , ,00 32

33 Internal Rate of Return NPV (,000s) IRR=12.96% Discount rate (%) 33

34 Internal Rate of Return Calculating the IRR can be a laborious task. Fortunately, financial calculators can perform this function easily. Note the previous example. 34

35 Internal Rate of Return Example You have two proposals to choice between. The initial proposal has a cash flow that is different than the revised proposal. Using IRR, which do you prefer? Project C 0 C 1 C 2 C 3 IRR NPV@7% Initial Proposal % $ 24,000 Revised Proposal % $ 59,000 35

36 Internal Rate of Return Example NPV You have two proposals to choice between. The initial proposal (H) has a cash flow that is different than the revised proposal (I). Using IRR, which do you prefer? (1 IRR ) (1 IRR ) (1 IRR ) % 0 NPV (1 IRR ) 14.29% 0 36

37 NPV $, 1,000s Internal Rate of Return Revised proposal IRR= 12.96% IRR= 14.29% 10 0 Initial proposal IRR= 12.26% Discount rate, %

38 Project Interactions When you need to choose between mutually exclusive projects, the decision rule is simple. Calculate the NPV of each project, and, from those options that have a positive NPV, choose the one whose NPV is highest. Note: The Internal rate of return rule will give the same answer (accept or reject) as the NPV rule as long as the NPV of a project declines smoothly as the discount rate increases. 38

39 IRR Rule IRR Rule: accept a project if IRR is greater than the opportunity cost of capital Advantages People like to look at returns (managers and investors) Comparable across projects of different sizes Useful in preparing analysis for outside investors (sometimes difficult to figure discount rate to apply NPV Rule) 39

40 Pretty good rule, but be careful Pitfall 1 - Lending or Borrowing? With some cash the NPV of the project increases as the discount rate increases This is contrary to the normal relationship between PV and discount rates. Pitfall 2 - Multiple Rates of Return Certain cash flows can generate NPV=0 at two different discount rates. Pitfall 3 - Mutually Exclusive Projects IRR sometimes ignores the magnitude of the project. The following two projects illustrate that problem. Another Issue Cash flows assumed to be reinvested at IRR 40

41 Pitfall 1: Lending or borrowing? Consider two investments: Obviously, these are not both good investments If we accepted both, we would have an investment with no cash flows obviously one is good and one is bad Be careful, pay attention to what is going on 41

42 $2, $2, $1, $1, Net Present Value $ $ % ($500.00) 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% 18.0% 20.0% 22.0% 24.0% 26.0% 28.0% 30.0% 32.0% 34.0% 36.0% 38.0% 40.0% Project A Project B ($1,000.00) ($1,500.00) ($2,000.00) 42 ($2,500.00) Discount Rate

43 Pitfall 2: Multiple Rates of Return When the sign of the cash flows changes more than once, we usually get multiple IRRs Which one do we use? Problem! Consider the following project cash flows Negative cash flows at the end of projects common for investments like nuclear power plants, coal mines, etc where there is significant clean up cost C 0 C 1 C 2 C 3 C 4 Project A -$1000 $600 $800 $900 -$700 43

44 Pitfall 2: Multiple Rates of Return $2, $1, $1, Net Present Value $ $ % % % % % % % % % -5.00% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00% 45.00% 50.00% NPV ($500.00) ($1,000.00) 44 ($1,500.00) Discount Rate

45 Pitfall 2: Multiple Rates of Return GOOD NEWS! This problem can be corrected using MIRR (modified internal rate of return. 45

46 Other Investment Criteria 4. Internal Rate of ReturnModified Internal Rate of Return (MIRR) IRR assumes that all cash flows are reinvested at the IRR until the end of the project Reinvestment at the opportunity cost of capital is a better assumption MIRR fixes this problem, and assumes that all cash flows are reinvested at the opportunity cost of capital 46

47 Calculating MIRR Method Bring all positive cash flows to the end using the opp. cost of capital as the rate Bring all negative cash flows to the beginning using the opp. cost of capital Find the IRR of the new cash flows, one at the beginning and one at the end Easier to see with an example 47

48 MIRR Example 1 Cost of Capital: 10% $1000 $300 $300 $400 $700 -$1000 Now find IRR of these cash flows $1000 $ (1 MIRR) 4 MIRR 17.44% $700 $440 $363 $399.3 $1,902.3 The IRR of the original cash flows was 21.24%, so the MIRR is less than the IRR in this case 48

49 MIRR Example 2 Cost of Capital: 10% $1000 $300 -$300 $400 $700 -$1000 -$247.9 Now find IRR of these cash flows $ $ (1 MIRR) 4 MIRR 5.39% $700 $440 $399.3 $

50 MIRR Rule Like IRR, accept project if MIRR > opportunity cost of capital MIRR is a pretty good rule, even better than IRR since it deals with reinvestment in a more practical way However, it has the same pitfalls as IRR so be careful where you apply it Doesn t always agree with the NPV rule 50

51 Pitfall 3: Mutually Exclusive Projects Mutually exclusive projects: can only accept one NPV rule tells us to pick the one with the higher NPV Does the IRR rule give us the same decisions? Not necessarily due to scale of projects C 0 C 1 C 2 C 3 IRR 10% Project A -$9000 $3000 $4000 $ % $ Project B -$2000 $750 $950 $ % $

52 $4, $3, $2, Net Present Value $1, $ % 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% 18.0% 20.0% 22.0% 24.0% 26.0% 28.0% 30.0% 32.0% 34.0% 36.0% 38.0% 40.0% Project A Project B ($1,000.00) ($2,000.00) 52 ($3,000.00) Discount Rate

53 Can we salvage IRR for mutually exclusive projects? We can use IRR to evaluate mutually exclusive projects Find IRR of incremental cash flows C 0 C 1 C 2 C 3 IRR 10% Project A -$9000 $3000 $4000 $ % $ Project B -$2000 $750 $950 $ % $ A-B -$7000 $2250 $3050 $ % $ Accept Project A since incremental cash flows have IRR above the opportunity cost of capital 53

54 So is IRR any good? We pointed out several pitfalls of using IRR. Does this mean it is not a good rule for making investment decisions? No. Used properly, it is a very useful rule We need to be aware of the potential for poor decisions using IRR It is a good idea to use NPV to make your decision, and IRR as a supporting measure to help managers better understand the decision 54

55 Conclusion NPV is Best IRR has problems with mutually exclusive projects project scale issues reinvestment at IRR If you want to use rates to judge projects use MIRR Reinvestment rate assumption is changed to reflect reinvestment at opportunity cost of capital. 55

56 Mutually Exclusive Projects When you need to choose between mutually exclusive projects, the decision rule is simple. Calculate the NPV of each project, and, from those options that have a positive NPV, choose the one whose NPV is highest. 56

57 Using the NPV Rule to Choose among Projects When choosing among mutually exclusive projects, calculate the NPV of each alternative and choose the highest positive-npv project. Example: Consider two projects, assuming a 10% opportunity cost of capital. Which project should be selected? Cash Flows Project C 0 C 1 C 2 NPV Project 1 - $1,000 $700 $500 $49.59 Project 2 - $1,000 $500 $700 $33.06 Challenges to the NPV Rule 1. The Investment Timing Decision 2. The Choice between Long and Short-Lived Equipment 3. When to Replace an Old Machine 57

58 More on Mutually Exclusive Projects Investment Timing Projects with unequal lives 58

59 1. Investment Timing Sometimes you have the ability to defer an investment and select a time that is more ideal at which to make the investment decision. Example A common example involves a tree farm. You may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet increase the cash flow. Assume an opportunity cost of capital of 10%. 59

60 1. Investment Timing Example A common example involves a tree farm. You may defer the harvesting of trees. By doing so, you defer the receipt of the cash flow, yet increase the cash flow. Assume an opportunity cost of capital of 10%. Year Cost Sales Value NPV

61 2. Projects with unequal lives NPV Analysis for projects with Unequal Lives OR set up projects for equal time periods ( common life / replacement chain method) & compare NPVs find NPVs as usual; then find EAAs and compare (choose project that adds more value per year) Equivalent Annual Annuity (EAA): annualized NPV find NPV; set NPV = PVA, solve for payment (the EAA) 61

62 Equivalent Annual Annuity Equivalent Annual Cost - The cash flow per period with the same present value as the cost of buying and operating a machine. Equivalent annual annuity = present value of cash flows annuity factor 62

63 Equivalent Annual Annuity Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual annuity method

64 Equivalent Annual Annuity Example (with a twist) Select one of the two following projects, based on the revenue they generate (r=9%). 64

65 Profitability Index Profitabil ity Index Initial NPV Investment Profitability Index Ratio of net present value to initial investment. 65

66 Profitability Index Profitability Project PV Investment NPV Index J /3 =.33 K /5 =.20 L /7 =.43 M /6 =.33 N /4 =.25 The pitfall of Profitability Index: it may favor small projects over larger projects with higher NPVs. 66

67 Capital Rationing Capital Rationing - Limit set on the amount of funds available for investment. Soft Rationing - Limits on available funds imposed by management. Hard Rationing - Limits on available funds imposed by the unavailability of funds in the capital market. 67

68 To sum up 68

69 Capital Budgeting Techniques 69