Measuring Investment Returns

Transcription

1 Measuring Investment Returns Aswath Damodaran Stern School of Business Aswath Damodaran 1

2 First Principles Invest in projects that yield a return greater than the minimum acceptable hurdle rate. The hurdle rate should be higher for riskier projects and reflect the financing mix used - owners funds (equity) or borrowed money (debt) Returns on projects should be measured based on cash flows generated and the timing of these cash flows; they should also consider both positive and negative side effects of these projects. Choose a financing mix that minimizes the hurdle rate and matches the assets being financed. If there are not enough investments that earn the hurdle rate, return the cash to stockholders. The form of returns - dividends and stock buybacks - will depend upon the stockholders characteristics. Aswath Damodaran 2

3 Measuring Returns Right: The Basic Principles Use cash flows rather than earnings. You cannot spend earnings. Use incremental cash flows relating to the investment decision, i.e., cashflows that occur as a consequence of the decision, rather than total cash flows. Use time weighted returns, i.e., value cash flows that occur earlier more than cash flows that occur later. The Return Mantra: Time-weighted, Incremental Cash Flow Return Aswath Damodaran 3

4 Steps in Investment Analysis Estimate a hurdle rate for the project, based upon the riskiness of the investment Estimate revenues and accounting earnings on the investment. Measure the accounting return to see if the investment measures up to the hurdle rate. Convert accounting earnings into cash flows Use the cash flows to evaluate whether the investment is a good investment. Time weight the cash flows Use the time-weighted cash flows to evaluate whether the investment is a good investment. Aswath Damodaran 4

5 I. Estimating the Hurdle Rate for an Investment If a firm is in only one business, and all of its investments are homogeneous: Use the company s costs of equity and capital to evaluate its investments. If the firm is in more than one business, but investments within each of business are similar: Use the divisional costs of equity and capital to evaluate investments made by that division If a firm is planning on entering a new business: Estimate a cost of equity for the investment, based upon the riskiness of the investment Estimate a cost of debt and debt ratio for the investment based upon the costs of debt and debt ratios of other firms in the business Aswath Damodaran 5

6 Analyzing Project Risk: Three Examples The Home Depot: A New Store The Home Depot is a firm in a single business, with homogeneous investments (another store). We will use The Home Depot s cost of equity (9.78%) and capital (9.51%) to analyze this investment. Boeing: A Super Jumbo Jet (capable of carrying 400+ people) We will use the cost of capital of 9.32% that we estimated for the aerospace division of Boeing. InfoSoft: An Online Software Store We will estimate the cost of equity based upon the beta for online retailers (1.725) and InfoSoft s debt ratio. We will use a much higher cost of debt for the project (7%) than InfoSoft s existing debt (6%) Cost of capital = 14.49% (.9338) + 7% (1-.42)(.0662) = 13.80% Aswath Damodaran 6

7 II. The Estimation Process Experience and History: If a firm has invested in similar projects in the past, it can use this experience to estimate revenues and earnings on the project being analyzed. Market Testing: If the investment is in a new market or business, you can use market testing to get a sense of the size of the market and potential profitability. Scenario Analysis: If the investment can be affected be a few external factors, the revenues and earnings can be analyzed across a series of scenarios and the expected values used in the analysis. Aswath Damodaran 7

8 The Home Depot s New Store: Experience and History The Home Depot has 700+ stores in existence, at difference stages in their life cycles, yielding valuable information on how much revenue can be expected at each store and expected margins. At the end of 1999, for instance, each existing store had revenues of $ 44 million, with revenues starting at about $ 40 million in the first year of a store s life, climbing until year 5 and then declining until year 10. Aswath Damodaran 8

9 The Margins at Existing Store Figure 9.3: Operating Expenses as % of Revenues % 88.5%-89% 89%-89.5% 89.5%-90% 90%-90.5% 90.5%-91% 91%-91.5% 91.5%-92% Operating Exp as % of Revenues Aswath Damodaran 9

10 Projections for The Home Depot s New Store For revenues, we will assume that the new store being considered by the Home Depot will have expected revenues of $ 40 million in year 1 (which is the approximately the average revenue per store at existing stores after one year in operation) that these revenues to grow 5% a year that our analysis will cover 10 years (since revenues start dropping at existing stores after the 10 th year). For operating margins, we will assume The operating expenses of the new store will be 90% of the revenues (based upon the median for existing stores) Aswath Damodaran 10

11 Scenario Analysis: Boeing Super Jumbo We consider two factors: Actions of Airbus (the competition): Produces new large capacity plane to match Boeing s new jet, Improves its existing large capacity plane (A- 300) or abandons this market entirely. Much of the growth from this market will come from whether Asia. We look at a high growth, average growth and low growth scenario. In each scenario, We estimate the number of planes that Boeing will sell under each scenario. We estimate the probability of each scenario. Aswath Damodaran 11

12 Scenario Analysis The following table lists the number of planes that Boeing will sell under each scenario, with the probabilities listed below each number. Airbus New Airbus A-300 Airbus abandons large plane large airplane High Growth in Asia (0.125) (0.125) (0.00) Average Growth in Asia (0.15) (0.25) (0.10) Low Growth in Asia (0.05) (0.10) (0.10) Expected Value = 120* * *0+100* * * * * *10 = 125 planes Aswath Damodaran 12

13 III. Measures of return: Accounting Earnings Principles Governing Accounting Earnings Measurement Accrual Accounting: Show revenues when products and services are sold or provided, not when they are paid for. Show expenses associated with these revenues rather than cash expenses. Operating versus Capital Expenditures: Only expenses associated with creating revenues in the current period should be treated as operating expenses. Expenses that create benefits over several periods are written off over multiple periods (as depreciation or amortization) Aswath Damodaran 13

14 From Forecasts to Accounting Earnings Separate projected expenses into operating and capital expenses: Operating expenses, in accounting, are expenses designed to generate benefits only in the current period, while capital expenses generate benefits over multiple periods. Depreciate or amortize the capital expenses over time: Once expenses have been categorized as capital expenses, they have to be depreciated or amortized over time. Allocate fixed expenses that cannot be traced to specific projects: Expenses that are not directly traceable to a project get allocated to projects, based upon a measure such as revenues generated by the project; projects that are expected to make more revenues will have proportionately more of the expense allocated to them. Consider the tax effect: Consider the tax liability that would be created by the operating income we have estimated Aswath Damodaran 14

15 Boeing Super Jumbo Jet: Investment Assumptions Boeing has already spent $ 2.5 billion in research expenditures, developing the Super Jumbo. (These expenses have been capitalized) If Boeing decides to proceed with the commercial introduction of the new plane, the firm will have to spend an additional $ 5.5 billion building a new plant and equipping it for production. Year Now Investment Needed $ 500 million 1 $ 1,000 million 2 $ 1,500 million 3 $ 1,500 million 4 $ 1,000 million After year 4, there will be a capital maintenance expenditure required of $ 250 million each year from years 5 through 15. Aswath Damodaran 15

16 Operating Assumptions The sale and delivery of the planes is expected to begin in the fifth year, when 50 planes will be sold. For the next 15 years (from year 6-20), Boeing expects to sell 125 planes a year. In the last five years of the project (from year 21-25), the sales are expected to decline to 100 planes a year. While the planes delivered in year 5 will be priced at $ 200 million each, this price is expected to grow at the same rate as inflation (which is assumed to be 3%) each year after that. Based upon past experience, Boeing anticipates that its cost of production, not including depreciation or General, Sales and Administrative (GS&A) expenses, will be 90% of the revenue each year. Boeing allocates general, selling and administrative expenses (G,S & A) to projects based upon projected revenues, and this project will be assessed a charge equal to 4% of revenues. (One-third of these expenses will be a direct result of this project and can be treated as variable. The remaining two-thirds are fixed expenses that would be generated even if this project were not accepted.) Aswath Damodaran 16

17 Other Assumptions The project is expected to have a useful life of 25 years. The corporate tax rate is 35%. Boeing uses a variant of double-declining balance depreciation to estimate the depreciation each year. Based upon a typical depreciable life of 20 years, the depreciation is computed to be 10% of the book value of the assets (other than working capital) at the end of the previous year. We begin depreciating the capital investment immediately, rather than waiting for the revenues to commence in year 5. Aswath Damodaran 17

18 Revenues: By Year Year Number of Planes Price per plane Expected Revenues 5 50 $ $ 10, $ $ 25, $ $ 26, $ $ 27, $ $ 28, $ $ 28, $ $ 29, $ $ 30, $ $ 31, $ $ 32, $ $ 33, $ $ 34, $ $ 35, $ $ 36, $ $ 37, $ $ 38, $ $ 32, $ $ 33, $ $ 34, $ $ 35, $ $ 36, Aswath Damodaran 18

19 Operating Expenses & S,G & A: By Year Year Revenues COGS GS&A Expense 5 $ 10,000 $ 9,000 $ $ 25,750 $ 23,175 $ 1,030 7 $ 26,523 $ 23,870 $ 1,061 8 $ 27,318 $ 24,586 $ 1,093 9 $ 28,138 $ 25,324 $ 1, $ 28,982 $ 26,084 $ 1, $ 29,851 $ 26,866 $ 1, $ 30,747 $ 27,672 $ 1, $ 31,669 $ 28,502 $ 1, $ 32,619 $ 29,357 $ 1, $ 33,598 $ 30,238 $ 1, $ 34,606 $ 31,145 $ 1, $ 35,644 $ 32,080 $ 1, $ 36,713 $ 33,042 $ 1, $ 37,815 $ 34,033 $ 1, $ 38,949 $ 35,054 $ 1, $ 32,094 $ 28,885 $ 1, $ 33,057 $ 29,751 $ 1, $ 34,049 $ 30,644 $ 1, $ 35,070 $ 31,563 $ 1, $ 36,122 $ 32,510 $ 1,445 Aswath Damodaran 19

20 Depreciation and Amortization: By Year Year Capital Depreciaton Book Value R&D Amortization Ending Value Deprecn & Expenditures Investment of R&D Amortization 0 $ 500 $ $ 1,000 $ 50 $ 1,450 $ 2,500 $ 167 $ 2,333 $217 2 $ 1,500 $ 145 $ 2,805 $ 2,333 $ 167 $ 2,167 $312 3 $ 1,500 $ 281 $ 4,025 $ 2,167 $ 167 $ 2,000 $447 4 $ 1,000 $ 402 $ 4,622 $ 2,000 $ 167 $ 1,833 $569 5 $ 250 $ 462 $ 4,410 $ 1,833 $ 167 $ 1,667 $629 6 $ 250 $ 441 $ 4,219 $ 1,667 $ 167 $ 1,500 $608 7 $ 250 $ 422 $ 4,047 $ 1,500 $ 167 $ 1,333 $589 8 $ 250 $ 405 $ 3,892 $ 1,333 $ 167 $ 1,167 $571 9 $ 250 $ 389 $ 3,753 $ 1,167 $ 167 $ 1,000 $ $ 250 $ 375 $ 3,628 $ 1,000 $ 167 $ 833 $ $ 250 $ 363 $ 3,515 $ 833 $ 167 $ 667 $ $ 250 $ 351 $ 3,413 $ 667 $ 167 $ 500 $ $ 250 $ 341 $ 3,322 $ 500 $ 167 $ 333 $ $ 250 $ 332 $ 3,240 $ 333 $ 167 $ 167 $ $ 250 $ 324 $ 3,166 $ 167 $ 167 $ - $ $ - $ 317 $ 2,849 $ $ - $ 285 $ 2,564 $ $ - $ 256 $ 2,308 $ $ - $ 231 $ 2,077 $ $ - $ 208 $ 1,869 $ $ - $ 187 $ 1,683 $ $ - $ 168 $ 1,514 $ $ - $ 151 $ 1,363 $ $ - $ 136 $ 1,227 $ $ - $ 123 $ 1,104 $123 Aswath Damodaran 20

21 Earnings on Project Year Revenues COGS GS&A Expense Deprecn & AmEBIT EBIT(1-t) 0 1 $0 $0 $0 $217 ($217) ($141) 2 $0 $0 $0 $312 ($312) ($203) 3 $0 $0 $0 $447 ($447) ($291) 4 $0 $0 $0 $569 ($569) ($370) 5 $10,000 $9,000 $400 $629 ($29) ($19) 6 $25,750 $23,175 $1,030 $608 $937 $609 7 $26,523 $23,870 $1,061 $589 $1,003 $652 8 $27,318 $24,586 $1,093 $571 $1,068 $694 9 $28,138 $25,324 $1,126 $556 $1,132 $ $28,982 $26,084 $1,159 $542 $1,197 $ $29,851 $26,866 $1,194 $529 $1,262 $ $30,747 $27,672 $1,230 $518 $1,327 $ $31,669 $28,502 $1,267 $508 $1,392 $ $32,619 $29,357 $1,305 $499 $1,458 $ $33,598 $30,238 $1,344 $491 $1,525 $ $34,606 $31,145 $1,384 $317 $1,760 $1, $35,644 $32,080 $1,426 $285 $1,854 $1, $36,713 $33,042 $1,469 $256 $1,946 $1, $37,815 $34,033 $1,513 $231 $2,038 $1, $38,949 $35,054 $1,558 $208 $2,129 $1, $32,094 $28,885 $1,284 $187 $1,739 $1, $33,057 $29,751 $1,322 $168 $1,815 $1, $34,049 $30,644 $1,362 $151 $1,891 $1, $35,070 $31,563 $1,403 $136 $1,968 $1, $36,122 $32,510 $1,445 $123 $2,045 $1,329 Aswath Damodaran 21

22 And the Accounting View of Return Year EBIT(1-t) Beginning BV Capital Exp Depreciation Ending BV Average BV Working Capital Return on Capital 1 ($140.83) $3, $1, $ $3, $3, $ % 2 ($202.58) $3, $1, $ $4, $4, $ % 3 ($290.66) $4, $1, $ $6, $5, $ % 4 ($369.93) $6, $1, $ $6, $6, $ % 5 ($18.77) $6, $ $ $6, $6, $1, % 6 $ $6, $ $ $5, $5, $2, % 7 $ $5, $ $ $5, $5, $2, % 8 $ $5, $ $ $5, $5, $2, % 9 $ $5, $ $ $4, $4, $2, % 10 $ $4, $ $ $4, $4, $2, % 11 $ $4, $ $ $4, $4, $2, % 12 $ $4, $ $ $3, $4, $3, % 13 $ $3, $ $ $3, $3, $3, % 14 $ $3, $ $ $3, $3, $3, % 15 $ $3, $ $ $3, $3, $3, % 16 $1, $3, $0.00 $ $2, $3, $3, % 17 $1, $2, $0.00 $ $2, $2, $3, % 18 $1, $2, $0.00 $ $2, $2, $3, % 19 $1, $2, $0.00 $ $2, $2, $3, % 20 $1, $2, $0.00 $ $1, $1, $3, % 21 $1, $1, $0.00 $ $1, $1, $3, % 22 $1, $1, $0.00 $ $1, $1, $3, % 23 $1, $1, $0.00 $ $1, $1, $3, % 24 $1, $1, $0.00 $ $1, $1, $3, % 25 $1, $1, $0.00 $ $1, $1, $3, % Average $ $3, $2, % Aswath Damodaran 22

23 Would lead use to conclude that... Invest in the Super Jumbo Jet The return on capital of 12.75% is greater than the cost of capital for aerospace of 9.32%; This would suggest that the project should not be taken. Aswath Damodaran 23

24 From Project to Firm Return on Capital Just as a comparison of project return on capital to the cost of capital yields a measure of whether the project is acceptable, a comparison can be made at the firm level, to judge whether the existing projects of the firm are adding or destroying value. Boeing Home Depot InfoSoft Return on Capital 5.82% 16.37% 23.67% Cost of Capital 9.17% 9.51% 12.55% ROC - Cost of Capital -3.35% 6.87% 11.13% Aswath Damodaran 24

25 Application Test: Assessing Investment Quality For the most recent period for which you have data, compute the aftertax return on capital earned by your firm, where after-tax return on capital is computed to be After-tax ROC = EBIT (1-tax rate)/ (BV of debt + BV of Equity) previous year For the most recent period for which you have data, compute the return spread earned by your firm: Return Spread = After-tax ROC - Cost of Capital For the most recent period, compute the EVA earned by your firm EVA = Return Spread * (BV of Debt +BV of Equity) Aswath Damodaran 25

26 IV. From Earnings to Cash Flows To get from accounting earnings to cash flows: you have to add back non-cash expenses (like depreciation and amortization) you have to subtract out cash outflows which are not expensed (such as capital expenditures) you have to make accrual revenues and expenses into cash revenues and expenses (by considering changes in working capital). For the Boeing Super Jumbo, we will assume that The depreciation used for operating expense purposes is also the tax depreciation. Working capital will be 10% of revenues, and the investment has to be made at the beginning of each year. Aswath Damodaran 26

27 Estimating Cash Flows: The Boeing Super Jumbo Year EBIT(1-t) Depreciation Cap Ex Change in WC Salvage Value FCFF 0 $ 3,000 $ (3,000) 1 $ (141) $ 217 $ 1,000 $ - $ (924) 2 $ (203) $ 312 $ 1,500 $ - $ (1,391) 3 $ (291) $ 447 $ 1,500 $ - $ (1,343) 4 $ (370) $ 569 $ 1,000 $ 1,000 $ (1,801) 5 $ (19) $ 629 $ 250 $ 1,575 $ (1,215) 6 $ 609 $ 608 $ 250 $ 77 $ $ 652 $ 589 $ 250 $ 80 $ $ 694 $ 571 $ 250 $ 82 $ $ 736 $ 556 $ 250 $ 84 $ $ 778 $ 542 $ 250 $ 87 $ $ 820 $ 529 $ 250 $ 90 $ 1, $ 862 $ 518 $ 250 $ 92 $ 1, $ 905 $ 508 $ 250 $ 95 $ 1, $ 948 $ 499 $ 250 $ 98 $ 1, $ 991 $ 491 $ 250 $ 101 $ 1, $ 1,144 $ 317 $ - $ 104 $ 1, $ 1,205 $ 285 $ - $ 107 $ 1, $ 1,265 $ 256 $ - $ 110 $ 1, $ 1,325 $ 231 $ - $ 113 $ 1, $ 1,384 $ 208 $ - $ (686) $ 2, $ 1,130 $ 187 $ - $ 96 $ 1, $ 1,180 $ 168 $ - $ 99 $ 1, $ 1,229 $ 151 $ - $ 102 $ 1, $ 1,279 $ 136 $ - $ 105 $ 1, $ 1,329 $ 123 $ - $ - $ 4,716 $ 6,168 Aswath Damodaran 27

28 The Depreciation Tax Benefit While depreciation reduces taxable income and taxes, it does not reduce the cash flows. The benefit of depreciation is therefore the tax benefit. In general, the tax benefit from depreciation can be written as: Tax Benefit = Depreciation * Tax Rate For example, in year 2, the tax benefit from depreciation to Boeing from this project can be written as: Tax Benefit in year 2 = $ 217 million (.35) = $ 76 million Proposition 1: The tax benefit from depreciation and other non-cash charges is greater, the higher your tax rate. Proposition 2: Non-cash charges that are not tax deductible (such as amortization of goodwill) and thus provide no tax benefits have no effect on cash flows. Aswath Damodaran 28

29 Depreciation Methods Broadly categorizing, depreciation methods can be classified as straight line or accelerated methods. In straight line depreciation, the capital expense is spread evenly over time, In accelerated depreciation, the capital expense is depreciated more in earlier years and less in later years. Assume that you made a large investment this year, and that you are choosing between straight line and accelerated depreciation methods. Which will result in higher net income this year? Straight Line Depreciation Accelerated Depreciation Which will result in higher cash flows this year? Straight Line Depreciation Accelerated Depreciation Aswath Damodaran 29

30 The Capital Expenditures Effect Capital expenditures are not treated as accounting expenses but they do cause cash outflows. Capital expenditures can generally be categorized into two groups New (or Growth) capital expenditures are capital expenditures designed to create new assets and future growth Maintenance capital expenditures refer to capital expenditures designed to keep existing assets. Both initial and maintenance capital expenditures reduce cash flows The need for maintenance capital expenditures will increase with the life of the project. In other words, a 25-year project will require more maintenance capital expenditures than a 2-year asset. Aswath Damodaran 30

31 To cap ex or not to cap ex Assume that you run your own software business, and that you have an expense this year of $ 100 million from producing and distribution promotional CDs in software magazines. Your accountant tells you that you can expense this item or capitalize and depreciate. Which will have a more positive effect on income? Expense it Capitalize and Depreciate it Which will have a more positive effect on cash flows? Expense it Capitalize and Depreciate it Aswath Damodaran 31

32 The Working Capital Effect Intuitively, money invested in inventory or in accounts receivable cannot be used elsewhere. It, thus, represents a drain on cash flows To the degree that some of these investments can be financed using suppliers credit (accounts payable) the cash flow drain is reduced. Investments in working capital are thus cash outflows Any increase in working capital reduces cash flows in that year Any decrease in working capital increases cash flows in that year To provide closure, working capital investments need to be salvaged at the end of the project life. Aswath Damodaran 32

33 V. From Cash Flows to Incremental Cash Flows The incremental cash flows of a project are the difference between the cash flows that the firm would have had, if it accepts the investment, and the cash flows that the firm would have had, if it does not accept the investment. The Key Questions to determine whether a cash flow is incremental: What will happen to this cash flow item if I accept the investment? What will happen to this cash flow item if I do not accept the investment? If the cash flow will occur whether you take this investment or reject it, it is not an incremental cash flow. Aswath Damodaran 33

34 Sunk Costs Any expenditure that has already been incurred, and cannot be recovered (even if a project is rejected) is called a sunk cost When analyzing a project, sunk costs should not be considered since they are incremental By this definition, market testing expenses and R&D expenses are both likely to be sunk costs before the projects that are based upon them are analyzed. If sunk costs are not considered in project analysis, how can a firm ensure that these costs are covered? Aswath Damodaran 34

35 Allocated Costs Firms allocate costs to individual projects from a centralized pool (such as general and administrative expenses) based upon some characteristic of the project (sales is a common choice) For large firms, these allocated costs can result in the rejection of projects To the degree that these costs are not incremental (and would exist anyway), this makes the firm worse off. Thus, it is only the incremental component of allocated costs that should show up in project analysis. How, looking at these pooled expenses, do we know how much of the costs are fixed and how much are variable? Aswath Damodaran 35

36 Boeing: Super Jumbo Jet The $2.5 billion already expended on the jet is a sunk cost, as is the amortization related that expense. (Boeing has spent the first, and it is entitled to the latter even if the investment is rejected) Two-thirds of the S,G&A expenses are fixed expenses and would exist even if this project is not accepted. Aswath Damodaran 36

37 The Incremental Cash Flows: Boeing Super Jumbo Year EBIT(1-t) Depreciation Cap Ex Change in WC Salvage Value FCFF Sunk Cost Fixed GS&A(1-t) Incremental FCFF 0 $0 $0 $3,000 $0 $0 ($3,000) ($2,500) ($500) 1 ($33) $50 $1,000 $0 $0 ($983) $0 $0 ($983) 2 ($94) $145 $1,500 $0 $0 ($1,449) $0 $0 ($1,449) 3 ($182) $281 $1,500 $0 $0 ($1,402) $0 $0 ($1,402) 4 ($262) $402 $1,000 $1,000 $0 ($1,859) $0 $0 ($1,859) 5 $90 $462 $250 $1,575 $0 ($1,273) $0 $173 ($1,100) 6 $718 $441 $250 $77 $0 $831 $0 $446 $1,278 7 $760 $422 $250 $80 $0 $852 $0 $460 $1,312 8 $802 $405 $250 $82 $0 $875 $0 $474 $1,349 9 $844 $389 $250 $84 $0 $899 $0 $488 $1, $886 $375 $250 $87 $0 $925 $0 $502 $1, $928 $363 $250 $90 $0 $952 $0 $517 $1, $971 $351 $250 $92 $0 $980 $0 $533 $1, $1,013 $341 $250 $95 $0 $1,010 $0 $549 $1, $1,056 $332 $250 $98 $0 $1,041 $0 $565 $1, $1,100 $324 $250 $101 $0 $1,073 $0 $582 $1, $1,144 $317 $0 $104 $0 $1,357 $0 $600 $1, $1,205 $285 $0 $107 $0 $1,383 $0 $618 $2, $1,265 $256 $0 $110 $0 $1,411 $0 $636 $2, $1,325 $231 $0 $113 $0 $1,442 $0 $655 $2, $1,384 $208 $0 ($686) $0 $2,277 $0 $675 $2, $1,130 $187 $0 $96 $0 $1,221 $0 $556 $1, $1,180 $168 $0 $99 $0 $1,249 $0 $573 $1, $1,229 $151 $0 $102 $0 $1,279 $0 $590 $1, $1,279 $136 $0 $105 $0 $1,310 $0 $608 $1, $1,329 $123 $0 $0 $4,716 $6,168 $0 $626 $6,794 Aswath Damodaran 37

38 VI. To Time-Weighted Cash Flows Incremental cash flows in the earlier years are worth more than incremental cash flows in later years. In fact, cash flows across time cannot be added up. They have to be brought to the same point in time before aggregation. This process of moving cash flows through time is discounting, when future cash flows are brought to the present compounding, when present cash flows are taken to the future The discount rate is the mechanism that determines how cash flows across time will be weighted. Aswath Damodaran 38

39 Present Value Mechanics Cash Flow Type Discounting Formula Compounding Formula 1. Simple CF CF n / (1+r) n CF 0 (1+r) n 2. Annuity A 1-1 (1+r) n r A (1 + r) n - 1 r 3. Growing Annuity 1 - A(1+g) (1 + g)n (1 + r) n r - g 4. Perpetuity A/r 5. Growing Perpetuity A(1+g)/(r-g) Aswath Damodaran 39

40 Discounted cash flow measures of return Net Present Value (NPV): The net present value is the sum of the present values of all cash flows from the project (including initial investment). NPV = Sum of the present values of all cash flows on the project, including the initial investment, with the cash flows being discounted at the appropriate hurdle rate (cost of capital, if cash flow is cash flow to the firm, and cost of equity, if cash flow is to equity investors) Decision Rule: Accept if NPV > 0 Internal Rate of Return (IRR): The internal rate of return is the discount rate that sets the net present value equal to zero. It is the percentage rate of return, based upon incremental time-weighted cash flows. Decision Rule: Accept if IRR > hurdle rate Aswath Damodaran 40

41 Closure on Cash Flows In a project with a finite and short life, you would need to compute a salvage value, which is the expected proceeds from selling all of the investment in the project at the end of the project life. It is usually set equal to book value of fixed assets and working capital In a project with an infinite or very long life, we compute cash flows for a reasonable period, and then compute a terminal value for this project, which is the present value of all cash flows that occur after the estimation period ends.. Aswath Damodaran 41

42 Salvage Value on Boeing Super Jumbo We will assume that the salvage value for this investment at the end of year 25 will be the book value of the investment. Book value of capital investments at end of year 25 = $1,104 million Book value of working capital investments: yr 25 = $3,612 million Salvage Value at end of year 25 = $4,716 million Aswath Damodaran 42

43 Considering all of the Cashflows The NPV Year FCFF Salvage Value FCFF + Salvage Present Value (@9.32%) 0 $ (500) $ - $ (500) $ (500) 1 $ (983) $ - $ (983) $ (899) 2 $ (1,449) $ - $ (1,449) $ (1,213) 3 $ (1,402) $ - $ (1,402) $ (1,073) 4 $ (1,859) $ - $ (1,859) $ (1,302) 5 $ (1,100) $ - $ (1,100) $ (704) 6 $ 1,278 $ - $ 1,278 $ $ 1,312 $ - $ 1,312 $ $ 1,349 $ - $ 1,349 $ $ 1,387 $ - $ 1,387 $ $ 1,427 $ - $ 1,427 $ $ 1,469 $ - $ 1,469 $ $ 1,513 $ - $ 1,513 $ $ 1,558 $ - $ 1,558 $ $ 1,606 $ - $ 1,606 $ $ 1,655 $ - $ 1,655 $ $ 1,956 $ - $ 1,956 $ $ 2,001 $ - $ 2,001 $ $ 2,048 $ - $ 2,048 $ $ 2,098 $ - $ 2,098 $ $ 2,952 $ - $ 2,952 $ $ 1,777 $ - $ 1,777 $ $ 1,822 $ - $ 1,822 $ $ 1,869 $ - $ 1,869 $ $ 1,918 $ - $ 1,918 $ $ 2,078 $ 4,716 $ 6,794 $ 732 Net Present Value = $ 4,019 Aswath Damodaran 43

44 Which makes the argument that.. The project should be accepted. The positive net present value suggests that the project will add value to the firm, and earn a return in excess of the cost of capital. By taking the project, Boeing will increase its value as a firm by $4,019 million. Aswath Damodaran 44

45 The IRR of this project NPV Profile: Boeing Super Jumbo $35, $30, $25, $20, $15, NPV $10, Internal Rate of Return $5, $0.00 ($5,000.00) Discount Rate Aswath Damodaran 45

46 The IRR suggests.. The project is a good one. Using time-weighted, incremental cash flows, this project provides a return of 14.88%. This is greater than the cost of capital of 9.32%. The IRR and the NPV will yield similar results most of the time, though there are differences between the two approaches that may cause project rankings to vary depending upon the approach used. Aswath Damodaran 46

47 Case 1: IRR versus NPV Consider a project with the following cash flows: Year Cash Flow Aswath Damodaran 47

48 Project s NPV Profile $60.00 $40.00 $20.00 $0.00 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32% 34% 36% 38% 40% 42% 44% 46% 48% 50% NPV ($20.00) ($40.00) ($60.00) ($80.00) ($100.00) Discount Rate Aswath Damodaran 48

49 What do we do now? This project has two internal rates of return. The first is 6.60%, whereas the second is 36.55%. Why are there two internal rates of return on this project? If your cost of capital is 12.32%, would you accept or reject this project? I would reject the project I would accept this project Explain. Aswath Damodaran 49

50 Case 2: NPV versus IRR Project A Cash Flow $ 350,000 $ 450,000 $ 600,000 $ 750,000 Investment $ 1,000,000 NPV = $467,937 IRR= 33.66% Project B Cash Flow $ 3,000,000 $ 3,500,000 $ 4,500,000 $ 5,500,000 Investment $ 10,000,000 NPV = $1,358,664 IRR=20.88% Aswath Damodaran 50

51 Which one would you pick? Assume that you can pick only one of these two projects. Your choice will clearly vary depending upon whether you look at NPV or IRR. You have enough money currently on hand to take either. Which one would you pick? Project A. It gives me the bigger bang for the buck and more margin for error. Project B. It creates more dollar value in my business. If you pick A, what would your biggest concern be? If you pick B, what would your biggest concern be? Aswath Damodaran 51

52 Capital Rationing, Uncertainty and Choosing a Rule If a business has limited access to capital, has a stream of surplus value projects and faces more uncertainty in its project cash flows, it is much more likely to use IRR as its decision rule. Small, high-growth companies and private businesses are much more likely to use IRR. If a business has substantial funds on hand, access to capital, limited surplus value projects, and more certainty on its project cash flows, it is much more likely to use NPV as its decision rule. As firms go public and grow, they are much more likely to gain from using NPV. Aswath Damodaran 52

53 An Alternative to IRR with Capital Rationing The problem with the NPV rule, when there is capital rationing, is that it is a dollar value. It measures success in absolute terms. The NPV can be converted into a relative measure by dividing by the initial investment. This is called the profitability index. Profitability Index (PI) = NPV/Initial Investment In the example described, the PI of the two projects would have been: PI of Project A = $467,937/1,000,000 = 46.79% PI of Project B = $1,358,664/10,000,000 = 13.59% Project A would have scored higher. Aswath Damodaran 53

54 Case 3: NPV versus IRR Project A Cash Flow $ 5,000,000 $ 4,000,000 $ 3,200,000 $ 3,000,000 Investment $ 10,000,000 NPV = $1,191,712 IRR=21.41% Project B Cash Flow $ 3,000,000 $ 3,500,000 $ 4,500,000 $ 5,500,000 Investment $ 10,000,000 NPV = $1,358,664 IRR=20.88% Aswath Damodaran 54

55 Why the difference? These projects are of the same scale. Both the NPV and IRR use timeweighted cash flows. Yet, the rankings are different. Why? Which one would you pick? Project A. It gives me the bigger bang for the buck and more margin for error. Project B. It creates more dollar value in my business. Aswath Damodaran 55

56 NPV, IRR and the Reinvestment Rate Assumption The NPV rule assumes that intermediate cash flows on the project get reinvested at the hurdle rate (which is based upon what projects of comparable risk should earn). The IRR rule assumes that intermediate cash flows on the project get reinvested at the IRR. Implicit is the assumption that the firm has an infinite stream of projects yielding similar IRRs. Conclusion: When the IRR is high (the project is creating significant surplus value) and the project life is long, the IRR will overstate the true return on the project. Aswath Damodaran 56

57 Solution to Reinvestment Rate Problem Cash Flow $ 300 $ 400 $ 500 $ 600 Investment <$ 1000> $300(1.15)3 $400(1.15)2 $500(1.15) $600 $575 $529 $456 Internal Rate of Return = 24.89% Modified Internal Rate of Return = 21.23% Terminal Value = $2160 Aswath Damodaran 57

58 Why NPV and IRR may differ.. A project can have only one NPV, whereas it can have more than one IRR. The NPV is a dollar surplus value, whereas the IRR is a percentage measure of return. The NPV is therefore likely to be larger for large scale projects, while the IRR is higher for small-scale projects. The NPV assumes that intermediate cash flows get reinvested at the hurdle rate, which is based upon what you can make on investments of comparable risk, while the IRR assumes that intermediate cash flows get reinvested at the IRR. Aswath Damodaran 58

59 Case: NPV and Project Life Project A $400 $400 $400 $400 $400 -$1000 NPV of Project A = $ 442 Project B $350 $350 $350 $350 $350 $350 $350 $350 $350 $350 -$1500 NPV of Project B = $ 478 Hurdle Rate for Both Projects = 12% Aswath Damodaran 59

60 Choosing Between Mutually Exclusive Projects The net present values of mutually exclusive projects with different lives cannot be compared, since there is a bias towards longer-life projects. To do the comparison, we have to replicate the projects till they have the same life (or) convert the net present values into annuities Aswath Damodaran 60

61 Solution 1: Project Replication Project A: Replicated $400 $400 $400 $400 $400 $400 $400 $400 $400 $400 -$1000 -$1000 (Replication) NPV of Project A replicated = $ 693 Project B $350 $350 $350 $350 $350 $350 $350 $350 $350 $350 -$1500 NPV of Project B= $ 478 Aswath Damodaran 61

62 Solution 2: Equivalent Annuities Equivalent Annuity for 5-year project = $442 * PV(A,12%,5 years) = $ Equivalent Annuity for 10-year project = $478 * PV(A,12%,10 years) = $ Aswath Damodaran 62

63 What would you choose as your investment tool? Given the advantages/disadvantages outlined for each of the different decision rules, which one would you choose to adopt? Return on Investment (ROE, ROC) Payback or Discounted Payback Net Present Value Internal Rate of Return Profitability Index Aswath Damodaran 63

64 What firms actually use.. Decision Rule % of Firms using as primary decision rule in IRR 53.6% 49.0% Accounting Return 25.0% 8.0% NPV 9.8% 21.0% Payback Period 8.9% 19.0% Profitability Index 2.7% 3.0% Aswath Damodaran 64

65 Boeing 747: What about exchange rate risk? A substantial portion of Boeing s cash flows on the Super Jumbo will come from sales to foreign airlines. Assuming that the price is set in U.S. dollars, this exposes Boeing to exchange rate risk. Should there be a premium added on to the discount rate for exchange rate risk? (Should we use a cost of capital higher than 9.32%?) Yes No Aswath Damodaran 65

66 Should there be a risk premium for projects with substantial foreign exposure? The exchange rate risk may be diversifiable risk (and hence should not command a premium) if the company has projects is a large number of countries (or) the investors in the company are globally diversified. For Boeing, it can be argued that this risk is diversifiable. The same diversification argument can also be applied against political risk, which would mean that it too should not affect the discount rate. It may, however, affect the cash flows, by reducing the expected life or cash flows on the project. For Boeing, this risk too is assumed to not affect the cost of capital. Any expenses associated with protecting against political risk (say, insurance costs) can be built into the cash flows. Aswath Damodaran 66

67 Equity Analysis: The Parallels The investment analysis can be done entirely in equity terms, as well. The returns, cashflows and hurdle rates will all be defined from the perspective of equity investors. If using accounting returns, Return will be Return on Equity (ROE) = Net Income/BV of Equity ROE has to be greater than cost of equity If using discounted cashflow models, Cashflows will be cashflows after debt payments to equity investors Hurdle rate will be cost of equity Aswath Damodaran 67

68 A New Store for the Home Depot It will require an initial investment of $20 million in land, building and fixtures. The Home Depot plans to borrow $ 5 million, at an interest rate of 5.80%, using a 10-year term loan. The store will have a life of 10 years. During that period, the store investment will be depreciated using straight line depreciation. At the end of the tenth year, the investments are expected to have a salvage value of $ 7.5 million. The store is expected to generate revenues of $40 million in year 1, and these revenues are expected to grow 5% a year for the remaining 9 years of the store s life. The pre-tax operating margin, at the store prior to depreciation, is expected to be 10% for the entire period. Aswath Damodaran 68

69 Interest and Principal Payments Year Outstanding debt Interest Expense Total Payment Principal Repaid Remaining Principa 1 $5,000, $290, $672, $382, $4,617, $4,617, $267, $672, $405, $4,211, $4,211, $244, $672, $428, $3,783, $3,783, $219, $672, $453, $3,329, $3,329, $193, $672, $479, $2,850, $2,850, $165, $672, $507, $2,342, $2,342, $135, $672, $537, $1,805, $1,805, $104, $672, $568, $1,237, $1,237, $71, $672, $601, $636, $636, $36, $672, $636, $0.00 Aswath Damodaran 69

70 Net Income on The Home Depot Store Year Revenues Operating Expenses Depreciation EBIT Interest Expense Taxable Income Taxes Net Income 1 $40,000,000 $36,000,000 $1,250,000 $2,750,000 $290,000 $2,460,000 $861,000 $1,599,000 2 $42,000,000 $37,800,000 $1,250,000 $2,950,000 $267,791 $2,682,209 $938,773 $1,743,436 3 $44,100,000 $39,690,000 $1,250,000 $3,160,000 $244,293 $2,915,707 $1,020,497 $1,895,209 4 $46,305,000 $41,674,500 $1,250,000 $3,380,500 $219,433 $3,161,067 $1,106,373 $2,054,693 5 $48,620,250 $43,758,225 $1,250,000 $3,612,025 $193,131 $3,418,894 $1,196,613 $2,222,281 6 $51,051,263 $45,946,136 $1,250,000 $3,855,126 $165,304 $3,689,823 $1,291,438 $2,398,385 7 $53,603,826 $48,243,443 $1,250,000 $4,110,383 $135,862 $3,974,521 $1,391,082 $2,583,438 8 $56,284,017 $50,655,615 $1,250,000 $4,378,402 $104,713 $4,273,689 $1,495,791 $2,777,898 9 $59,098,218 $53,188,396 $1,250,000 $4,659,822 $71,757 $4,588,065 $1,605,823 $2,982, $62,053,129 $55,847,816 $1,250,000 $4,955,313 $36,890 $4,918,423 $1,721,448 $3,196,975 Aswath Damodaran 70

71 The Hurdle Rate The analysis is done in equity terms. Thus, the hurdle rate has to be a real cost of equity The cost of equity for the Home Depot is 9.78%. Since the Home Depot s investments are assumed to be homogeneous, the cost of equity for this project is also assumed to be 9.78%. Aswath Damodaran 71

72 ROE on this Project Year Average BV of Equity Net Income Return on Equity 0 1 $ 17,766,459 $ 1,599, % 2 $ 17,070,481 $ 1,743, % 3 $ 16,405,356 $ 1,895, % 4 $ 15,772,810 $ 2,054, % 5 $ 15,174,665 $ 2,222, % 6 $ 14,612,846 $ 2,398, % 7 $ 14,089,386 $ 2,583, % 8 $ 13,606,431 $ 2,777, % 9 $ 13,166,249 $ 2,982, % 10 $ 12,771,236 $ 3,196, % Average $ 15,043,592 $ 2,345, % Aswath Damodaran 72

73 From Project ROE to Firm ROE As with the earlier analysis, where we used return on capital and cost of capital to measure the overall quality of projects, we can compute return on equity and cost of equity to pass judgment on whether a firm is creating value to its equity investors. Boeing Home Depot InfoSoft Return on Equity 7.58% 22.37% 33.47% Cost of Equity 10.58% 9.78% 13.19% ROE - Cost of Equity -2.99% 12.59% 20.28% Aswath Damodaran 73

74 Additional Assumptions Working capital is assumed to be 8% of revenues and the investment in working capital is at the beginning of each year. At the end of the project life, the book value of the store is assumed to be equal to the salvage value. Aswath Damodaran 74

75 An Incremental CF Analysis Year Net Income Depreciation Capital Expendituresssued/Principal Repnge in Working Ca Salvage Value FCFE 0 ($20,000,000) $5,000,000 ($3,200,000) ($18,200,000) 1 $1,599,000 $1,250,000 ($382,917) ($160,000) $2,306,083 2 $1,743,436 $1,250,000 ($405,127) ($168,000) $2,420,309 3 $1,895,209 $1,250,000 ($428,624) ($176,400) $2,540,185 4 $2,054,693 $1,250,000 ($453,484) ($185,220) $2,665,989 5 $2,222,281 $1,250,000 ($479,786) ($194,481) $2,798,014 6 $2,398,385 $1,250,000 ($507,614) ($204,205) $2,936,566 7 $2,583,438 $1,250,000 ($537,055) ($214,415) $3,081,968 8 $2,777,898 $1,250,000 ($568,205) ($225,136) $3,234,557 9 $2,982,242 $1,250,000 ($601,160) ($236,393) $3,394, $3,196,975 $1,250,000 ($636,028) $4,964,250 $7,500,000 $16,275,198 Aswath Damodaran 75

76 NPV of the Store Year FCFE PV at Cost of Equity 0 ($18,200,000) ($18,200,000) 1 $2,306,083 $2,100,640 2 $2,420,309 $2,008,281 3 $2,540,185 $1,919,976 4 $2,665,989 $1,835,547 5 $2,798,014 $1,754,825 6 $2,936,566 $1,677,646 7 $3,081,968 $1,603,856 8 $3,234,557 $1,533,307 9 $3,394,689 $1,465, $16,275,198 $6,401,681 $4,101,613 Aswath Damodaran 76

77 Internal Rate of Return: The Home Depot Store NPV Profile for The Home Depot $30,000,000 $25,000,000 $20,000,000 $15,000,000 $10,000,000 $5,000,000 Internal Rate of Return $0 ($5,000,000) ($10,000,000) ($15,000,000) Discount Rate Aswath Damodaran 77

78 The Role of Sensitivity Analysis Our conclusions on a project are clearly conditioned on a large number of assumptions about revenues, costs and other variables over very long time periods. To the degree that these assumptions are wrong, our conclusions can also be wrong. One way to gain confidence in the conclusions is to check to see how sensitive the decision measure (NPV, IRR..) is to changes in key assumptions. Aswath Damodaran 78

79 Viability of New Store: Sensitivity to Operating Margin NPV and Operating Margin $10,000 $8,000 $6,000 $4,000 $2,000 NPV $- 6% 7% 8% 9% 10% 11% 12% $(2,000) $(4,000) $(6,000) Operating Margin Aswath Damodaran 79

80 What does sensitivity analysis tell us? Assume that the manager at The Home Depot who has to decide on whether to take this plant is very conservative. She looks at the sensitivity analysis and decides not to take the project because the NPV would turn negative if the operating margin drops below 8%. Is this the right thing to do? Yes No Explain. Aswath Damodaran 80

81 The Consistency Rule for Cash Flows The cash flows on a project and the discount rate used should be defined in the same terms. If cash flows are in one currency, the discount rate has to be a dollar (baht) discount rate If the cash flows are nominal (real), the discount rate has to be nominal (real). If consistency is maintained, the project conclusions should be identical, no matter what cash flows are used. Aswath Damodaran 81

82 The Home Depot: A New Store in Chile It will require an initial investment of 4700 million pesos for land, building and fixtures. The Home Depot plans to borrow 1880 million pesos, at an interest rate of 12.02%, using a 10-year term loan. The store will have a life of 10 years. During that period, the store will be depreciated using straight line depreciation. At the end of the tenth year, the investments are expected to have a salvage value of 2,350 million pesos. The store is expected to generate revenues of 7,050 million pesos in year 1, and these revenues are expected to grow 12% a year for the remaining 9 years. The pre-tax operating margin at the store, prior to depreciation, is expected to be 6% for the entire period. The working capital requirements are estimated to be 10% of total revenues, and investments will be made at the beginning of each year. Aswath Damodaran 82

83 The Home Depot Chile Store: Cashflows in Pesos Year Net Income Depreciation Capital Expenditures Debt Issued/Principal Repayment Change in Working Capital Salvage Value FCFE 0 (4,700.00) 1, (705.00) (3,525.00) 1 (22.83) (107.01) (84.60) (119.87) (94.75) (134.29) (106.12) (150.43) (118.86) (168.52) (133.12) (188.78) (149.09) (211.48) (166.99) (236.91) (187.02) (265.39) (209.47) (297.30) 1, , , Aswath Damodaran 83

84 The Home Depot Chile Store: Cost of Equity in Pesos Cost of Equity for a U.S. store = 9.78% Estimating the Country Risk Premium for Chile Default spread based on Chilean Bond rating = 1.1% Relative Volatility of Chilean Equity to Bond Market = 2.2 Country risk premium for Chile = 1.1% * 2.2 = 2.42% Cost of Equity for a Chilean Store (in U.S. $) = 5% (5.5% %) = 11.88% Assume that the expected inflation rate in Chile is 8% and the expected inflation rate in the U.S. is 2%. Cost of Equity for a Chilean Store (in Pesos) = [(1 + Cost of Equity in $)* (1 + inflation Chile )/ (1 + inflation US )] - 1 =[ * (1.08/1.02)] -1 = 18.46% Aswath Damodaran 84

85 NPV in Pesos Year FCFE in pesos (millions PV at Peso Cost of Equi 0-3, , , ,319 Aswath Damodaran 85

86 Converting Pesos to U.S. dollars This entire analysis can be done in dollars, if we convert the peso cash flows into U.S. dollars. If you want the analysis to yield consistent conclusions, expected exchange rates have to be estimated based upon expected inflation rates: Current Exchange Rate = 470 pesos Expected Rate t = Exchange Rate* (1 + inflation Chile )/ (1 + inflation US )] Expected Exchange Rate in year 1 = 470 pesos * (1.08/1.02) = Aswath Damodaran 86

87 Analyzing the Project: U.S. Dollars Year FCFE in pesos (millions) Expected Exchange Rate FCFE in $ $ (7,500,000) $ 41, $ 67, $ 94, $ 121, $ 148, $ 176, $ 204, $ 233, $ 263, $ 5,747,306 Aswath Damodaran 87

88 NPV in U.S. Dollars Year FCFE in $ PV at $ cost of equity 0 $ (7,500,000) $ (7,500,000) 1 $ 41,327 $ 36,938 2 $ 67,797 $ 54,161 3 $ 94,457 $ 67,445 4 $ 121,391 $ 77,471 5 $ 148,686 $ 84,812 6 $ 176,428 $ 89,949 7 $ 204,707 $ 93,282 8 $ 233,612 $ 95,148 9 $ 263,235 $ 95, $ 5,747,306 $ 1,870,008 NPV (in U.S. $) $ (4,934,960) In Pesos Aswath Damodaran 88

89 Dealing with Inflation In our analysis, we used nominal dollars and pesos. Would the NPV have been different if we had used real cash flows instead of nominal cash flows? It would be much lower, since real cash flows are lower than nominal cash flows It would be much higher It should be unaffected Aswath Damodaran 89

90 From Nominal to Real : The Home Depot To do a real analysis, you need a real cost of equity or capital Nominal cost of equity for The Home Depot = 9.78% Expected Inflation rate = 2% Real Cost of Equity = (1.0978/1.02)-1 = 7.59% To estimate cash flows in real terms Real Cash flow t = Nominal Cash flow t / (1+ Expected Inflation rate) t Aswath Damodaran 90

91 Nominal versus Real Year FCFE (nominal) PV (nominal) Deflation factor FCFE (Real) PV (Real) 0 ($18,200,000) ($18,200,000) ($18,200,000) $ (18,200,000) 1 $2,826,083 $2,574, $2,769,830 $ 2,574,315 2 $2,966,309 $2,461, $2,849,397 $ 2,461,331 3 $3,113,485 $2,353, $2,931,242 $ 2,353,299 4 $3,267,954 $2,250, $3,015,429 $ 2,250,003 5 $3,430,077 $2,151, $3,102,025 $ 2,151,234 6 $3,600,232 $2,056, $3,191,098 $ 2,056,796 7 $3,778,817 $1,966, $3,282,720 $ 1,966,497 8 $3,966,249 $1,880, $3,376,963 $ 1,880,157 9 $4,162,966 $1,797, $3,473,900 $ 1,797, $17,081,888 $6,718, $13,970,716 $ 6,718,984 NPV $8,010,219 $ 8,010,219 Aswath Damodaran 91

92 Side Costs and Benefits Most projects considered by any business create side costs and benefits for that business. The side costs include the costs created by the use of resources that the business already owns (opportunity costs) and lost revenues for other projects that the firm may have. The benefits that may not be captured in the traditional capital budgeting analysis include project synergies (where cash flow benefits may accrue to other projects) and options embedded in projects (including the options to delay, expand or abandon a project). The returns on a project should incorporate these costs and benefits. Aswath Damodaran 92