NPV: DOING IT BETTER

Herbert Kierulff

Donald Snellman Professor of Entrepreneurship and Finance

School of Business and Economics

Seattle Pacific University

3307 Third Avenue West

Seattle, WA 98119

Phone: (206) 281-3523

Fax: (206) 281-2733

hkierulf@spu.edu

NPV: DOING IT BETTER

Abstract: Net Present Value has become the single most important tool in investment

analysis and capital budgeting. It is a valuable method that is significantly limited by

seven basic suppositions that almost always attend its use. These suppositions are either

unknown, ignored, or treated in a cursory way by those who practice and write about the

method. We ignore these assumptions at our peril because doing so easily leads to

erroneous financial conclusions. This article examines the five and shows how

academics, practitioners, and students can deal with them without undue effort. Doing so

leads to a better NPV.

Key Words: Net Present Value, Present Value, Discounted Cash Flow, Capital

Budgeting, Discount Rate, Risk Adjusted Discount Rate, Capital Asset Pricing Model.

1

INTRODUCTION

Ryan and Ryan’s (2002) survey indicates that 85% of Fortune 1000

companies use Net Present Value (NPV) 75-100% of the time in making investment

decisions. Earlier studies (Burns & Walker, 1987; Gitman & Forrester, 1977) show a

similar preference among executives, and a propensity to use NPV over others such

as payback and return on funds employed. The model prevails in the textbooks,

articles, computer spreadsheets, and calculators.

The literature tends to make seven basic and important suppositions when

discussing NPV that are rarely examined in sufficient detail. The central message of this

article is that these suppositions can easily lead to very large errors—errors that may lead

to bad decisions. Academics, executives, and finance professionals can deal with the

negative consequences of all of these assumptions with relative ease if they recognize

that they exist and apply the simple measures discussed here to deal with them.

The article begins with an introduction to the assumptions and then

demonstrates their implications using an example. Finally, it introduces briefly

other factors beyond the scope of this paper that may bring needed adjustments to

NPV.

2

WHAT ARE THE ASSUMPTIONS; WHAT ARE THEIR IMPLICATIONS

The discounted cash flow models presented in textbooks and other educational

materials in the finance literature typically take for granted seven suppositions. These

seven are either potentially misleading or completely wrong:

1. All cash flows, including the initial investment, come at the end

of the year in which they occur.

2. The initial investment happens all at once.

3. The initial investment is not risky.

4. The firm uses its cost of capital or the project hurdle rate to

discount fixed costs and investments made after the initial one.

5. The firm uses its cost of capital or the project hurdle rate to

discount the project terminal value.

6. The cost of capital or project hurdle rate is appropriate to

measure the required rate of return on the free cash flows

resulting from the investment.

7. The positive cash flows resulting from the investment are

reinvested at the cost of capital or project hurdle rate.

The following example, similar to ones found in articles and textbooks, is used to

demonstrate the logical and practical inconsistencies in the assumptions:

The initial investment for the new Apex Project is $5 million at the end of

year 0, of which $4 million is tax-deductable research and development (R&D). The

rest is equipment. The expected sales are $22 million over six years, at which time

the product will become obsolete and the project liquidated. The $4 million R&D

includes start-up costs and constitutes the entire year 0 operating costs. The

3

company expects the TV of the patents, working capital, and equipment to be $1

million after taxes at the end of year 5. The riskless rate of interest is 5.5% and the

beta-adjusted risk factor is 10%, giving a hurdle rate of 15.5%. The tax rate is 34%,

and depreciation on the capital expenditures (CAPX) is 5 years, straight line. Table 1

shows the calculation of NPV.

[Table 1 (below) about here.]

This project is clearly desirable, with a NPV of $1,286,000.

The Half-Year Convention

Table 1 contains the assumption that all cash flows, including the first, occur

exactly at the end of the year. For most companies, it is more reasonable to assume that

cash flows occur evenly throughout the year. The year-end assumption has resulted in an

overstatement of the value of the project in this case. The half-year convention discounts

cash flows assuming that they occur at mid-year rather than year-end.

Applying the half-year convention involves moving cash flows back by a six

months, such that year 0 is discounted by (1 + i)0.5,, year one by (1 + i)1.5, year two by (1

+i )2.5, and so on (Pratt, 253). Year 0 becomes year 0.5, with the initial investment

beginning at the start of year 0 and the funds being spread evenly throughout the first

year. The TV occurs at the end of the final year rather than at the middle. Table 2

demonstrates the half-year convention, using the operating cash flows and the TV from

Table 1. The NPV drops from $1,286,000 to $1,170,000.

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[Table 2 about here]

The reduction in NPV comes about because the initial investment is large and is

discounted by only a half-year, while the inflows are relatively small at first and then

increase. As the inflows increase in size over time, the discount rate increases

geometrically, reducing the inflows geometrically. When the reverse is true—small up-

front investment and large, earlier cash inflows—NPV may increase (Bruckner, 1991).

All up-front investment occurs at one time

Tables 1 and 2 are seriously flawed in that they fix all R&D and CAPX in period

0. If the company is purchasing a relatively small piece of easily installed equipment that

goes to work immediately, it is reasonable to assume that the entire outlay will take place

at the end of time 0. However, for major projects in such industries as aerospace,

pharmaceuticals, mining, and large-scale construction, this assumption is far off the

mark. In these and other industries, CAPX and R&D begin many years before product

launch and continue after positive cash flow generation.

There is disagreement regarding the value of NPV analysis during the early stages

of project research. The issue is whether an early-stage forecast can be based upon

information that is sufficiently reliable (Varila & Sievanen, 2005; Uppal & Van Gool,

1991). However, at some point during the R&D cycle—well before product roll out—

discounted cash flow analysis becomes highly relevant. For company acquisitions and

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most (if not all) R&D and plant and equipment purchase decisions, NPV analysis is

relevant from the start.

Table 3 demonstrates the dramatic shift in NPV when the company spreads the

same amount of initial R&D and CAPX over a period of four years instead of the end of

time 0. NPV drops from $1,170,000 to $437,000.

[Table 3 about here.]

Risky costs and capital investments

Tables 2 and 3 deal with the investment in capital and R&D costs in the traditional

way—by discounting them over time for inflation, the real rate of interest, maturity or

investment rate risk, and market risk. However, simple logic would indicate that risk-

averse managers should increase costs to account for risk over time, not decrease them.

This means lowering the discount rate—perhaps using a rate less than one.

Literature discussions that took place in the 1970s and early 1980s deal with this

issue (Lewellen, 1977; Lewellen, 1979; Celec & Pettway, 1979; Berry and Dyson, 1980;

Booth, 1982). It seems clear from that discussion that variable costs and working capital

changes should be discounted at the same rate as revenues, and that the above simple

logic misses the point. Booth’s (1982, p. 299) summary explains why: “In evaluating

cash outflows, remember that a negative correlation between the value of a project’s cash

6

flows and the market rate of return translates into a positive correlation between the

project’s rate of return and the market rate of return.”

In other words, the variable components of a typical set of cash outflows are

correlated to sales in a direct way. If sales over five periods were 4, 8, 12, 8, and 4

respectively, the associated variable costs plus changes in working capital should follow

a similar pattern; say -3, -6, -9, -6, and -3. The two are perfectly negatively correlated.

If the discount rate for sales were 15.5%, the discount rate for the variable costs and

working capital changes would also have to be 15.5% to maintain the correlation at

minus 100%. Any other discount rate would disrupt the relationship and would

invalidate the logic behind the definition of variable costs and changes in working capital

as those elements that vary directly with sales.

Note that it is the free cash flow, not the sales or variable costs and working capital

changes, which is being measured. If investment and fixed costs are not involved, the

correlation between sales and the resulting cash flow (1, 2, 3, 2, and 1) is 100%.

However, up-front costs such as R&D and expenditures on plant and equipment

where there are no sales are another matter. The same is true of depreciation and other

fixed costs. Experienced investors are familiar with the impact on free cash flow of cost

overruns, delays, and mid-course changes in R&D and capital expenditures—especially

in those industries involved with technology (Davis, 2002; Uppal, 2001).

It is not unusual for managers to increase original R&D cost estimates by 5% to

200% to establish certainty equivalent proxies for risk prior to market introduction. One

executive who managed the new technical projects division at a Global-100 manufacturer

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occasionally used pi (3.14159) as a cost multiplier for up-front costs in highly risky

projects (Personal conversation, 2008). Estimates such as these, when transformed into

risk adjusted discount rates (RADRs), can yield discount rates of considerably less than

one.

Everett and Schwab (1979) demonstrate that the discount rate could actually be

less than one if the risks are great enough. Booth (1982, p. 299) concludes: “Given risk-

free revenues and cost uncertainty, the cost stream for a normal firm with a positive risk

premium attached to its cash flows must be discounted with a RADR below the risk-free

rate.” Risk-free revenues are consistent with the revenues of zero that attend up-front

investment and maintenance of that investment (if any) after start-up.

The exceptions would include cases of contractual arrangements such as fixed-

price contracts and other riskless costs (Hartl, 1990). In these cases, the discount rate

would be the risk-free rate.

When the initial and subsequent investments are spread out over a period of time

the issue of systematic risk may become relevant. The business cycle may well affect

investment costs. Spreading expenditures over a longer period will affect the present

value through the discount rate.

What to do with fixed investments? As proxy variables for risk, the S & P 500

and other similar measures already reflect fixed investments and other fixed costs

intrinsic to the companies that constitute them. Therefore, since risk is measured by cash

flow variation, company or project fixed costs and investments are already reflected to

8

some extent in the beta. Nevertheless, companies with high fixed costs will tend to have

higher than average betas because fixed costs intensify variation.

Table 4 demonstrates the difference in cash flow variation between a high fixed

cost/high investment and a low fixed cost/low investment company. The average return

in each of the three examples is $334. The variation, as measured by standard deviation,

is over three times greater in the high fixed cost/high investment firm—$659 vs. $210—

and will influence the firm’s beta. Other things equal, that firm will have a significantly

higher beta and therefore a higher cost of capital. The firm that varies its investments

with sales (Table 4 C) modifies its standard deviation to $434.

[Table 4 about here]

It follows from the table above that the firm should treat its fixed costs differently

from its variable costs notwithstanding the fact that fixed costs are captured in the proxy

variable such as the S&P 500 when beta is calculated. Although the science is imperfect,

start-up costs and investments in property, plant, and equipment prior to start-up should

be discounted separately in cases where significant investment is contemplated. In the

absence of forecast bias, it may be reasonable to discount these outlays at no more than

the risk-free rate. That rate should be adjusted downward if systematic risk such as

timing with the business cycle is involved.

When the company spreads the same amount of R&D and CAPX over a period of

four years instead of one, discounts R&D, CAPX, and depreciation by 5.5% (assuming

no systematic risk), uses the half-year convention, and assumes that the discount rate

9

after market introduction is reasonably accurate at 15.5%, NPV drops to a negative

$278,000.

Terminal Values

Terminal value systematic risks and biases may be significantly different from

operating cash flow risks and may be more or less difficult to forecast. Even forecasts of

the same terminal value using different methods can produce significantly different

results. The market value of future cash flows will produce one estimate, while models

that forecast free cash flow into perpetuity will produce another.

A 4% factor for terminal value added to the normal discount rate will reduce NPV

by an additional $71,000. When the terminal value is large, as in corporate acquisitions,

the amount can become highly significant. Table 5 demonstrates the effect of all of the

adjustments. As a result of the above analysis, NPV moved from a positive $1,286,000

in Table 1 to a negative $349,000. This $1.6 million shift represents nearly 33% of the

initial $5 million investment.

[Table 5 about here]

OTHER ADJUSTMENTS

In recent years, critics of NPV have pointed out that NPV models are incomplete

because they are deterministic. Among other things, they tend to underestimate the value

of real options and alternative outcomes (Boer, 2003; Carter, 1992).

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Real options are those outcomes under management control (Benninga &

Tolkowsky, 2002; Brealey, et. al. 2006, p. 597; Olafsson, 2003). They include

opportunities to:

1. Expand a project to include other prospects.

2. Abandon a project entirely at various stages in its development or rollout.

3. Delay investment –wait and see.

4. Change a project.

Practitioners and academics have examined these approaches in depth over the last

few decades and have offered alternatives to complement NPV. These alternatives

appear under the headings of scenario (“what if”) and contingency analyses, decision

trees, and Monte Carlo simulations. They are used to examine a range of possible

outcomes beyond the control of management as well as those outcomes management can

reasonably expect to control.

However, this author knows of no peer-reviewed study that has demonstrated their

superiority over the NPV models in forecasting project or company attractiveness.

Presumably, studies comparing the methods will be forthcoming. A further discussion of

these more complex approaches is beyond the scope of this article, but may be found in

most finance texts and in many articles and cases.

One need not abandon or seriously readjust NPV to apply the less sophisticated

methods—scenario and contingency analyses—in their more straightforward modes. For

example, companies frequently invest in projects with the expectation that they will lead

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to further opportunities. What if the Adams Company could build upon its proposed

R&D by making an additional investment of $500,000 one year after the Apex product

rollout? Assume this would lead to other products with subsequent free cash flows of

$250,000 per year for the following 5 years. The value of this alternative discounted to

the present would bring the total Apex NPV well into the positive column.

CONCLUSION AND TAKEAWAYS

NPV remains the most extensively used financial tool in evaluating investments.

Its wide applicability—from simple equipment purchases to corporate acquisitions—

combines with its relatively straightforward application to make it a valuable method.

However, it has been misunderstood and misapplied both in the literature and in practice.

This is partly because it ignores potential options, it has not been thoroughly or well

explained, and because examples have been incomplete or in error.

The intent of this article has been to demonstrate how decisions using NPV can be

improved simply by:

1. Adjusting the timing of free cash flows to reflect the reality of their

occurrence. Most cash flows do not come exactly at the end of the year,

treating them as if they do biases the result. Many projects have initial

R&D, fixed asset purchases, and other expenditures that extend more or

less evenly over one or more years.

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2. Appreciating the difference between systematic and unsystematic risk and

accounting for systematic biases in forecasting.

3. Recognizing fixed costs in investments and other expenditures and using

different discount rates for these costs.

4. Noting that the terminal value of an investment generally exhibits different

systematic risk characteristics from the other free cash flows and requires a

different discount rate.

5. Considering other opportunities (real options) that may be brought about by

investing in a given project.

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References

Benninga, S. & Tolkowsky, E. (2002). Real options: an introduction and an application to R&D valuation. The Engineering Economist, 47(2), 151-168.

Berry, R. H. & Dyson, R. G. (1980). On the negative risk premium for risk adjusted discount rates. Journal of Business Finance& Accounting, 7(3), 427-436.

Boer, F. P. (2003). Risk-adjusted valuation of R & D projects. Research Technology Management, 46(5), 50-58.

Booth, L. D. (1982). Correct procedures for the evaluation of risky cash outflows. Journal of Financial and Quantitative Analysis, 17(2), 287-300.

Brealey, R. A., Myers, S. C. & Allen, F. (2006). Principles of Corporate Finance (8th ed.). Boston: McGraw-Hill/Irwin.

Bruckner, K. L. (1991). Mid-year versus year-end present worth factors in DCF analysis. The Appraisal Journal, 59(1), 126-130.

Burns, R. M., & Walker, J. (1987). Investment techniques among the Fortune 500: A rationale approach. Managerial Finance, 23(9), 3-15.

Carter, W. K (1992). To invest in new technology or not? New tools for making the decision. Journal of Accountancy, 173(5), 58-62.

Celec, S. E. & Pettway, R. H. (1979). Some observations on risk-adjusted discount rates: A comment. The Journal of Finance, 34(4), 1061-1063.

Davis, C.R. (2002). Calculated risk: A framework for evaluating product development. MIT Sloan Management Review, 43(4), 71-77.

Everett, J. E. & Schwab, B. (1979). On the proper adjustment for risk through discount rates in a mean-variance framework. Financial Management, 8(2), 61-65.

Financial Accounting Standards Board (2000). Statement of financial accounting concepts no. 7: using cash flow information and present value in accounting measurements. Norwalk, CT: Financial Accounting Foundation.

Gitman, L. J., & Forrester, J. R. (1977). A survey of capital budgeting techniques used by

major U. S. firms. Financial Management, 6(3), 66-71.

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Graves, S. B. & Ringuest, J. L. (1991). Evaluating competing R&D investments. Research Technology Management, 34(4), 32-36.

Hartl, R. J. (1990). DCF analysis: The special case of risky cash outflows. Real Estate Appraiser and Analyst, 56(2), 67-72.

Hollmann, J. K. (2007). The Monte-Carlo challenge: A better approach. 2007 AACE International Transactions, Risk 3, 1-7.

Lev, Baruch (1974). On the association between operating leverage and risk. Journal of Financial and Quantitative Analysis, 9(4), 627-641.

Lewellen, W. G. (1977). Some observations on risk-adjusted discount rates. The Journal of Finance, 32(4), 1331-1337.

Lewellen, W. G. (1979). Reply to Pettway and Celec. The Journal of Finance, 34(4), 1065-1066.

Olafsson, S. (2003). Making decisions under uncertainty—Implications for high technology investments. BT Technology Journal, 21(2), 170-183.

Personal conversation, August, 2008.

Pratt, S.P. (2008). Valuing a business (5th ed.). New York: McGraw Hill.

Ryan, P. A., & Ryan, G. P. (2002). Investment practices of the Fortune 1000: How have things changed? Journal of Business and Management, 8(4), 355-364.

Uppal, K. B. (2001). Estimating? The number/confidence/resources, or what? Cost Engineering, 43(2), 35-40

Uppal, K. B. & Van Gool, H. (1991). R&D phase—Capital cost-estimating. Transactions of American Association of Cost Engineers, 1, ABI/INFORM Research, A.4.1.

Varila, M. & Sievanen, M. (2005). Profitability estimation of pioneering R&D project. AACE International Transactions, EST.19.1-8.

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TABLE 1: THE APEX PROJECT ($000)Time Periods In Years 0 1 2 3 4 5 6Sales Per Year 1,000 2,500 4,000 6,000 5,000 2,000 Cost of Goods Sold (250) (625) (1,000) (1,500) (1,250) (500)Operating Costs (4,000) (150) (375) (600) (900) (750) (300)Depreciation (200) (200) (230) (320) (380) (180) (180)Earnings Before Interest and Taxes (4,200) 400 1,270 2,080 3,220 2,820 1,020 Taxes @ .34 1,428 (136) (432) (707) (1,095) (959) (347)Earnings Before Interest After Taxes (2,772) 264 838 1,373 2,125 1,861 673 Depreciation 200 200 230 320 380 180 180 Working Capital Change (100) (150) (150) (200) 100 600 CAPX (1,000) (150) (450) (200)Operating Cash Flow (3,572) 428 768 1,093 2,105 2,141 1,453 Terminal Value After Taxes 1,000 Free Cash Flow (3,572) 428 768 1,093 2,105 2,141 2,453 NPV 1,286

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TABLE 2. THE APEX PROJECT ($000): HALF-YEAR CONVENTION

Half-Year Convention 0.50 1.5 2.5 3.5 4.5 5.5 6.5Sales Per Year 1,000 2,500 4,000 6,000 5,000 2,000 Cost of Goods Sold (250) (625) (1,000) (1,500) (1,250) (500)Operating Costs (4,000) (150) (375) (600) (900) (750) (300)Depreciation (200) (200) (230) (320) (380) (180) (180)Earnings Before Interest and Taxes (4,200) 400 1,270 2,080 3,220 2,820 1,020 Taxes @ .34 1,428 (136) (432) (707) (1,095) (959) (347)Earnings Before Interest After Taxes (2,772) 264 838 1,373 2,125 1,861 673 Depreciation 200 200 230 320 380 180 180 Working Capital Change (100) (150) (150) (200) 100 600 Capital Expenditure (CAPX) (1,000) (150) (450) (200)Annual Operating Cash Flow (3,572) 364 768 1,093 2,105 2,141 1,453 Discounted Operating Cash Flow (3,324) 293 536 660 1,101 969 570 Discounted Terminal Value (7 years) 365 Net Present Value @ 15.5% 1,170

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TABLE 3: INITIAL INVESTMENT SPREAD OVER FOUR YEARS ($000)

Time Periods 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5

Sales Per Year 0 0 0 01,00

02,50

0 4,000 6,000 5,000 2,000

Cost of Goods Sold (250)(625

)(1,000

)(1,500

) (1,250) (500)

Operating Costs (150)(375

) (600) (900) (750) (300)

R&D(100

)(1,000

)(1,400

)(1,500

)

Depreciation (20) (60) (120) (200) (200)(210

) (260) (240) (160) (160)Earnings Before

Interest and Taxes(120

)(1,060

)(1,520

)(1,700

) 4001,29

0 2,140 3,360 2,840 1,040

Taxes @ .34 41 360 517 578 (136)(439

) (728)(1,142

) (966) (354)Earnings Before Interest After Taxes (79) (700)

(1,003)

(1,122) 264 851 1,412 2,218 1,874 686

Depreciation 20 60 120 200 200 210 260 240 160 160Change In Working Capital (100)

(150) (150) (200) 100 600

Capital Expenditure(100

) (200) (300) (400)(150

) (450) (200)

Cash Flow(159

) (840)(1,183

)(1,322

) 364 761 1,072 2,058 2,134 1,446

Discounted (148

) (676) (825) (798) 190 345 420 698 627 368Discounted Terminal Value 237NPV @ 15.5% 437

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Table 4. COMPARISON OF HIGH AND LOW FIXED COST COMPANIES ($000)

Year 1 Year 2 Year 3 Year 4

Year 5 Standard

A. High Fixed Cost Company DeviationSales 1,000 2,000 3,000 2,000 1,000 Variable Costs (including taxes) (100) (200) (300) (200) (100)Fixed Costs (950) (950) (950) (950) (950)Change in Working Capital (20) (40) (60) (40) (20)Investments (300) (300) (300) (300) (300)Free Cash Flow (370) 510 1,390 510 (370) 659 Average Return: Free Cash Flow = 334

B. High Variable Cost CompanySales 1,000 2,000 3,000 2,000 1,000 Variable Costs (including taxes) (700) (1,400) (2,100) (1,400) (700)Fixed Costs (70) (70) (70) (70) (70)Working Capital (20) (40) (60) (40) (20)Investments (100) (100) (100) (100) (100)Free Cash Flow 110 390 670 390 110 210 Average Return: Free Cash Flow = 334

C. Investment Varies with SalesSales 1,000 2,000 3,000 2,000 1,000

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Variable Costs (including taxes) (100) (200) (300) (200) (100)Fixed Costs (710) (710) (710) (710) (710)Change in Working Capital (20) (40) (60) (40) (20)Investments (300) (600) (900) (600) (300)Free Cash Flow (130) 450 1,030 450 (130) 434

Average Return: Free Cash Flow = 334

TABLE 5. COMBINING THE ADJUSTMENTS ($000)

Time Periods 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5Sales Per Year 0 0 0 0 1,000 2,500 4,000 6,000 5,000 2,000 Cost of Goods Sold (250) (625) (1,000) (1,500) (1,250) (500)Operating Costs (150) (375) (600) (900) (750) (300)Research and Development (100) (1,000) (1,400) (1,500)Depreciation (Fixed) (20) (60) (120) (200) (200) (210) (260) (240) (160) (160)Earnings Before Interest and Taxes (120) (1,060) (1,520) (1,700) 400 1,290 2,140 3,360 2,840 1,040 Taxes @ .34 41 360 517 578 (136) (439) (728) (1,142) (966) (354)Earnings Before Interest After Taxes (79) (700) (1,003) (1,122) 264 851 1,412 2,218 1,874 686 Depreciation (Fixed) 20 60 120 200 200 210 260 240 160 160 Chg. In Working Capital (100) (150) (150) (200) 100 600 CAPX (Fixed) (100) (200) (300) (400) (150) (450) (200)Free Cash Flow (159) (840) (1,183) (1,322) 364 761 1,072 2,058 2,134 1,446

Free Cash Flow (Fixed) (159) (840) (1,183) (1,322) 68 (79) (362) (118) 54 54 DCF @ adjusted rate (155) (775) (1,035) (1,096) 53 (59) (255) (79) 35 33 Free Cash Flow (Variable) 0 0 0 0 296 840 1,434 2,176 2,080 1,392 DCF @ hurdle rate 0 0 0 0 155 380 562 738 611 354 Sum Adjusted Discounted FCF (155) (775) (1,035) (1,096) 208 322 307 659 646 387 Terminal Value 184Net Present Value (349)

DEPRECIATION SCHEDULE ($000)Depreciation (Fixed) (20) (20) (20) (20) (20)

(40) (40) (40) (40) (40)

20

(60) (60) (60) (60) (60)(80) (80) (80) (80) (80)

(20) (60) (120) (200) (200) (180) (140) (80) 0 0

Depreciation on CAPX After Start-up (30) (30) (30) (30) (30)

(90) (90) (90) (90)(40) (40) (40)

(30) (120) (160) (160) (160)

Total Depreciation (20) (60) (120) (200) (200) (210) (260) (240) (160) (160)

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