Pretax Versus Posttax DCF in Loss and Damage Calculations. Reprinted with permissions from Business Valuation Resources, LLC

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1 Vol. 2, No. 1, January 2015, 1 Qtr. TIMELY NEWS, ANALYSIS, AND RESOURCES FOR DEFENSIBLE VALUATIONS BUSINESS VALUATION AUSTRALIA Pretax Versus Posttax DCF in Loss and Damage Calculations By John-Henry Eversgerd Introduction. Many in the Australian and international valuation community have challenged the accuracy and appropriateness of pretax discounted cash flow (DCF) analyses. Pretax DCF analyses continue to be used in practice, however, particularly in the context of calculating loss and damage when quantifying claims in commercial disputes. There are a number of useful articles and discussions on this topic. 1 In this article, I have endeavoured to build on those and to provide more detailed illustrative examples I hope will be useful to valuation practitioners, forensic accountants, lawyers, judges, arbitrators, and others who are faced with assessing whether a pretax or posttax discounted cash flow analysis is appropriate in a given situation. In particular, I will compare the results of various DCF scenarios to illustrate how pretax DCF calculations can in many cases result in materially incorrect and/or inconsistent results. Methodology. The DCF scenarios discussed in this article are based on the following example. Assume a litigant has lodged a lawsuit against a defendant where a component of the damages relates to a lost business opportunity. The assessment of the loss requires an estimate of the value of the future cash flows that were expected to be generated by the business, i.e., 1 Including Davis, Lonergan, Shefftz, and Stillwell. Please refer to the references at the end of this article for more details. an estimate of the value of the business. 2 In the year leading up to the date of the alleged loss, the business generated $100 in pretax earnings before interest, taxes, depreciation, and amortisation (EBITDA) and its effective tax rate is 30%. I have also assumed that any award received by the plaintiff will be taxed at the same 30% tax rate and the defendant is responsible to compensate the plaintiff for their loss inclusive of expected taxes on the claim. The results of two pretax DCF methods used in practice to quantify damages are compared to the results of a posttax DCF method. The value of the business (i.e., lost business opportunity) is calculated using the perpetuity growth model, 3 which is more concise to present in an article and mathematically equivalent to a full DCF with constant growth rates into perpetuity. The three methods I compare are as follows: Posttax DCF method Free cash flow is calculated using assumptions for growth, EBITDA, depreciation, corporate taxes, capital expenditures, and working capital requirements. 2 Damages are commonly calculated as the difference between two scenarios, what actually happened and what would have happened but for the actions of the defendant. For illustrative purposes, I have assumed the full value of the business opportunity is lost, the actual cash flows from the business opportunity are nil, and there was no ability for the plaintiff to mitigate the loss. 3 The perpetuity growth model is a formula that calculates the present value of a stream of future cash flows assuming a constant rate of growth and discount rate (present value = cash flow * (1 + growth rate) (discount rate - growth rate)).

2 BUSINESS VALUATION AUSTRALIA Chair, Editorial Advisory Board: Publisher: Editor: Managing Editor: Desktop Editor: Customer Service: VP of Sales: President: CEO: John-Henry Eversgerd Sarah Andersen Sonia Nair Janice Prescott Monique Nijhout Retta Dodge Lexie Gross Lucretia Lyons David Foster EDITORIAL ADVISORY BOARD SIMON DALGARNO LEADENHALL CORPORATE ADVISORY ADELAIDE, SA JOHN E GIBSON CBV FCA BRENDAN P. HALLIGAN HALLIGAN & CO Business Valuation Australia (ISSN ) is published quarterly by Business Valuation Resources, LLC, 1000 SW Broadway, Suite 1200, Portland, OR U.S.A. The annual subscription price for the Business Valuation Australia is $451 AUD. Low-cost site licenses are available for those who wish to distribute the BVA to their colleagues at the same firm. Contact our sales department for details. Please contact us via at customerservice@bvresources.com, phone at , fax at or visit our website at BVResources.com/Australia. Editorial and subscription requests may be made via , mail, fax or phone. Please note that by submitting material to BVA, you are granting permission for the newsletter to republish your material in electronic form. Although the information in this newsletter has been obtained from sources that BVR believes to be reliable, we do not guarantee its accuracy, and such information may be condensed or incomplete. This newsletter is intended for information purposes only, and it is not intended as financial, investment, legal, or consulting advice. Copyright 2014, Business Valuation Resources, LLC (BVR). All rights reserved. No part of this newsletter may be reproduced without express written consent from BVR. ABOUT About BVR RICHARD STEWART PRICEWATERHOUSECOOPERS TIM HEBERDEN GRIFFITH HACK IAN JEDLIN KPMG AUSTRALIA WAYNE LONERGAN LONERGAN EDWARDS & ASSOCIATES, LIMITED Business Valuation Resources is pleased to offer premier products and services to the business valuation profession around the globe. Top business valuation firms depend on BVR for authoritative market data, continuing professional education, and expert opinion. BVR is your one-stop shop for newsletters, merger and acquisition data, guides and books, research reports, continuing education, and more. Once free cash flow is calculated, the perpetuity growth model is applied, assuming a 14% posttax weighted average cost of capital to calculate the present value of the business. As we have assumed that the plaintiff would be compensated for taxes on the damages award, I gross up the posttax present value of the business s cash flows by dividing it by (1 - the tax rate). Pretax DCF method 1 Pretax DCF method 1 is calculated the same way as the posttax DCF method, except for two differences. First, corporate taxes are excluded from the calculation of free cash flow (i.e., not deducted from free cash flow). Second, the discount rate is calculated by applying a common (but incorrect) mechanical calculation of dividing the posttax discount rate by (1 - the tax rate), which in this case results in an implied pretax discount rate of 20%. In practice, this DCF method is intended to result in the same value as a posttax method since both the cash flows and discount rate purportedly 4 exclude taxes. Therefore, as in the posttax DCF method, I then gross up the value by dividing it by (1 - the tax rate) to compensate the plaintiff for taxes on the damages award. Pretax DCF Method 2 Pretax DCF method 2 is calculated the same way as the posttax DCF method, except for two differences. Like pretax DCF method 1, corporate taxes are excluded from the calculation of free cash flow (i.e., not deducted from free cash flow). However, unlike pretax DCF method 1, a 14% posttax discount rate is utilised instead of a pretax discount rate. Mixing pretax cash flows and a posttax discount rate is intended to automatically gross up the damages calculation for taxes to be paid on the award. Therefore, no additional gross up for taxes is applied in my calculations. We are delighted to announce the launch of BVR Down Under! We have partnered with a network of business valuation practitioners, writers, and associations in Australia to deliver news, training, and resources to anyone in need of Australian-specific business valuation content. 4 By adjusting the discount rate by taxes, taxes are not in fact excluded, but rather incorporated in, the discount rate rather than the cash flows. 2 Business Valuation Australia January 2015, 1 Qtr.

3 The following discussion summarises my findings from comparing the values generated from these three methods by applying the same underlying assumptions in three scenarios: Scenario A, Scenario B, and Scenario C. Results. Scenario A: The first set of assumptions applied to all three methods reflects a scenario of no cash flow growth, no working capital requirement, and capital expenditures to be exactly equal to taxable depreciation each year. Below are the results of applying these assumptions to the three DCF methods. In this very simplified scenario shown in Exhibit 1, all three methods generate equivalent answers of 571. Why do all three methods result in the same number? Because they are mathematically equivalent. If there is no growth, no nontaxable or deductable cash flows, the perpetuity growth model formula 5 is reduced to (cash flow discount rate). It doesn t matter whether you multiply the numerator (cash flow) by (1 - the tax rate) or divide denominator (discount rate) by (1 - the tax rate); the answer will necessarily be the same. 5 Present value = cash flow * (1 + growth rate) (discount rate - growth rate) This result is somewhat misleading, however. Pretax method 1 will not be equivalent to the other methods if the cash flows required to assess loss do not go on in perpetuity. This is important since many damages calculations cover a discrete period into the future, such as the date of expiry of a breached contract. An illustration is presented in Exhibit 2, which is a graph of the cumulative present value from each DCF method over time. As shown in Exhibit 2, while the posttax DCF method and pretax DCF method 2 have equivalent values regardless of the time frame of the cash flows, pretax DCF method 1 is only correct (equivalent to posttax DCF method) in the long term and overstates value significantly in the short to medium term. Why is this the case? Because adjusting the discount rate downwards by the tax rate has, inappropriately, a very small impact to present value in the early years and a very large impact to value in the later years. 6 6 As an example, in year 1, the posttax discount factor is 1/(1 + 14%), or , while the implied pretax discount factor is 1/(1 + 14% 0.7), or These discount factors are only 5% different from each other in year 1, causing the pretax DCF method 1 to overvalue the cash flows dramatically in year 1. One would intuitively expect this difference in discount Exhibit 1. Scenario A: 0% Growth, Depreciation = Capital Expenditures, No Working Capital Requirement Method: Posttax Pretax 1 Pretax 2 Free cash flows Posttax Pretax Pretax Discount rate Posttax Pretax Posttax Free cash flow calculation EBITDA Less: Depreciation (20) (20) (20) Equals: EBIT Less: Corporate taxes (24) - - Equals: After tax debt-free earnings 56 n.a. n.a. Plus: Depreciation Less: Capital expenditure (20) (20) (20) Less: Working capital requirement Equals: Free cash flow Perpetuity calculation Multiplied by: (1 + growth rate) / (discount rate - growth rate) Equals: Present value of future free cash flow Tax gross up Plus: Gross up for tax on damages N.A. Total implied loss & damage January 2015, 1 Qtr. 3

4 Exhibit 2. Scenario A: 0% Growth, Depreciation = Capital Expenditures, No Working Capital Requirement Cumulative Present Value 1,000 Present value including tax gross up Years Posttax DCF Method Pretax DCF Method 1 Pretax DCF Method 2 Scenario B: The second set of assumptions applied to all three methods reflects the same assumptions as in Scenario A, except growth is now assumed to be 5% rather than nil. Exhibit 3 presents the results of applying this set of assumptions to the three DCF methods. Exhibit 3 illustrates that simply adding a 5% growth assumption to the DCF calculations results in the pretax DCF method 1 to understate the value with a present value of 800 versus the posttax DCF method present value of 933. The understatement of present value in this growth scenario seen in pretax DCF method 1 is caused by a combination of: (1) the fact that cash flows in the outer years are now larger, due to growth, than in earlier years; and (2) pretax factors should really be equivalent to the tax rate of 30% if the method of calculating the pretax discount rate was correct. The direction of the error in this method reverses in the later years. As an example, in year 20, the posttax discount factor is 1/(1 + 14%)^20, or , while the implied pretax discount factor is 1/(1 + 14% 0.7)^20, or Due to compounding of the tax adjustment to the discount rate, the pretax discount factor is 66% lower than the posttax discount factor in year 20, undervaluing the cash flows dramatically in that year. DCF method 1, as discussed earlier, overvalues cash flows in the early years and undervalues cash flows in the outer years regardless of growth. Taking a look at the cumulative present values of each method under this 5% growth scenario, Exhibit 4 illustrates that the pretax DCF method 1 understates the value in the long run but actually overstates value in the short to medium term. Pretax DCF method 2 still produces the same value as the posttax DCF method, since they remain equivalent mathematically, 7 despite adding a growth rate. Scenario C: Scenario C has the same set of assumptions as in Scenario B except for capital expenditures. It is not uncommon in many businesses for there to be a timing difference between depreciation and capital expenditures. To reflect an assumed permanent timing 7 Dividing the sum of every year s posttax present value (pretax cash flow (1 - tax) posttax discount factor) by (1 - tax) is mathematically equivalent to the sum of every year s present value of pretax cash flow (pretax cash flow discount factor) when using the same posttax discount rate and pretax cash flow is equal to taxable income. 4 Business Valuation Australia January 2015, 1 Qtr.

5 Exhibit 3. Scenario B: 5% Growth, Depreciation = Capital Expenditures, No Working Capital Requirement Method: Posttax Pretax 1 Pretax 2 Free cash flows Posttax Pretax Pretax Discount rate Posttax Pretax Posttax Free cash flow calculation EBITDA Less: Depreciation (20) (20) (20) Equals: EBIT Less: Corporate taxes (24) - - Equals: After tax debt-free earnings 56 n.a. n.a. Plus: Depreciation Less: Capital expenditure (20) (20) (20) Less: Working capital requirement Equals: Free cash flow Perpetuity calculation Multiplied by: (1 + growth rate) / (discount rate - growth rate) Equals: Present value of future free cash flow Tax gross up Plus: Gross up for tax on damages N.A. Total implied loss & damage Exhibit 4. Scenario B: 5% Growth, Depreciation = Capital Expenditures, No Working Capital Requirement Cumulative Present Value 1,000 Present value including tax gross up Years Posttax DCF Method Pretax DCF Method 1 Pretax DCF Method 2 difference, Scenario C s capital expenditure assumption is set to be 10 higher than depreciation. Exhibit 5 presents the results of applying this set of assumptions to the three DCF methods. its taxable income as capital expenditure 8 is not tax deductible. Pretax DCF method 1 is incorrect again for these same reasons, and the reasons it was As can be seen in Exhibit 5, this capital expenditure assumption now causes the pretax DCF method 2 to underestimate the value to be 700 compared to the posttax DCF method value of 767. This difference occurs because Scenario C s cash flows are for the first time not the same as 8 Similar outcomes to Scenario C result if you add working capital requirements to the discounted cash flow analysis, so I have not included a separate scenario. Scenarios with other non-tax-deductible and nontaxable cash flows would also have similar results. January 2015, 1 Qtr. 5

6 incorrect in Scenario B, overstating the value to be 817 versus 767 calculated by the posttax DCF method. Looking at the cumulative present values over time in Scenario C, Exhibit 6 illustrates that pretax method 1 overstates the value in the short to medium term and understates the value it in the long term. Pretax method 2 overstates the value in every year. Conclusion. According to the discounted cash flow scenarios summarised in this article, both pretax methods can produce results that are different, when flexing certain assumptions, from the more traditional posttax discounted cash flow method. Pretax method 1 (using pretax cash flows and pretax a discount rate mechanically calculated by dividing a posttax discount rate by one minus the tax rate) fails in most scenarios over the short and medium term. Merely introducing Exhibit 5. Scenario C: 5% Growth, Capital Expenditures > Depreciation, No Working Capital Requirement Method: Posttax Pretax 1 Pretax 2 Free cash flows Posttax Pretax Pretax Discount rate Posttax Pretax Posttax Free cash flow calculation EBITDA Less: Depreciation (20) (20) (20) Equals: EBIT Less: Corporate taxes (24) - - Equals: After tax debt-free earnings 56 n.a. n.a. Plus: Depreciation Less: Capital expenditure (30) (30) (30) Less: Working capital requirement Equals: Free cash flow Perpetuity calculation Multiplied by: (1 + growth rate) / (discount rate - growth rate) Equals: Present value of future free cash flow Tax gross up Plus: Gross up for tax on damages N.A. Total implied loss & damage ,000 Exhibit 6. Scenario C: 5% Growth, Capital Expenditures > Depreciation, No Working Capital Requirement Cumulative Present Value Present value including tax gross up Years Posttax DCF Method Pretax DCF Method 1 Pretax DCF Method 2 6 Business Valuation Australia January 2015, 1 Qtr.

7 growth will cause this method to produce inaccurate results in the long term as well. I strongly advise avoiding this method. Pretax method 2 (using pretax cash flows and a posttax discount rate) appears to withstand the introduction of growth into the DCF model but fails when pretax free cash flow is not equivalent to pretax earnings. If performing a posttax DCF is not practical, pretax method 2 can in limited circumstances produce the same results as a posttax DCF, but it is important to be cognisant of the areas where it fails. Ultimately the calculations presented in this article support the view that it is preferable to perform discounted cash flow analyses on a posttax basis. This will often result in a more mathematically accurate outcome and has the added benefit of increasing transparency regarding the underlying tax assumptions in the analysis. u John-Henry Eversgerd is a partner of McGrathNicol s forensic practice and the firm s national head of valuations. He is the chair of Business Valuation Australia s editorial advisory board and was the chair of the ICAA s NSW chapter of its Business Valuation Special Interest Group from 2012 to He can be reached on and jeversgerd@mcgrathnicol.com. References Kevin Thomas Davis, Why Pretax Discount Rates Should Be Avoided, 2010, working paper. Jan Jindra and Torben Voetmann, Discussion of the Pre- and Post-tax Discount Rates and Cash Flows A Technical Note, 2010, The Journal of Applied Research in Accounting and Finance, vol. 5, no.1, pp Wayne Lonergan, Pre- and Post-tax Discount Rates and Cash Flows A Technical Note, 2009, The Journal of Applied Research in Accounting and Finance, vol. 4, no. 1, pp Jonathan Shefftz, Taxation Considerations in Economic Damages Calculations, 2008, Draft, Experts.com. Caleena Stilwell, It s the Cash Flows That Are Important!, presentation at the March 2008 Institute of Chartered Accountants in Australia s Business Valuation and Forensic Accounting conference in Sydney. January 2015, 1 Qtr. 7