A Value Driver Approach to Valuation Using a Declining Growth Rate Model

Transcription

1 A Value Driver Approach to Valuation Using a Declining Growth Rate Model by Larry C. Holland, PhD CFA University of Arkansas at Little Rock Little Rock, AR lcholland@ualr.edu Telephone: (501) January 16, 2018

2 A Value Driver Approach to Valuation Using a Declining Growth Rate Model Abstract Identifying the value drivers in a valuation analysis provides a robust approach to valuation, although existing valuation models do not offer much flexibility to include them. Maintaining consistent accounting relationships is also important. A new declining growth rate valuation model is used to illustrate the impact of selected value drivers, including consistent changes in each value driver over time. Two equivalent approaches demonstrate a complete valuation analysis, using dividends and residual income. Overall, a comprehensive example illustrates a robust valuation procedure that incorporates changing value drivers, maintains consistent accounting, and uses a flexible declining growth valuation model. Key Words: Equity valuation, valuation model, declining growth model, value drivers, and consistent accounting relationships. 2

3 A Value Driver Approach to Valuation Using a Declining Growth Rate Model Analysts use stock valuation models in fundamental analysis to determine a fair value from the present value of cash flow streams such as dividends, free cash flow to the firm (FCFF), free cash flow to equity (FCFE), or residual income (RI). However, the cash flows used for valuation are determined by other factors, which can be identified as the key value drivers in a firm. For example, the growth in sales, the EBIT profit margin, the invested capital to sales ratio, and the debt to invested capital ratio are key value drivers from the financial statements of a firm. Changes in these variables over time will directly affect the intermediate values of the return on invested capital and return on equity, which in turn determine the level of cash flows that ultimately lead to a complete valuation analysis. At the same time, it is important to maintain consistent accounting relationships among the various forecasted cash flows on pro forma financial statements by choosing appropriate retention and reinvestment rates for the level of growth assumed. This often will result in different growth rates for sales, EBIT, interest expense, net income, dividends, invested capital, and debt. In the following sections, a valuation model is developed that utilizes key value drivers to determine the valuation cash flows for a firm and also allows for declining growth rates and accounting consistency. Literature Review There is a large literature on equity valuation; however, there is much less devoted to incorporating directly into the valuation analysis the effect of declining growth rates in the forecasted cash flows, the impact of key value drivers, and maintaining accounting consistency in the forecast of future cash flows. A survey of the state of the art for this portion of the 3

4 literature can be summarized from several practitioner oriented books devoted exclusively to equity valuation: Pinto, Robinson, Stowe (2010), Viebig, Poddig, Varmaz (2008), Damodaran (2010 and 2012), Koller, Goedhart, Wessels (2010), and Lundholm, Sloan (2004 and 2017). Pinto, Henry, Robinson, and Stowe (2010) identify dividends, Free Cash Flow to Equity (FCFE) and Free Cash Flow to the Firm (FCFF) as cash flows that can be used to value a firm with a discounted cash flow approach. They also illustrate the use of the Gordon constant dividend growth formula, multi-stage valuation with constant growth segments, and the H-Model which is a rough estimate of a declining growth model. There is little mention of the value drivers that influence the valuation or accounting consistency in the forecast of cash flows. Viebig, Poddig, and Vamaz (2008) highlight several different models and approaches utilized by practitioners in valuation analysis. They place much emphasis on identifying key financial value drivers, and note that these value drivers change over time. These changes are generally incorporated into the analysis through a manual forecast five to ten years into the future, followed by a terminal value assuming constant mature values of selected value drivers thereafter. Although several different models are described, those models do not generally incorporate continuous declining growth rates over time in some cases, some constant growth segments are considered in order to account for changing growth rates over time. And finally, in one case (the Morgan Stanley s ModelWare approach) an attempt is made to maintain accounting relationships over time in a forecast of valuation cash flows. Damodaran (2010 and 2012) shows that companies grow at declining growth rates according to the business life cycle theory. He accommodates the declining growth rates with a valuation model that uses multiple constant growth segments that step down the growth rates followed by a terminal value at the mature stage based on the Gordon constant growth formula. 4

5 In terms of accounting consistency, the mature growth rate is matched with a mature reinvestment rate using a formula similar to the sustainable growth rate popularized by Higgins (1977), which assumes a constant capital structure. He also points out that the choice of which cash flows to use in a present value approach is a matter of convenience because using dividends, FCFE, FCFF, or residual income should theoretically yield the same valuation. Keller, Goedhart, and Wessels (2010) focus on the value drivers of a valuation analysis, and identify sales growth and Return On Invested Capital (ROIC) as key value drivers. They define ROIC as NOPLAT divided by Invested Capital. The ROIC can be further divided into an after-tax profitability margin (NOPLAT/Sales) and a productivity ratio (Sales/IC). They define NOPLAT as Net Operating Profit Less Adjusted Taxes, which is closely related to EBIT (1-t), further adjusted for changes in deferred taxes. For a valuation model, they utilize a two-stage model with an initial constant growth segment (a fixed term annuity) followed by a constant growth terminal value. The adjustment for changes in growth rates is approximated through constant growth segments, and there is little attempt to maintain accounting consistency in estimating future cash flows. Lundholm and Sloan (2004 and 2017) identify Residual Income (RI), FCFE, and FCFF as cash flows. As will be mentioned in the next section, they also identify key value drivers, and incorporate these value drivers into a spreadsheet to forecast 23 years of cash flows, with a constant growth model as a terminal value at year 23. A major innovation in their approach is that accounting consistency is maintained throughout their valuation forecasts, which is a feature not generally included in other valuation approaches (with the exception of the Morgan Stanley ModelWare). However, they do not provide a closed form solution to their valuation analysis the valuation is mostly controlled in a hard-coded manner within the spreadsheet model itself. 5

6 To summarize, the current state of the art in valuation analysis does not provide a flexible means to incorporate a continuous declining growth rate in valuation cash flows, which is a feature of the life cycle theory of a firm. At the same time, consistency with accounting theory is generally incorporated through assumed step function changes in the reinvestment rate. And finally, the key value drivers in a valuation analysis are often summarized by an assumption of an on-going Return on Equity (ROE) or Return on Invested Capital (ROIC) rather than the components that make up those ratios. The purpose of this paper is to provide a detailed example of applying a declining growth valuation model while maintaining consistent accounting relationships among the key forecasted cash flows. At the same time, key value drivers that change over time are explicitly included in the valuation analysis, that result in reasonable values of ROE, ROIC, and a reinvestment rate. These key value drivers are identified in the next section. Identifying the Key Value Drivers in A Valuation Analysis The first step in a complete valuation analysis is to identify the factors that are the key value drivers for a firm. The following paragraphs identify the factors that will be used in an example valuation analysis in the next three sections of this paper, with verification from the valuation literature. A primary factor in driving a valuation analysis is the growth in top line sales. Viebig, Poddig, and Varmaz (2008) state that Top line growth is arguably one of the most important value drivers of a firm. Modeling future revenues starts with carefully analyzing historical revenues recorded on a company s income statements. (p. 59). They continue this thought with 6

7 the idea that sales growth would also be expected to decline over time with their statement, Initial high revenue growth rates usually slow down when the revenue base increases ( base effect ) and when companies enter into a more mature stage of their life cycle. (p. 62). Therefore, initial sales growth and a decline in this growth rate over time would be an important key value driver to begin a valuation analysis. Lundholm and Sloan (2004 and 2017) verify the importance of the growth in sales with their statement, the growth in sales is the key long-term driver of growth in all other metrics. (2004, p. 78). They also point out that the growth rates in key cash flows will be different from the growth in sales because of several key variables, with bracketed comments added for emphasis: Asset growth will differ from sales growth when a firm s level of assets that is required to generate a given level of sales [Assets/Sales] is also changing. Common Equity growth will differ from sales growth because of changes in both the amount of assets [Assets/Sales] and the amount of debt that is used to finance the assets that generate the sales [Debt/Assets]. Earnings growth will differ from sales growth because of changes in the firm s profit margin [EBIT/Sales]. Thus, they have generally identified three additional value drivers, which they expect to change over time: Assets/Sales, Debt/Assets, and EBIT/Sales. Piotroski (2000) identifies several key factors in the construction of his F-SCORE. Among others, this includes the change in operating margin (EBIT/Sales), turnover (Sales/Assets), and the relative level of debt (Debt/Assets). Also, Soliman (2008) relates key value factors directly to the simple DuPont relationship, extending the work of Fairfield and Yohn (2001), Nissim and Penman (2001 and 2002), and Penman and Zhang (2002). The simple DuPont formula is presented in numerous textbooks (e.g. Ross, Westerfield, Jordan (2006), Berk, DeMarzo, and Harford (2015), Graham, Smart, and Megginson (2010), Parrino and Kidwell 7

8 (2017), Block and Hirt (2015), Cornett and Nofsinger (2006), and others), and decomposes the return on equity (ROE) as follows: Net Income ROE = ( ) ( Sales Sales Assets ) (Assets Equity ) (1) Soliman (2008) specifically focuses on return on net operating assets (NOA) rather than total assets in the simple DuPont formula. The finance literature more often utilizes a concept similar to NOA, which is invested capital (IC), defined as total assets less non-operating current liabilities. Through the DuPont relationship, Soliman identifies profitability (defined as operating income or EBIT divided by NOA) and total asset turnover (Sales divided by Assets) as key factors, along with financial leverage. Lundholm and Sloan (2017) and others also define an extended DuPont formula that decomposes ROE more cleanly into the return on invested capital (ROIC) based on operating earnings and the financial leverage. One form of the extended DuPont formula is EBIT (1 t) ROE = ( ) ( Sales INT ) (1 Sales IC EBIT ) ( IC Equity ) (2) The first two terms are equal to the ROIC, and the last two terms incorporate the reduction in leverage from additional interest expense and the increase in leverage from additional debt. Overall, the extended DuPont relationship identifies several value drivers in common with the references cited earlier. Taking into account all the cited references and the DuPont relationships, typical value drivers in a valuation analysis would include the growth in top line sales, the operating 8

9 profitability, the production efficiency, and the financial leverage. In addition, some analysts specify that the ROE over time should approach the required return on equity during maturity. For example, Viebig and Poddig (2008) make a point about the effect of competition on the return on capital when they state, under perfect competition return on capital fades to cost of capital over time, p. 71. The return on capital relates to the ROE with the addition of financial leverage, i.e. increasing the level of debt increases the ROE. As a result, the approach used in this paper will demonstrate a method for choosing a long-term financial leverage (Debt/IC) that will result in the long-term ROE approaching the required return on equity. In the following sections, an example problem will illustrate the application of key value drivers to valuation analysis using a declining growth valuation model. In some cases, a ratio is inverted in comparison to references in the literature to simplify the application of the model. The following variables are specified as value drivers, all of which will be allowed to decline over time to a mature level: (1) Growth in sales, (2) Profitability (EBIT/Sales), (3) Production efficiency (IC/Sales), and (4) Relative level of debt (Debt/IC) which can be specified such that the ROE will decline asymptotically to the Required Rate of Return. These four value drivers will be utilized to develop future cash flows that maintain consistent accounting relationships and lead to an estimate of future potential dividends (i.e., Free Cash Flow to Equity) 1 as a plug factor in a pro forma analysis. And finally, two equivalent approaches will be used to illustrate a complete and comprehensive valuation analysis the present value of future dividends and the present value of residual income. 1 Free Cash Flow to Equity (FCFE) represents the level of dividends that potentially could be paid with a balance in the level of internal cash flows of the firm. A firm could choose to pay dividends less that the FCFE and accumulate excess cash, or pay dividends higher than the FCFE supported by additional funding such as borrowing more debt. 9

10 A Declining Growth Valuation Model The model used to illustrate valuation with a value driver approach is a model developed by Holland (2017), which incorporates a declining growth function. This model is based on the subtraction of two cash flow streams that grow at different constant rates. The simplest formulation of the model assumes a constant growth for a larger cash flow stream at a long-term mature growth rate and a zero growth for a second smaller cash flow stream, as follows: C t = C 0 [(H C )(1 + g L ) t (H C 1)] (3) or C t = C 0 [( g S g L ) (1 + g L ) t ( g S g L 1)] (4) where Ct = a cash flow at time t which is a component of the cash flows to be valued, HC = the declining growth factor related to cash flow Ct, defined as gs/gl, gs = the initial growth rate of Ct from time 0 to time 1, and gl = the long-term mature growth rate. The cash flow stream to be valued in this model (Ct) will have an initial growth rate of gs from time 0 to time 1 and the growth rate will decline over time, asymptotically approaching a longterm mature growth rate of gl. The present value of the two component cash flow streams can be found by using the constant growth valuation model on the first term and the present value of a perpetuity for the second term. Thus, the valuation model with a declining growth rate function is as follows: V 0 = C 0 ( (H C)(1 + g L ) (H C 1) ) (5) R g L R 10

11 or V 0 = C 0 ( ( g S g L ) (1 + g L ) R g L ( g S g 1) L ) (6) R where R = the required rate of return for the cash flow stream, Ct. A nice feature of this model is that one cash flow series in a valuation analysis can easily be related to a second multiplicative or additive cash flow series while specifying a function of changing growth rates. This allows a significant level of flexibility in forecasting pro forma cash flows that incorporate accounting consistency as well as changes in the value drivers. For example, the components of the financial statements of a firm (that are additive factors) can easily be modeled, which allows consistent accounting relationships to be maintained over time in a forecast of cash flows. Therefore, relationships such as a clean accounting surplus can be maintained as well as a reinvestment or payout choice for a firm. At the same time, the key value drivers (which are multiplicative factors) can be specified as a function that changes over time. This allows for a robust valuation with changing growth rates for multiple intermediate cash flow streams leading to an ultimate overall valuation analysis. Modeling the Value Drivers An example problem with complete financial statements is utilized in this section to illustrate how the four value drivers identified earlier can be directly incorporated into a valuation analysis. The income statement and balance sheet for this example are shown in the 11

12 first column of Table 1. Let Sales follow a growth path with an initial growth rate of gs = 24% from time t=0 to time t=1, and which declines over time to a long-term growth rate of gl = 2%. Following Equation 3, a declining growth rate series can be established as an estimate of future Sales, as follows: H Sales = g S = 24% g L 2% = 12 (7) Sales t = Sales 0 [H Sales (1 + g L ) t (H Sales 1)] (8) Sales t = 10 [ 12 (1.02) t 11] = 120 (1.02) t 110 (9) This Sales forecast has a growth path over the next 30 as shown in Figure 1. Table 1 shows the first four years of the forecast while holding the other value drivers constant. Changes in the other three value drivers can also be accommodated within the declining growth model. For example, another value driver identified earlier is the profitability, or the EBIT margin (m = EBIT/Sales). Assume that the EBIT margin is forecast to decline over time from the current short-term margin of m0 = EBIT0/Sales0 to a long-term margin of ml = EBITL/SalesL. Note that Sales multiplied times the margin will yield an estimate of EBIT. Appendix 1 shows that this multiplicative relationship can be modeled from the Sales estimate while at the same time changing the EBIT margin. For the example problem, assume that the EBIT margin declines from the current m0 = 15% to a long-term margin of ml = 10%. From Appendix 1, future EBIT can be modeled from Sales while the margin declines over time as H EBIT = g S g L m L m 0 = H Sales m L m 0 = 12 ( 10% 15% ) = 8 (10) 12

13 EBIT t = EBIT 0 [H EBIT (1 + g L ) t (H EBIT 1)] (11) EBIT t = 1.25 [ 8 (1.02) t 7] = 12 (1.02) t (12) Note that Equation 10 is equivalent to a declining series for EBIT with an initial growth of 16% declining to a long-term growth of 2%. The initial growth of EBIT is simply scaled down from the initial growth in Sales by a ratio of the decline in EBIT margin (i.e., 24% x10%/15% = 16%). The growth path over the next 30 years for EBIT is also shown in Figure 1. Other value drivers can be estimated in a similar manner. For example, another value driver identified earlier is the production efficiency (or capital intensity). Assume that the production efficiency (p = IC/Sales) changes from p0 = IC0/Sales0 to pl = ICL/SalesL gradually over time while at the same time Sales is following a declining growth pattern. For example, in the same manner as the estimate of future EBIT, it can be shown that an increase in the future capital intensity from p0 = 0.80 to pl = 1.20 can be estimated as H IC = g S g L p L p 0 = H p L Sales = 12 ( 1.20 ) = 18 (13) p IC t = IC 0 [H IC (1 + g L ) t (H IC 1)] (14) IC t = 8 [18 (1.02) t 17] = 144 (1.02) t 136 (15) Note that HIC = 18 in Equation 13 is equivalent to a cash flow stream with an initial growth of 18 (2%) = 36% per year declining asymptotically to a growth of 2% per year. 13

14 Following the same procedure as before, the level of Debt over time can be estimated as an increase in the Debt to Invested Capital ratio or financial leverage (f = Debt/IC). Assume the financial leverage changes from f0 = Debt0/IC0 to f0 = Debt0/IC0. Any reasonable level of debt can be specified at this point. However, suppose an analyst prefers to assume the ROE will decline asymptotically to the required rate of return over the long run. Appendix 2 shows that the long-term level of debt that will result in the ROE declining over time to the required rate of return (while the EBIT margin and IC/Sales changes as shown earlier) can be determined as Debt L IC L = [ROE L m L (1 t) p L ] ROE L i (1 t) (16) Using the numbers in our example, this establishes a long-term Debt/IC ratio of Debt L IC L = 0.10 (1 0.20)) [ ] (1 0.20) = = (17) An increase in the financial leverage (Debt/IC) from f0 = 0.50 to fl = while the Invested Capital and Sales are also changing can be estimated as H Debt = g S g L p L p 0 f L f 0 = H f L IC = 18 ( ) = 24 (18) f Debt t = Debt 0 [H Debt (1 + g L ) t (H Debt 1)] (19) Debt t = 4 [24 (1.02) t 23] = 96 (1.02) t 92 (20) Again note that HDebt = 24 in Equation 18 is equivalent to the Debt growing at an initial rate of 48% per year and declining asymptotically to 2% per year. 14

15 Given the above forecasts for Sales, EBIT, Invested Capital (IC), and Debt, the four value drivers have been defined and allowed to change over time. The trend over the next 20 years in the profitability margin (EBIT/Sales), the capital productivity (IC/Sales), and the financial leverage (Debt/IC) is shown in Figures 2, 3, and 4. Figure 5 also shows that the Return on Equity is forecast to decline asymptotically from 25% to the required return on equity of 10%. Maintaining Accounting Consistency in the Analysis The forecast of Debt in Equation 20 makes possible a forecast of Interest Expense. If the interest rate on debt is assumed to be constant, interest expense will remain a constant proportion of Debt (0.25/4.0 = 6.25%). This means that Interest Expense can be estimated as INT t = INT 0 [H Debt (1 + g L ) t (H Debt 1)] (21) INT t = 0.25 [24 (1.02) t 23] = 6 (1.02) t 5.75 (22) Given the above individual components of EBIT and Interest Expense, Net Income (NI) can be estimated by subtracting Equation 22 (INT) from Equation 12 (EBIT) and multiplied by one minus the tax rate. Given a tax rate of 20% yields NI t = (EBIT t INT t )(1 t) (23) NI t = ([12 (1.02) t 10.50] [6 (1.02) t 5.75])(1 0.20) (24) NI t = 4.8 (1.02) t 3.8 (25) 15

16 Note that the forecast for Net Income is equivalent to a cash flow stream with an initial growth rate of 4.8 (2%) = 9.6% per year declining asymptotically to 2% per year. The growth path for Net Income over the next 30 years is again shown in Figure 1. The last step in preparing a pro forma income statement is to subtract the Additions to Retained Earnings (ARE) from NI to arrive at the potential Dividends (or FCFE) paid out to investors. If a clean surplus relationship is assumed and no new equity is issued, then the increase in Equity will be the amount necessary to meet the Debt/IC assumption. This means that the change in Equity will equal the ARE subtracted from NI, and potential Dividends (or FCFE) will be determined as a plug factor. Equity over time (EQt) is defined as ICt minus Debtt. Substituting ICt from Equation 14 and Debtt from Equation 19 yields EQ t = IC t Debt t EQ t = IC 0 [H IC (1 + g L ) t (H IC 1)] Debt 0 [H Debt (1 + g L ) t (H Debt 1)] (26) The change in Equity ( EQ) is the difference between EQt+1 and EQt. EQ t+1 = IC 0 [H IC (1 + g L ) t+1 (H IC 1)] Debt 0 [H Debt (1 + g L ) t+1 (H Debt 1)] (27) EQ t = IC 0 [H IC (1 + g L ) t (H IC 1)] Debt 0 [H Debt (1 + g L ) t (H Debt 1)] (28) Subtracting EQt from EQt+1 and simplifying yields EQ t = EQ t EQ t 1 = (IC 0 H IC Debt 0 H Debt ) (1 + g L ) t g L (1 + g L ) (29) Applying the numbers in the example yields EQ t = (8 (18) 4 (24)) (1.02) t (1.02) = (1.02)t (30)

17 The Dividend (DIVt) is equal to Net Income (NIt) minus the Additions to Retained Earnings (AREt). Again assuming a clean surplus relationship and no new equity, then the EQt = AREt. Subtracting Equation 30 from Equation 25 yields DIV t = NI t ARE t = NI t EQ t (31) DIV t = [4.8 (1.02) t 3.8] [ (1.02) t ] (32) DIV t = (1.02) t 3.8 (33) Equation 33 indicates that the dividend cash flow stream of this firm can be simulated with two cash flow streams: One cash flow stream with an initial value of that grows at a constant rate of 2% per year, and a second cash flow stream that remains constant at -3.8 each year into perpetuity. These two cash flow streams can be valued easily with the constant growth model and a perpetuity. Therefore, from Equation 33, a fair value for this stock given Sales declining in growth from 24% to 2%, the EBIT margin declining from 15% to 10%, the asset intensity increasing from 0.80 to 1.2, the Debt ratio increasing from 50% to 66.67%, and a required rate of return on equity of 10% evaluates at V 0 = (1.02) = = 11.2 (34) Residual Income Approach to Valuation Another approach equivalent to a valuation based on the present value of future dividends is the residual income approach. In this case, the total valuation of equity is the current book value of equity added to the present value of future residual income, as follows: 17

18 V 0 = EQ 0 + RI t (1 + R E ) t t=1 RI t = NI t R E EQ t 1 (35) (36) where RIt = Residual Income at time t, and RE = the required rate of return on equity. The equity over time was defined earlier in Equation 26. Applying numbers from the example problem (including HIC=18 from Equation 13 and HDebt=24 from Equation 18) yields EQ t = IC t Debt t EQ t = IC 0 [H IC (1 + g L ) t (H IC 1)] Debt 0 [H Debt (1 + g L ) t (H Debt 1)] (37) EQ t = 8 [18 (1.02) t (18 1)] 4[24 (1.02) t (24 1)] (38) EQ t = 48 (1.02) t 44 (39) From the definition of residual income in Equation 36 and net income from Equation 25, RI t = NI t R E EQ t 1 (40) R E EQ t 1 = (0.10)[48 (1.02) t 1 6] = 4.8 (1.02) t (41) RI t = [4.8 (1.02) t 3.8] [4.8 (1.02) t 1 4.4] (42) RI t = (1.02) t (43) The present value of the residual income cash flow stream can be determined with a constant growth model for the first term in Equation 43 and a perpetuity for the second term. For a 18

19 valuation of the equity of this firm, adding the beginning book value of equity to the present value of the residual income according to Equation 35 yields V 0 = (1.02) = = 11.2 (44) Note that this yields the same result as the present value of future dividends. As a point of comparison, Figure 6 shows the trend of the present values in the two approaches to valuation. Note that the present value of dividends increases at first, as the growth rate exceeds the required return on equity. However, a peak is reached in year 11 when the growth in the dividend equals the required rate of return, and declines thereafter as the growth rate continues to decline. Also note in Figure 7 that the retention rate declines from a high of to at maturity. This means that the firm retains more dividends while the growth rate is high, but gradually decreases the retention as the growth rate declines into maturity. These charts indicate that the cash flows, key value drivers, and resultant ROE and reinvestment rates are all reasonable as the growth rates decline and accounting consistency is maintained. Summary This paper adds several contributions to the literature on equity valuation. The first contribution is to demonstrate a procedure for incorporating the effect of key value drivers directly into a valuation analysis. An example valuation problem was used to incorporate a declining growth in sales and three other factors identified from the valuation literature and the DuPont relationships. As an added feature, a procedure was included for choosing an appropriate long-term capital structure (i.e., Debt/IC) such that the ROE declines asymptotically 19

20 to the required rate of return on equity over time. A second contribution is to demonstrate the flexibility of a new declining growth valuation model. The growth in sales was modeled to decrease from the current level to a mature, long-term growth rate comparable to the growth in the overall economy. In addition, the other value drivers in the valuation analysis were allowed to change over time to a level appropriate for a mature firm. A third contribution is to demonstrate a procedure for maintaining consistency in accounting relationships over time for the estimates of future cash flows. This means that the estimates for future cash flows are consistent with accounting theory in the preparation of future pro forma income statements and balance sheets. And finally, reasonable values for ROE, ROIC, and the reinvestment rate are a result of the assumed changes in value drivers. In summary, this paper demonstrates the process of completing a robust valuation analysis using a declining growth valuation model while maintaining consistent accounting and incorporating key value drivers. 20

21 References Berk, Jonathan, Peter DeMarzo, and Jarrad Harford (2015), Fundamentals of Corporate Finance 3 rd Ed., Pearson Education, One Lake Street, Upper Saddle River, NJ Block, Stanley and Geoffrey Hirt (2017), Foundations of Financial Management 16 th Ed., McGraw-Hill Irwin, 1221 Avenue of the Americas, New York, NY Cornett, M., Adair, T., and Nofsinger, J. (2012), Finance: Applications & Theory, 2ed., McGraw Hill, New York, N.Y. Damodaran, Aswath (2010), The Dark Side of Valuation 2 nd Ed., Pearson Education, Inc. Upper Saddle River, New Jersey Damodaran, Aswath (2012), Investment Valuation 3 rd University Ed., John Wiley and Sons, 111 River Street, Hoboken, NJ Fairfield, P. an T. Yohn (2001), Using Asset Turnover and Profit Margin to Forecast Changes in Profitability, Review of Accounting Studies (December), p Graham, John, Scott Smart, and William Megginson (2010), Corporate Finance: Linking Theory to What Companies Do, South-Western Cengage Learning, 5191 Natorp Boulevard, Mason, OH Higgins, Robert (1977), How much growth can a firm afford, Financial Management 6 (3), p Holland, Larry (2018), A Flexible Valuation Model Incorporating Declining Growth Rates, Accounting and Finance Research 7 (1), p

22 Koller, Tim, Marc Goedhart, and David Wessels (2010), Valuation: Measuring and Managing the Value of Companies, 5 th University Ed., John Wiley and Sons, 111 River Street, Hoboken, NJ Lundholm, Russell and Richard Sloan (2004), Equity Valuation and Analysis 1 st Ed., McGraw- Hill/Irwin, 1221 Avenue of the Americas, New York, NY Lundholm, Russell and Richard Sloan (2017), Equity Valuation and Analysis 4 th Ed., Copyright by Russell Lundholm and Richard Sloan. Nissim, Doron and Stephen Penman (2002), Financial Statement Analysis of Leverage and How it Informs About Profitability and Price to Book Ratios, Working Paper, Columbia University. Nissim, Doron and Stephen Penman (2001), Ratio Analysis and Equity Valuation: From Research to Practice, Review of Accounting Studies (March), p Ohlson, J. and B. Juettner-Nauroth (2005). Expected EPS and EPS growth as determinants of value, Review of Accounting Studies 10, Parrino, Robert and David Kidwell, Fundamentals of Corporate Finance 3 rd Ed., John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ Penman, Stephen (2015), "Valuation Models: An Issue of Accounting Theory," In Routledge Companion to Financial Accounting Theory. Abingdon: Routledge. Penman, Stephen (1998), A synthesis of equity valuation techniques and terminal value calculation for the dividend discount model, Review of Accounting Studies 2,

23 Penman, Stephen and X. Zhang (2004), Modeling Sustainable Earnings and P/E Ratios Using Financial Statement Information, Working Paper, Columbia University. Pinto J., E. Henry, T. Robinson, and J. Stowe (2010), Equity Asset Valuation, 2 nd Ed., John Wiley and Sons, Hoboken, N.J. Piotroski, Joseph (2001), Value Investing: The Use of Historical Financial Statement Information to Separate Winners from Losers, Journal of Accounting Research Vol. 38, Supplement 2000, p Ross, S., R. Westerfield, and B. Jordan (2006), Fundamentals of Corporate Finance, McGraw Hill, New York, N.Y. Soliman, Mark (2008), The Use of DuPont Analysis by Market Participants, The Accounting Review Vol 83, No. 3, p Viebig, Jan, Thorsten Poddig, and Armin Varmaz (2008), Equity Valuation: Models from Leading Investment Banks, John Wiley and Sons, Hoboken, N.J. 23

24 Table 1: Four-Year Forecast for Example Financial Statements: Sales Growth Only Year 1 Year 2 Year 3 Year 4 Actual g 1 = 24% g 2 = 19.74% g 3 = 16.82% g 4 = 14.68% Income Statement Sales CGS 7.50 SG&A 0.50 Depreciation 0.50 EBIT Interest Expense EBT % Net Income Dividends Additions to RE FCFF Retention Rate (b) Balance Sheet Cash Accounts Receivable Inventory Current Assets Net Fixed Assets Total Assets Current Liabilities LT Debt Common Stock Retained Earnings Total L&OE Invested Capital LT Debt Common Stock Retained Earnings Total Equity Invested Capital ROIC 15.00% 15.00% 15.00% 15.00% 15.00% Return on Equity 25.00% 25.00% 25.00% 25.00% 25.00% Debt/IC Ratio 50.00% 50.00% 50.00% 50.00% 50.00% EBIT/Sales 15.00% 15.00% 15.00% 15.00% 15.00% IC/Sales

25 Table 2: Four-Year Forecast for Example Financial Statements: Value Drivers Change Year 1 Year 2 Year 3 Year 4 Actual g 1 = 24% g 2 = 19.74% g 3 = 16.82% g 4 = 14.68% Income Statement Sales CGS 7.50 SG&A 0.50 Depreciation 0.50 EBIT Interest Expense EBT % Net Income Dividends Additions to RE FCFF Retention Rate (b) Balance Sheet Cash Accounts Receivable Inventory Current Assets Net Fixed Assets Total Assets Current Liabilities LT Debt Common Stock Retained Earnings Total L&OE Invested Capital LT Debt Common Stock Retained Earnings Total Equity Invested Capital ROIC 15.00% 12.79% 11.49% 10.63% 10.02% Return on Equity 25.00% 22.93% 21.34% 20.07% 19.04% EBIT/Sales 15.00% 14.03% 13.37% 12.88% 12.51% IC/Sales Debt/IC 50.00% 54.41% 57.02% 58.74% 59.96% 25

26 Appendix 1 Derive a Multiplicative Declining Growth Factor, HEBIT Establish a multiplicative relationship between Sales and EBIT, where From Equation 8, EBIT t = m t Sales t (45) Sales t = Sales 0 [H Sales [(1 + g L ) t 1] + 1] (46) Let EBIT also follow a declining growth pattern, EBIT t = EBIT 0 [H EBIT [(1 + g L ) t 1] + 1] (47) Substituting Equation 45 into Equation 47 yields m t Sales t = m 0 Sales 0 [H EBIT [(1 + g L ) t 1] + 1] (48) Dividing Equation 48 by Equation 46 yields m t Sales t Sales t = m t = m 0 Sales 0[H EBIT [(1 + g L ) t 1] + 1] Sales 0 [H Sales [(1 + g L ) t 1] + 1] (49) As t gets very large, the effect of adding 1 to the numerator and denominator diminishes to zero, and mt approaches ml. Therefore, taking the limit as t approaches infinity yields Solving for HEBIT yields lim m H EBIT t = m L = m 0 (50) t H Sales H EBIT = g S g L m L m 0 (51) 26

27 Appendix 2 Derive the Debt/IC Which Causes ROE to Approach RE The Return on Equity (ROE) is defined as Net Income divided by Equity. Substituting for the definitions of Net Income and Equity yields ROE t = NI t EQ t = (EBIT t INT t ) (1 t) IC t Debt t (52) Define Interest as a constant yield (i) times the level of Debt, or ROE t = (EBIT t i Debt t ) (1 t) IC t Debt t (53) Multiplying both sides by the denominator of ICt Debtt yields ROE t (IC t Debt t ) = (EBIT t i Debt t ) (1 t) (54) Dividing both sides by ICt yields ROE t (1 Debt t ) = ( EBIT t i Debt t ) (1 t) (55) IC t IC t IC t Solving for (Debtt/ICt) yields Debt t IC t = [ROE t EBIT L (1 t) IC L ] ROE t i (1 t) (56) Dividing EBIT and IC by Sales in the numerator of the term on the right side yields Debt t IC t = EBIT t (1 t) Sales [ROE t t IC ] t Sales t ROE t i (1 t) (57) Substituting the definition of m=(ebit/sales) and p=(ic/sales), and evaluating at time L yields Debt L IC L = [ROE L m L (1 t) p L ] ROE L i (1 t) (58) 27

28 Figure 1 Growth Rate of Sales, EBIT, and Net Income Declining Towards a 2% Long-Term Growth Rate 25% Sales 20% 15% EBIT 10% NI 5% 0% Figure 2 Trend in EBIT/Sales Declining Asymptotically from 15% To 10% 15% 14% 13% 12% 11% 10%

29 Figure 3 Trend in IC/Sales Increasing Asymptotically from 0.8 To Figure 4 Trend in Debt/IC Increasing Asymptotically from 0.50 To

30 Figure 5 Trend in ROE and ROIC ROE Declining from 25% To 10% ROIC Declining from 15% to 6.667% 25% 20% ROE 15% 10% ROIC 5% 0% Figure 6 Present Value of Dividends and Residual Income (Required Return = 10%) RI DIV

31 Figure 7 Trend in the Retention Rate (b) Decreasing from to