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Integrating Financial Statement Modeling and Sales Forecasting

John T. Cuddington, Colorado School of Mines Irina Khindanova, University of Denver

ABSTRACT

This paper shows how to integrate financial statement modeling and sales forecasting using the EViews software package. A model is developed to carry out stochastic simulations of the effects of estimated future sales forecasts (with the associated uncertainty) on various income and balance sheet items, along with their respective confidence intervals. We illustrate how the analyst can easily study the likelihood that cash balances will be exhausted – a clear indicator of ‘financial distress’ -- under various sales scenarios.

INTRODUCTION

Most business school programs include classes in financial accounting, including pro forma statement analysis. Often more extensive treatments of financial modeling – are discussed. See, e.g., Benninga (2008). In addition, students are typically exposed to introductory statistical and econometric methods, including forecasting (esp. sales forecasting). See, e.g., Diebold (2007) for a representative treatment. While practitioners are exposed to both tools – financial modeling and forecasting -- there is seldom an attempt to integrate them within a unified framework. The purpose of this paper is to show how this can be done using the EViews econometrics package, which is often used in introductory econometrics and forecasting courses.

The paper begins with a simple sales-driven model that Benninga (2008, Ch.3) develops using the Excel spreadsheet program. We show how to set up the same model in EViews and confirm that our results match those in Benninga’s Excel model. The EViews model has the advantage of being more transparent and easier to audit and debug because the equations in the model are written out explicitly in the MODEL object in EViews. The Excel formulation, on the other hand, will be more familiar to students who are comfortable with Excel.

Next a very simple univariate sales forecasting equation along the lines of the example in Diebold (2007, pp.87-94) is estimated using EViews. It is a quadratic trend model for LOG(SALES) with an AR(2) error process. This forecasting equation is then linked to the pro forma statement model. We demonstrate how the sales equation can be used to generate a forecast of the time path of future sales, which is the pivotal ‘driving’ variable in the Benninga model (and many similar ‘sales driven’ financial models). The estimated error process in the sales equation and the standard error of regression are used to obtain conditional forecasts for sales and the associated standard errors. Using this information from the sales equation, the EViews MODEL can be used to calculate forecasts and associated confidence intervals for all items in the pro forma financial statements. This provides a wealth of useful additional

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information to the financial analyst. She obtains not only the expected future values for the various pro forma statement items, but also the associated confidence intervals used to assess the degree of uncertainty of the financial forecasts. Our illustration focuses on sales forecast implications for the net cash position of the firm over time. The deterioration of the cash position towards zero would be a clear indicator of ‘financial distress’ in most situations.

The remainder of the paper is structured as follows. Section II discusses how to implement pro forma statement models in EViews. Section III develops an illustrative sales forecasting equation. The linking of the sales forecast to the pro forma model is covered in Section IV, and Section V summarizes our findings. PRO FORMA STATEMENT MODELING IN EVIEWS Benninga (2008, Ch.3) introduces a series of increasingly complicated models to demonstrate various aspects of corporate financial strategy. Typically, the models begin with a set of hypothesized initial figures for income statement and balance sheet items, such as those presented in Table 1 below. In real-world applications, these figures would be taken from actual financial statement information. For ease of reference, we have added to the left-most column of Table 1 our chosen EViews variable or series names.1 When implementing a pro forma model in EViews, one must first set up an annual (or quarterly or monthly) frequency workfile and then declare series that have appropriate initial values, such as those in Table 1. If one has historical time series data on each of these items, rather than just the 2005 values, so much the better. For the sales forecasting exercise in Section III below, we’ll need historical data for sales, but only the 2005 values for the other financial statement items. Appendix B (available on request) provides detailed instructions on how to get your Excel dataset into EViews and how to run both the deterministic and stochastic versions of the model, where the stochastic version is driven by the error process and coefficient estimation uncertainty implied by the sales forecasting equation. Table 1: Initial Year Data and EViews Series Names*

EViews Series Name INCOME STATEMENT 2005

Initial Condition Needed

SALES Sales 1000.0 Yes COGS Cost of Goods Sold 500.0 No INT_DEBT Interest Expense on Debt 32.0 No INT_CASH Interest Earnings on Cash & Securities 6.0 No DEPN Depreciation Expense 100.0 No PBT Profit Before Taxes 374.0 No TAXES Taxes 149.6 No PROFIT After-Tax Profit 224.4 No DIVIDENDS Dividends 89.8 No RET_EARNINGS Retained Earnings 134.6 No BALANCE SHEET

1 Note that EViews series names cannot contain spaces or unusual characters.

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CASH Cash and Marketable Securities 80.0 Yes OCA Other Current Assets 150.0 No FA_COST Fixed Assets at Cost 1070.0 Yes ACC_DEPN Accumulated Depreciation 300.0 Yes NFA Net Fixed Assets 770.0 No ASSETS TOTAL ASSETS 1000.0 No CL Current Liabilities 80.0 No DEBT Debt Outstanding 320.0 Yes LIAB Total Liabilities 400.0 No CAPITAL Paid-in Capital 450.0 Yes ACC_EARNINGS Accumulated Retained Earnings 150.0 Yes EQUITY Total Equity 600.0 No Total Liabilities + Equity 1000.0 No * Initial conditions are given for Model 1 in Benninga, 2008, p. 111.

Benninga lays out a simple set of equations to describe the interrelationships among his income and balance sheet variables at each future date. These formulas are shown in Table 2. Because many of these equations involve variables lagged one period, denoted by (-1) after the series name, the model is, in effect, a system of first-order difference equations. Given the initial conditions (e.g., the 2005 values), the system of equations is solved recursively going forward to obtain future-period values.

Table 2: Formulas For Pro-Forma Financial Statements*

EViews Variable Name Formula for Subsequent Periods Assumptions

SALES SALES = SALES(-1)*1.10 Constant Sales growth rate

COGS COGS = 0.50*SALES Sales Driven INT_DEBT INT_DEBT = .10*(DEBT+DEBT(-1))/2 Ratio assumption INT_CASH INT_CASH = .08*(CASH+CASH(-1))/2 Ratio assumption DEPN DEPN = .10*(FA_COST+FA_COST(-1))/2 Ratio assumption

PBT PBT = SALES - COGS - INT_DEBT + INT_CASH - DEPN Identity

TAXES TAXES = .40*PBT Ratio assumption PROFIT PROFIT = PBT - TAXES Identity DIVIDENDS DIVIDENDS = .40*PROFIT Ratio assumption RET_EARNINGS RET_EARNINGS = PROFIT - DIVIDENDS Identity CASH CASH = LIAB + EQUITY - NFA - OCA The "Plug" OCA OCA = .15*SALES Sales Driven FA_COST FA_COST = NFA + ACC_DEPN Identity ACC_DEPN ACC_DEPN = ACC_DEPN(-1) + DEPN Identity NFA NFA = .77*SALES Sales Driven

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ASSETS ASSETS = CASH + OCA + NFA Identity CL CL = .08*SALES Sales Driven

DEBT DEBT = DEBT(-1) Debt remains constant

LIAB LIAB = CL + DEBT Identity

CAPITAL CAPITAL = CAPITAL(-1) Paid-in Capital remains constant

ACC_EARNINGS ACC_EARNINGS = ACC_EARNINGS(-1) + RET_EARNINGS Identity

EQUITY EQUITY = CAPITAL + ACC_EARNINGS Identity * Ratio assumptions match those for Model 1 in Benninga, 2008, p. 111.

Note that sales growth rate is assumed to be a constant 10% over time, so current sales equal

last year’s sales multiplied by 1.10. Several of the key variables are proportional to sales: cost of goods sold (COGS), other current assets (OCA), net fixed assets (NFA), and current liabilities (CL). This is the sense in which the model is ‘sales driven.’ To complete the model, Benninga assumes that:

• Interest expense is 10% on the average debt outstanding (where average means the beginning and end of the period values divided by two).

• Interest income is 8% of the average cash and marketable securities. • Depreciation expense is 10% of average fixed assets at cost. • Dividend payout rates and corporate tax rates are constant at 40 and 40 percent,

respectively. The model contains a number of identities, identified as such in the Table 2, and importantly, it is assumed that the cash and marketable securities item (CASH) adjusts to insure that the balance sheet identity holds. That is, CASH is the so-called ‘plug’ that closes the model.

The Benninga model is straightforward to implement and solve using EViews. After creating the annual frequency workfile and declaring series with the initial values assumed in Table 1, we create a blank MODEL object. Then, in text mode, the model equations are entered one-by-one using the syntax given in Table 2. Comment lines can be inserted in the MODEL object, as needed, to help readers interpret the various equations; these lines begin with a single quotation mark.

Figure 1 shows the equations as entered into the EViews MODEL. The MODEL object is capable of solving first or higher-order (potentially) simultaneous equation systems using initial and/or terminal conditions, as appropriate. In the current application with first-order difference equations and initial conditions for the year 2005, the MODEL is solved from 2006 forward (for as many periods as the analyst is interested in). Figure 1: Benninga’s Model 1 in the EViews MODEL Object ' ================================================= ' Model 1 – Cash and marketable securities is the plug. Debt is constant. ' ' This model replicates the first Excel pro forma statement model in Benninga (2008, Ch. 3, p. 111). SALES = SALES(-1) * 1.10

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' Balance Sheet OCA = 0.15 * SALES CL = 0.08 * SALES NFA = 0.77 * SALES DEPN = 0.10 * (FA_COST(-1) + FA_COST) / 2 ACC_DEPN = ACC_DEPN(-1) + DEPN FA_COST = NFA + ACC_DEPN LIAB = DEBT + CL EQUITY = CAPITAL + ACC_EARNINGS CASH = LIAB + EQUITY - OCA - NFA ASSETS = CASH + OCA + NFA ' Income Statement COGS = 0.50 * SALES INT_DEBT = (DEBT(-1) + DEBT) / 2 * 0.10 INT_CASH = (CASH(-1) + CASH) / 2 * 0.08 PBT = SALES - COGS - INT_DEBT + INT_CASH - DEPN TAXES = 0.40 * PBT PROFIT = PBT - TAXES DIVIDENDS = 0.40 * PROFIT RET_EARNINGS = PROFIT - DIVIDENDS ACC_EARNINGS = ACC_EARNINGS (-1) + RET_EARNINGS ' =================================================

Figure 2 illustrates the EViews generated pro forma balance sheet and income statements. One can confirm that values of financial statements items coincide with those in Benninga’s Excel pro-forma statements (Benninga, 2008, p. 111).

Note that the company’s cash balance position may rise or fall over time depending, in a complicated way, on both the sales growth rate and various ratio assumptions in the model. As Benninga points out, this model has the shortcoming that it is possible for CASH to become negative and to grow larger and larger in absolute value over time. This is surely unrealistic for any going concern! Therefore, he then goes on to generalize the model to eliminate this (and other) shortcomings. For example, one might assume that once the cash position hits zero (indeed even before that dire moment), the firm takes on additional debt. If the debt grows in a way that moves the firm from its target debt/equity ratio, then additional equity financing may ultimately be undertaken.

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Figure 2: EViews-generated Financial Statements

While these complications are interesting and straightforward to implement in EViews, we

omit them here to simplify the exposition of how to integrate sales forecasting with a simple financial model.

THE SALES FORECASTING EQUATION

This section summarizes the estimation of a univariate sales forecasting equation, which will then be used in Section IV to forecast sales for future years. This variable is the exogenous ‘driver’ in Benninga pro forma statement model. For purposes of illustration, aggregate U.S. retail sales published by the Bureau of Economic Analysis (rather than the sales for a particular corporation) will be used.2 The seasonally adjusted monthly series is aggregated to annual frequency and rebased to create an index that equals 1000 in the year 2005 so that the resulting SALES series has an initial condition matching that used by Benninga.

The estimated equation is a quadratic time trend model for the natural logarithm of SALES: 2

1 2( )t tLOG SALES t tα β β ε= + + + (3.1)

2 This series was obtained from the Haver Analytics USECON database (series:RS@USECON).

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The residual correlogram and Ljung-Box Q statistics from this OLS estimation were examined to check for the presence of serially correlated errors. The correlogram suggested that the residuals followed an AR(2) process: 1 1 2 2t t t tuε ρ ε ρ ε− −= + + (3.2) Thus, our chosen specification is equation (3.1) with the AR(2) error process in (3.2). The regression output for the selected model is shown in Table3. The Q(3) statistic is reported as confirmation that we are unable to reject the null hypothesis that the innovations in the AR(2) process are white noise.

In our stochastic version of the Benninga model in Section IV, the SALES equation is used to forecast future sales and confidence intervals for future sales are obtained by Monte Carlo simulation. The Monte Carlo simulation assumes that the error process in the sales equation has a normal distribution with mean zero and standard Table 3: Estimated SALES Equation

Dependent Variable: LOG(SALES)

Variable CoefficientStd. Error t-Statistic Prob.

C 6.201 0.009 664.770 0.000 @TREND 0.067 0.003 19.637 0.000 @TREND^2 -0.001 0.000 -4.299 0.004 AR(1) 0.548 0.251 2.185 0.065 AR(2) -0.868 0.261 -3.331 0.013

R-squared 0.998 Adjusted R-squared 0.996 Q(3) Stat 2.384 S.E. of regression 0.011 p-value 0.123

deviation equal to the estimated standard error of regression (s.e.=0.011).3 Coefficient uncertainty (as the OLS estimates are only estimates of the true but unknown parameters) is also taken into account in the simulations below.

Parenthetically, the procedures outlined in this paper can be implemented with any sales forecasting equation one prefers; it may be a single equation or one equation in a multi-equation model. It is straightforward to introduce several sources of uncertainty into the analysis by including several estimated equations in the model. In this case, the forecasts correctly capture interactions among the forecasted variables. Confidence intervals reflect the error variances in all equations as well as their covariances.

3 EViews also has the option of using bootstrapping rather than assuming that error terms are multivariate normal, if one prefers.

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INTEGRATING THE SALES FORECAST AND THE PRO FORMA STATEMENT MODEL

This section presents a stochastic generalization of Benninga’s model for financial statements described in Section II. First, SALES are forecasted into the future. Then, using the sales forecasts and associated standard errors, forecasts and confidence bands for all (or specified) items in pro-forma statements are derived. Lastly, uncertainty of the financial forecasts for particular variables – here, PROFIT and CASH balances – are analyzed.

We use the sales equation estimated in Section III (SALES_EQ) to forecast future sales. The sales equation is used to replace the constant sales growth equation in Benninga’s model, as in EViews in Section II by linking the estimated equation in the workfile to the MODEL object. This is done by typing :SALES_EQ in the MODEL object. (The colon creates the link to the estimated equation in the workfile.) In solving the MODEL, we elect to account coefficients uncertainty. By using the stochastic solution feature in EViews, one can easily produce forecasted future SALES and a 95% (or other user selected) confidence band as shown in Figure 3.

Figure 3: SALES Forecasts

900

1,000

1,100

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1,700

1,800

2006 2008 2010 2012 2014 2016 2018 2020

SALES (Baseline Upper)SALES (Baseline Lower)SALES (Baseline Mean)

The forecasted time path of SALES, of course, differs from Benninga’s illustrative constant

sales growth rate assumption. Figure 4 shows the implied SALES growth rate over time with the 95% confidence bounds. The SALES forecast equation implies that the SALES growth rate varies between 0% and 5%, while trending down slowly over time. The 95% confidence band for SALES widens over time, reflecting growing SALES uncertainty as one goes further into the future. The width of the SALES confidence band in 2020 reaches 683.1, which equals 49.4% of expected SALES in that year.

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Figure 4. SALES Growth Rate

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2006 2008 2010 2012 2014 2016 2018 2020

SALES Growth Rate (Baseline Upper)SALES Growth Rate (Baseline Lower)SALES Growth Rate (Baseline Mean)

We examine impacts of sales forecasts on other financial variables in the MODEL under two

scenarios. In the first scenario, we assume that the ratio of cost of goods sold to sales (COGS/SALES) equals 0.50 as in Benninga’s first model. Next we consider an alternative scenario where COGS/SALES = 0.75 – a value that produces quite different outcomes for the company’s future cash position.

Figures 5 and 6 show the time paths of CASH and PROFIT, respectively, in the COGS/SALES = .50 case. CASH balances increase over time, with a relatively narrow 95% Figure 5: CASH Balances for the COGS/SALES = .50 Scenario

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CASH (Baseline Upper)CASH (Baseline Lower)CASH (Baseline Mean)

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Figure 6: PROFIT for the COGS/SALES = .50 Scenario

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2006 2008 2010 2012 2014 2016 2018 2020

PROFIT (Baseline Upper)PROFIT (Baseline Lower)PROFIT (Baseline Mean)

confidence band that slowly widens over time. The width of the CASH confidence band in 2020 is 194.8 (or 10.8% of expected CASH balances). PROFIT increases in the initial four years with a growth rate of up to 4 % and then declines. The 95% confidence band for PROFIT expands to 148.7 in 2020, which equals 90.8% of expected PROFIT.

Comparing the SALES, PROFIT, and CASH forecasts in the COGS/SALES = 0.50 case, one finds that the PROFIT forecasts have highest degree of uncertainty (90.8%), measured by the ratio of the width of the 95% confidence band to the mean or expected forecast level; the SALES projections have lower degree of uncertainty (49.4%); and the CASH forecasts exhibit the lowest degree of uncertainty (10.8%). An analysis of volatilities (standard deviations) of the SALES, PROFIT, and CASH projections shows that SALES have highest volatility, followed by CASH, and PROFIT. See Figure 7. Figure 7: Volatilities of SALES, CASH, PROFIT for the COGS/SALES = .50 Scenario

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2006 2008 2010 2012 2014 2016 2018 2020

SALES (Baseline S.D.)PROFIT (Baseline S.D.CASH (Baseline S.D.)

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The model forecasts are quite different if we assume that the COGS/SALES ratio equals 0.75, rather than 0.50. CASH balances increase in the initial four years, then level off in the following four years. After 2012, the CASH position rapidly declines, becoming negative from 2018 forward (see Figure 8)4. While SALES increase over the forecasted period and the CASH balances increase in the initial periods, the PROFIT levels decline after 2007, becoming negative after 2014 (Figure 9). In 2020, the width of the 95% confidence band for CASH reaches 463.8, Figure 8: CASH Balances for the COGS/SALES = .75 Scenario

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Figure 9: PROFIT Levels for the COGS/SALES = .75 Scenario

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4 Benninga’s Model 2 (2008, p. 120) prevents CASH from becoming negative by increasing debt levels as needed. We have also implemented this slightly more complicated financial model in EViews. See Appendix A for a brief description.

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which is 196.8% of (the absolute value of) of expected CASH balances. In the same year (2020), the width of the 95% confidence band for PROFIT is equal to 20.3% of expected PROFIT. The confidence band around PROFIT is narrower than the confidence bands around SALES and CASH, what implies less uncertainty in PROFIT levels. As in the COGS/SALES = 0.50 scenario, volatility of SALES is greater than volatility of CASH, which in turn is greater than volatility of PROFIT, as shown in Figure 10. Figure 10: Volatilities of SALES, CASH, PROFIT for the COGS/SALES = .75 Scenario

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SALES (Baseline S.D.)PROFIT (Baseline S.D.)CASH (Baseline S.D.)

A comparison of the two scenarios for the COGS/SALES ratio shows that the PROFIT

forecasts have greater uncertainty in the first scenario (COGS/SALES = 0.50), while the CASH forecasts demonstrate higher uncertainty in the second scenario (COGS/SALES = 0.75). These comparisons illustrate that a sales-driven pro-forma statement model can result in different degrees of uncertainty in financial forecasts for various variables depending on the underlying ratio assumptions.5 This emphasizes the nontrivial nature of the interdependences among financial variables that must be taken into account when assessing the degree of uncertainty for various financial statement variables. These interdependences are easily captured when using stochastic simulations to study how sales forecast uncertainty impacts other variables in the pro forma financial statement model.

Another benefit of integrating the sales forecasting and financial model simulation using EViews is that it is straightforward to allow for the coefficient uncertainty that is inherent in the econometric estimation. In the current application, a comparison of forecasts with and without coefficients uncertainty suggests that: (i) confidence bands are narrower under the ‘no coefficient uncertainty’ assumption, implying these confidence bands overestimate the precision of financial forecasts; (ii) volatility of variables is lower under the ‘no coefficients uncertainty’ assumption; (iii) confidence bands widen faster in the ‘coefficients uncertainty’ case.

5 These ratio assumptions could, in principle, be replaced by estimated relationships.

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CONCLUSIONS

This paper demonstrates how to integrate pro forma financial statements with sales forecasting. The integration was performed in five steps: (i) modeling of financial statements using the MODEL object in the EViews econometrics software package; (ii) estimation of a sales forecasting equation; (iii) linkage of the sales forecasting equation and the EViews model of financial statements; (iv) forecasting sales and other items in the pro forma statements and constructing confidence intervals for those forecasts; and (v) analysis of uncertainty of financial forecasts.

The illustration developed in this paper shows that EViews modeling of financial statements has the benefit of being more transparent and easier to audit and debug than the same financial model implemented in the Excel spreadsheet program. Advantages of the use of sales forecasting equation include projection of the sales series with a realistic (and typically variable) growth rate, consideration of coefficient uncertainty, estimation of the expected values for various pro forma statement items, obtaining the confidence bands for financial forecasts. The confidence intervals can be used to assess the degree of uncertainty associated with the financial forecasts.

The procedures outlined in the paper can be implemented with any sales forecasting equation. It may be a single equation or one equation in a multiple equation model. It is possible to introduce several sources of uncertainty into the analysis, with accounting for correlations among the error terms. We intend to develop financial modeling with multiple sources of uncertainty in our future work. REFERENCES Diebold, Francis X. 2007. Elements of Forecasting. Fourth Edition. South-Western College Publishing Co. Simon Benninga. 2008. Financial Modeling. Third Edition. Cambridge, MA: MIT Press. Ch. 3: Financial Statement Modeling.

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APPENDIX A: BENNINGA’S MODEL 2 IN THE EVIEWS MODEL OBJECT In an extension of his first model (discussed in this paper), Benninga (2008, Ch. 3, p. 120) develops a model where CASH is the plug as long as cash balances are non-negative. The possibility that CASH could become negative is precluded by additional borrowing (DEBT increases) as needed. To implement this model in EViews, we need to construct a dummy variable (DUM) to determine the sign of CASH balances in the absence of the non-negativity constraint. When CASH>0, it is the plug. When CASH would become negative, it is constrained to equal zero and DEBT becomes the plug. Below, we reproduce the equations to be entered into the MODEL object in order to implement this model in EViews. ============================= ' Model 2 – Cash and marketable securities is the plug as long as it is non-negative. Debt is increased as needed to prevent negative cash balances from materializing. ' This model replicates the second Excel pro forma statement model in Benninga (2008, Ch. 3, page 120) SALES = SALES(-1) * 1.20 ' Balance Sheet OCA = 0.20 * SALES CL = 0.08 * SALES NFA = 0.80 * SALES DEPN = 0.10 * (FA_COST(-1) + FA_COST) / 2 ACC_DEPN = ACC_DEPN(-1) + DEPN FA_COST = NFA + ACC_DEPN EQUITY = CAPITAL + ACC_EARNINGS ' create a dummy variable DUM that is equal to one when (OCA + NFA) exceed ' (CL - DEBT(-1) - EQUITY) and zero otherwise DUM = OCA + NFA - CL - DEBT(-1) - EQUITY > 0 ' DEBT equals its value from the previous period unless there is a need to ' undertake additional borrowing to prevent CASH from becoming negative: DEBT = (OCA + NFA - CL - EQUITY) * DUM + DEBT(-1) * (1 - DUM) LIAB = DEBT + CL ' CASH equals the minimum of its value in model 1 or zero; it can’t be negative CASH = (LIAB - OCA - NFA + EQUITY) * (1 - DUM) ASSETS = CASH + OCA + NFA

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' Income Statement COGS = 0.50 * SALES INT_DEBT = (DEBT(-1) + DEBT) / 2 * 0.10 INT_CASH = (CASH(-1) + CASH) / 2 * 0.08 PBT = SALES - COGS - INT_DEBT + INT_CASH - DEPN TAXES = 0.40 * PBT PROFIT = PBT - TAXES DIVIDENDS = 0.50 * PROFIT RET_EARNINGS = PROFIT - DIVIDENDS ACC_EARNINGS = ACC_EARNINGS (-1) + RET_EARNINGS ' ======================================================