Introduction to Financial Modeling 1-1 The Gutenberg Approach to Financial Modeling & Equity Valuation Demonstration Video Series Chapter 1: Introduction to Financial Modeling Chapter 2: DCF Inputs (ERP, Beta, CAPM, & WACC) Chapter 3: Discounted Cash Flow Valuation Chapter 4: Market Multiple Valuation Chapter 5: Using Regression Analysis to Predict Earnings Video Series Overview When creating an earnings model for a company, our goal is to have an example of a potential financial scenario, which we can dynamically change using a set of assumptions, and instantly see the estimated impact on earnings and share price valuation. This document is a tutorial of the modeling approach we use to analyze earnings results, and should be read in conjunction with our demonstration video series available on our website: www.gutenbergresearch.com/education. In this series we will be using our Apple Inc (NASDAQ:AAPL) Earnings & Valuation Model to demonstrate our methodology, with examples of specific topics for Tesla Motors (NASDAQ:TSLA), Alphabet Inc (NASDAQ:GOOGL), Starbucks Corp (NASDAQ:SBUX), and The Boeing Co (NYSE:BA). Please visit our website www.gutenbergresearch.com/education to download these free example models. Keep in mind that our models are typically updated four times per quarter, so the values in this demonstration have changed. For the purpose of supporting this demonstration, the models shown including our Apple model, Constant Sharpe/DCF analysis, and SBUX/BA regression models will be available in their current state as of the publishing date of this series (December 4, 2015). The latest updates are available on our Free Model Downloads page. Be sure to tune into our YouTube Channel for our earnings preview and review videos which analyze company earnings results using the financial models discussed in this document. By viewing our content, you are deemed to have read and agreed to our Terms of Use (www.gutenbergresearch.com/terms-of-use). Gutenberg 2014. The Gutenberg logo is among the registered and unregistered trademarks of Gutenberg Research. All rights reserved.
Introduction to Financial Modeling 1-2 Table of Contents Chapter 1 Introduction to Financial Modeling... 1-4 Section 1: Earnings Model Layout... 1-4 Section 2: Income Statement Modeling... 1-5 Section 3: GAAP & Non-GAAP Earnings... 1-7 Section 4: Model Calibration... 1-8 Section 5: Balance Sheet Modeling... 1-9 Section 6: Cash Flow Statement Modeling... 1-9 Section 7: Financial Statement Links... 1-10 Retained earnings... 1-10 Income Statement links to the Cash Flow Statement... 1-10 Balance Sheet links to the Cash Flow Statement... 1-11 Property, Plant, & Equipment... 1-11 Cash Flow links to the Balance Sheet... 1-11 Section 8: How to use the Earnings Model... 1-12 Chapter 2 DCF Inputs (ERP, Beta, CAPM, & WACC)... 2-13 Section 1: Calculating the Equity Risk Premium... 2-13 Section 2: Review of the Historic Constant Sharpe ERP... 2-14 Section 3: Deriving Beta Using Excel... 2-15 Section 4: Using Beta and the CAPM to calculate the Required Return on Equity... 2-17 Section 5: Calculating the Weighted Average Cost of Capital... 2-17 Chapter 3 Discounted Cash Flow Valuation... 3-18 Section 1: Our DCF Approach... 3-18 Section 2: Stage-One Calculation... 3-18 Section 3: Stage-Two Calculation... 3-19 Section 4: Final DCF-Based Valuation... 3-19 Market ERP... 3-19 CAPM... 3-19 WACC... 3-19 Volatility... 3-19 Interest Rates... 3-19 Beta... 3-19 Section 5: DCF Sensitivity Analysis... 3-20
Introduction to Financial Modeling 1-3 Section 6: Final Note on DCF Valuation... 3-20 Chapter 4 Market Multiple Valuation... 4-21 Section 1: Which Multiple to Use... 4-21 Industry/Sector... 4-21 Cyclical vs non-cyclical... 4-21 Lifecycle stage... 4-21 Section 2: Separating Cash from the Valuation... 4-22 Section 3: Calculating Share Value Using the Multiple... 4-22 Chapter 5 Using Regression Analysis to Predict Earnings... 5-23 Section 1: Data Selection... 5-23 Section 2: Running the Regression... 5-25 Section 3: Model Testing... 5-26 P-value and t-stat review... 5-26 Breusche-Pagan test... 5-27 Serial correlation test... 5-28 The normal distribution assumption... 5-29 Model stability... 5-29 Other Considerations... 5-29 F-stat review... 5-30 Significance F... 5-30 Multicolinearity... 5-30 Section 4: Analyzing the Output... 5-30 Section 5: Back Testing... 5-32 Section 6: Model Limitations & Improvements... 5-32 Terms of Use... 5-34
Introduction to Financial Modeling 1-4 Chapter 1 Introduction to Financial Modeling Section 1: Earnings Model Layout Section 5: Balance Sheet Modeling Section 2: Income Statement Modeling Section 6: Cash Flow Modeling Section 3: GAAP & Non-GAAP Earnings Section 7: Financial Statement Links Section 4: Model Calibration Section 8: How to use the Model Section 1: Earnings Model Layout To get started it is important to take a few minutes to get comfortable with how our models are setup. We use a basic cell color coding scheme: blue cells represent our key assumptions, purple cells represent management guidance, and orange cells represent consensus estimates. Historic values come from company reports (SEC filings, investor press releases, and presentations). Some future period cells are not color coded, which indicates that the cell is populated based on an equation, or it does not represent a significant assumption in the model. Apple Model: Color Coding Chapter 1 Overview When we model a company s earnings we are trying to breakdown the financial results into small, digestible pieces. If someone asks you whether or not Apple will beat the consensus EPS estimate this quarter, it would be very difficult to answer without thinking about how many iphones, Macs, ipads, and watches the company would sell, the average price for each, and what the gross margin and operating expenses would be. A financial model shows all of these parts and how they work together to get to a final bottom-line EPS estimate. This demonstrates why a financial model is such an important tool for investors. Without running through the scenario you think is most likely to occur, how could you possibly have a reasonable basis for making your investment decision.
Introduction to Financial Modeling 1-5 We have two categories of models: Tier 1 and Tier 2. Apple is a Tier 1 model which includes the Income Statement, segment details, Balance Sheet, Cash Flow Statement, and uses two valuation methods: 1) A market multiple, and 2) Discounted Cash Flow (DCF) approach. Our Tier 2 models include the Income Statement, segment details and a market multiple valuation only. The column headings in our models have two shades of gray. The dark gray represents historic details, which come from the company s Securities and Exchange Commission (SEC) filings, press releases, or investor presentations. The light gray columns represent future period forecasts. Section 2: Income Statement Modeling If you drill into the equations on the Income Statement you will notice that it is simply a summary of the results in the assumptions from the segment details section. The segment details are company specific, so this section will change for each model. We choose the categories to use in the segment section based on the information the company provides in their SEC filings and quarterly presentations. For Apple the segment section starts with a breakdown of revenue by geography, however since these cells are not blue, they are merely informational based on our key assumptions in blue, which start with the Average Selling Price (ASP) by Product and unit sales growth rates. Apple Model: Segment Section Now you should be able to see how the smaller pieces fit together. If you know a new iphone will launch next quarter, you can increase the ASP and the unit growth rate. You can also increase the unit growth
Introduction to Financial Modeling 1-6 rates for the December quarter to reflect the holiday shopping season, or decrease the ipad growth rates to reflect the trend of decreasing overall demand. The ASP and unit growth rates are used to derive the top-line revenue estimate. After that we need to make an assumption for gross margin. If you think Apple will have a favorable mix in iphone Plus and high storage capacity models, you can increase the gross margin, or if you think they will sell a greater proportion of lower-margin iphone C models you can decrease the gross margin. This will now bring you down to the gross profit line on the income statement. Management typically gives a target range for the corporate average gross margin (not at a product level), which we use for our baseline gross margin estimate. From there we need to make some assumptions about the operating expense (opex) items. For most of our models we have separate assumptions for each opex line, in this case SG&A and R&D. We calculate each as a percentage of total sales and use the historic trends to help inform what the future ratio should be each quarter. Then each expense line will calculate automatically based on our ratio estimate, and our new forecasted sales. We take a similar approach with the provisions for taxes except we calculate the historic effective tax rate as a percentage of pre-tax earnings. The share count can be a bit complex since it tends to fluctuate over time based on a number of different factors. We strip out the impact of share repurchases to calculate a trend in the percentage change over time. Then we set the share price and dollar amount of repurchases to estimate the new share count. After all of these assumptions have been setup, the EPS calculation is easy: Net income divided by total shares outstanding = EPS. Apple Model: Building the Income Statement
Introduction to Financial Modeling 1-7 Section 3: GAAP & Non-GAAP Earnings Most companies use non-gaap adjustments to show what they believe to be is a more accurate representation of the company s true earning capacity. The non-gaap adjustments are relatively consistent between companies (usually adjustments for stock based compensation, amortization of intangibles, and the tax impact of these items). The adjustments are typically divided between reductions in costs of goods sold, reductions of operating expense, and adjustments directly to net income. Apple generally does not disclose non-gaap adjustments so we will use our Google (NASDAQ:GOOGL) Model to demonstrate how we treat non-gaap items. Google reports stock-based compensation broken out between cost of goods sold, Research & Development, Sales & Marketing, and General & Administrative expenses. The tax effect of these adjustments are reported as a direct adjustment to net income. You can see that we report the non-gaap Income Statement embedded in the GAAP Income Statement. The stock-based compensation adjustments sections are referenced in rows 12 and 19, and the tax impact is reflected in row 29. Although it appears that the GAAP and Non-GAAP Income Statements are mixed together, the calculations are actually separate. This allows us to have two distinct bottom-line diluted EPS estimates, one on a GAAP basis and one on a non-gaap basis. To predict the future period non-gaap adjustments, we apply a quarterly average of the total stock-based compensation as a percentage of revenue, or if the company gave specific guidance on the expectation for the next quarter we use the guidance. The breakdown of stock-based compensation to cost of goods sold, and the three opex categories is based on the previous period s percentages for each. If the company includes amortization of intangibles in their non-gaap adjustments the value tends to stay relatively consistent each quarter, so we usually set the future periods equal to the latest reported value. Google Model: Non-GAAP Adjustments
Introduction to Financial Modeling 1-8 Section 4: Model Calibration We keep our models representing a baseline type of scenario. This allows our users to easily incorporate their opinions into the model by changing the key assumptions throughout the financial statements. To maintain the baseline view, we calibrate the model to meet consensus revenue and EPS estimates prior to the quarterly earnings release. We then update the quarter s actual results the night of the release, and re-calibrate the future periods to meet management s new guidance the night of the earnings call. Management typically give a range for each guided line item, so we calibrate to the mid-point and insert a comment with the full details. After all the analysts have had a chance to update their forecasts to include the latest results, we re-calibrate our model again to meet the new consensus estimates (typically a few days after the release). Apple Model: Management s Guidance
Introduction to Financial Modeling 1-9 Section 5: Balance Sheet Modeling Our Tier 1 models use the changes in working capital to calculate the cash flow from operations, which is used in our free cash flow calculation. This will impact the discounted cash flow valuation. As a result, we tend to focus Balance Sheet forecasts on accounts receivable, inventory, and accounts payable. To do this we apply the operating ratios calculated in the section below the Balance Sheet, and make assumptions about these ratios in future periods. These ratios and the results from operations reflected in our future Income Statement, drive the future balances for these assets and liabilities. Apple Model: Building the Balance Sheet Capital expenditures (capex) is also used in the free cash flow calculation so we need to estimate the change to this line as well. We do this by adjusting the capex growth rate at the bottom of the Cash Flow Statement. The Property, Plant & Equipment (PP&E) balance on the Balance Sheet will automatically adjust based on the capex assumptions and the depreciation reflected in the Cash Flow Statement. Most of the other Balance Sheet accounts are very difficult to forecast and are not as important in our valuation approach so we set them equal to the last reported value. Section 6: Cash Flow Statement Modeling Cash Flow Statement modeling is more important for some companies and less important for others. Apple has plenty of cash, so a shortfall is less likely than for a developing company such as Telsa Motors (NASDAQ:TSLA). Tesla is ramping new production lines at an astonishing rate, and burning through substantial cash each quarter. If we take a quick look at our Tesla Model (below), we can see that simply
Introduction to Financial Modeling 1-10 changing the capex for 2016 to equal that of 2015, under our consensus-based operating scenario, will result in a cash shortfall without the issuance of additional debt or equity. Of course there are a number of operating assumptions we need to make for this analysis, such as the ratios for the cash conversion cycle inputs, and that there would be no change to the company s financing terms (or mix of leased vs purchased cars). Still this shows how valuable Cash Flow Statement Modeling can be, particularly for developing companies. Tesla Model: Cash Flow Statement Modeling Going back to our Apple model, our main reason for modeling the cash flow statement is to arrive at a free cash flow estimate to use in our DCF valuation. There are only a few calculations which are unique to our cash flow statement: 1) Depreciation & amortization, and 2) Property, Plant & Equipment (PP&E). Depreciation & amortization is calculated based on the ratio of depreciation & amortization to average property plant & equipment and acquired intangible assets (this is only an approximation since intangibles are tested for impairment over time not amortized on a straight-line basis). The capex outflow (shown in the Cash Flow Statement as Payments for acquisition of PPE ) is estimated using a capex growth rate. The remaining cash flow items represent changes in Balance Sheet accounts. Section 7: Financial Statement Links Before you begin using the earnings model you should make sure you understand how the different financial statements are linked together. Here is a list of some of the primary links: Retained earnings - GAAP net income flows through retained earnings on the Balance Sheet. Dividends are also paid out of retained earnings, and if the company does not disclose treasury shares separately in the equity section, we also subtract share repurchases from this account. The beginning retained earnings balance of $92.3B, plus net income of $18.2B, minus dividends of $2.9B, minus share repurchases of $6.0B, equals the ending retained earnings balance of $101.6B. (Refer to tick mark a below) Income Statement links to the Cash Flow Statement - GAAP net income is the starting point for the Cash Flow Statement. Depreciation and amortization expense are also added back to net income on the cash flow statement, although many companies do not isolate these items as separate lines on the Income Statement. (Refer to tick mark b below)
Introduction to Financial Modeling 1-11 Balance Sheet links to the Cash Flow Statement - All of the changes in the Balance Sheet accounts are reflected in the Cash Flow Statement. For example, accounts receivable increased by $7.3B [$24.1B minus $186.8B equals $7.3B], which is a use of cash reflected on the Cash Flow Statement. (Refer to tick mark c below) Property, Plant, & Equipment - The Balance Sheet and Cash Flow Statement are also linked by Property, Plant, & Equipment (PP&E). The beginning PP&E balance of $22.4B, plus capex outflows on the Cash Flow Statement of $3.5B, minus depreciation of $2.4B, equals the ending PP&E balance of $23.5B (see comment about amortization in Section 9 above). (Refer to tick mark d below) Cash Flow links to the Balance Sheet - The Cash Flow Statement will add all the sources and uses of cash to the beginning cash balance to get to the ending cash balance which will flow to the Balance Sheet. (Refer to tick mark e below) Apple Model: Financial Statement Links
Introduction to Financial Modeling 1-12 Section 8: How to use the Earnings Model Now that you understand how the model works you can try changing some of the inputs to see what the impact would be. Maybe change the unit growth rates or ASP, and the opex assumptions to see what it would take to beat the consensus EPS estimate. Or use it to analyze where the consensus estimates stand relative to management s guidance for the quarter, and whether or not the forecast makes sense relative to historic results. After the company reports results, you can fill in the new guidance and use the model to assess whether or not the after-hours price move makes sense. None of the cells are locked so you can change anything. Keep in mind that it is better to stick to our primary assumption cells in blue when changing the estimates to maintain the integrity of the underlying equations in the model. Up next We will continue with the Apple Inc example in Chapter 2 with the calculation of the inputs to our Discount Cash Flow valuation model.
DCF Inputs (ERP, Beta, CAPM, & WACC) 2-13 Chapter 2 DCF Inputs (ERP, Beta, CAPM, & WACC) Section 1: Calculating the Equity Risk Premium Section 2: Review of the Historic Constant Sharpe ERP Section 3: Deriving Beta Using Excel Section 4: Using Beta and the CAPM to calculate the Required Return on Equity. Section 5: Calculating the Weighted Average Cost of Capital Chapter 2 Overview Many investors struggle with the concept of linking risk metrics, particularly volatility, to stock valuation. This is due in part to the complexity of valuation techniques which incorporate volatility, relative to a simplistic market multiple approach. Adopting a Discounted Cash Flow (DCF) valuation technique is an effective way to link risk to equity valuation. In this chapter we will discuss the approach we use in our DCF models which links the change in volatility and interest rates to share value, through the Equity Risk Premium (ERP). Section 1: Calculating the Equity Risk Premium The market ERP is a measure of the total return an investor requires in excess of the risk-free rate (typically a U.S. Treasury security), to compensate for the additional risk of the investment. There is a direct relationship between the ERP and required return, which means that as an investment s risk increases, investors will expect a higher return, and conversely, as risk decreases the required return on equity will also decrease. There are many different approaches to measuring the market s Equity Risk Premium. Each method has different assumptions, pros, cons, and results. We use the Constant Sharpe approach. If you would like to follow along, our ERP calculation spreadsheet is available for download on our education page at www.gutenbergresearch.com/education. The source links are included in the file so you can update the ERP as new data is released. There are two primary steps to calculate the Constant Sharpe ERP. First is a calculation of the market s historic average Sharpe ratio, which is the average S&P500 total return, less the risk-free rate (we use the 10-year U.S. Treasury rate), divided by the standard deviation of S&P500 returns. In the chart below you can see we used data back through 1963 to calculate the excess return over the risk-free rate each year, then we took the average and divided it by the standard deviation in returns to arrive at the Constant Sharpe ratio of 0.30 for the index.
DCF Inputs (ERP, Beta, CAPM, & WACC) 2-14 Constant Sharpe Calculation The second step is the application of volatility to the Constant Sharpe. The volatility measure for the S&P500 is the Chicago Board of Trade s (CBOE) Volatility index known as the VIX. The VIX is a measure of implied short-term volatility of S&P500 options, quoted in percentage terms. As market uncertainty increases, the VIX increases, and equity valuations fall. When market uncertainty decreases, the VIX decreases, and equity valuations rise. To link the ERP to market volatility we multiply the Constant Sharpe by the VIX. Using a constant Sharpe ratio of 0.30 and the current average VIX index value for the fourth quarter (quarter-to-date, as of December 2, 2015) of 16.4%, we estimate the ERP to be 5.0%. Section 2: Review of the Historic Constant Sharpe ERP The chart below plots our Constant Sharpe-based ERP through history. Three periods stand out when the ERP increased well above the long-term average for a sustained period of time. All three were driven by events which triggered periods of greater financial uncertainty. The first spike occurred in 1998 around the time of Long-Term Capital Management s collapse. The second occurred in 2001 after the September 11 th attacks. The third occurred at the end of 2008 as a result of the U.S. recession and credit crisis. The higher discount rates during these periods resulted in lower net present values of cash flows, since the discount rate is in the denominator of the discounting equation, and lower stock valuations to reflect the heightened level of risk.
DCF Inputs (ERP, Beta, CAPM, & WACC) 2-15 ERP Trend Using the Constant Sharpe 18% 16% 14% 12% 10% 8% 6% 4% 2% LTCM Collapse 9/11 Attack '08 Recession Quarterly ERP Average ERP Source: U.S. Federal Reserve and Gutenberg estimates Section 3: Deriving Beta Using Excel The ERP from Section 2 represents the risk premium for the entire market, however for our purposes we need a risk premium for a specific stock. We use beta to make the link between the broader market and the company we are analyzing. Beta is a measure of correlation between the change in value of an individual stock, and the change in value for an index. Many financial data providers publish beta for stocks; however, if you do not have access to these sources you can derive beta by regressing the stock s returns against the S&P500 (the regression beta coefficient is equal to the stock s beta). In this section we will demonstrate this calculation using Excel and our Apple example. First download the daily price of Apple shares and the S&P500 Index value (this will be our market proxy). Then calculate the percentage change for each observation. Next you will need the Data Analysis Tool in Excel. If you have not installed it go to File, Options, Addins, Analysis ToolPak, Go to install. Now you can run the regression. Select Data Analysis on the Data tab, then select Regression. The first variable is the percentage change in Apple shares and the second variable is the percentage change in the index. Select an output range and click OK.
DCF Inputs (ERP, Beta, CAPM, & WACC) 2-16 Apple vs S&P500 Regression Input The regression Beta is the slope coefficient in the regression equation, which is 0.895 in this example. The interpretation of the result is simple: the slope represents the expected percentage change in the value of Apple shares based on the percentage change in the S&P500 index. Beta is the key to linking the ERP for the entire market back to Apple shares, which is the next step in the equation. Notice that the t-stat is very high and the P-value is very low. This indicates that the correlation between the two variables is statistically significant, and the S&P500 index is likely the correct market proxy to measure Apple against. The R Square is relatively low which also makes sense since there are many other factors which cause Apple shares to go up or down in value besides what the general market does (interpretation of the R Square: approximately 27% of the variation in Apple shares is explained by changes in the S&P500 index). For additional details on regression analysis, please refer to Chapter 5 in this series. Apple vs S&P500 Regression Output
DCF Inputs (ERP, Beta, CAPM, & WACC) 2-17 Section 4: Using Beta and the CAPM to calculate the Required Return on Equity Beta and the ERP are not direct inputs into the Weighted Average Cost of Capital (WACC) calculation, which is the discount rate we use to value shares. Instead these metrics are used to derive the required return on equity. To do this we utilize the Capital Asset Pricing Model (CAPM) which states that the required return on equity for a stock is equal to the risk-free rate, plus beta times the ERP. After inputting the beta, ERP, and risk-free rate into the CAPM equation, we can solve for the required return. We calculate the required return on equity in the DCF section of each of our Tier 1 models. In our Apple example the required return on equity is 6.5% calculated as the risk-free rate of 2.1%, plus a beta of 0.895 times the market risk premium of 4.9%. Section 5: Calculating the Weighted Average Cost of Capital Now that we have the required return on equity, we can calculate the Weighted Average Cost of Capital (WACC). This calculation is also done in the DCF section of our Tier 1 models. We simply apply the weight of equity in the company s capital structure to the cost of equity, and add the result to the weight of debt times the after tax cost of debt. The result is the final WACC which we use as the discount rate in our valuation. Rather than calculating the WACC, some analysts use a competitor s WACC, a competitor s beta in the calculation, or use a sector average WACC. You can change any of the inputs in our models, however, if you choose one of these options keep in mind that you will need to make an adjustment to account for the differences in capital structure between the companies. Up next Now that we have our WACC and cash flow estimates from Chapter 1, we can calculate a DCF-based valuation, which we will demonstration in Chapter 3.
Discounted Cash Flow Valuation 3-18 Chapter 3 Discounted Cash Flow Valuation Section 1: Our DCF Approach Section 4: Final DCF-Based Valuation Section 2: Stage-One Calculation Section 5: DCF Sensitivity Analysis Section 3: Stage-Two Calculation Section 6: Final Note on DCF Valuation Chapter 3 Overview In this chapter we will be demonstrating how to use the inputs we calculated in Chapter 2, to derive a DCF-based share valuation. Keep in mind that the DCF is much more complicated than a market multiple-based valuation, with many more required inputs and assumptions. DCF analysis is rooted in the fundamental idea that any asset s fair value is equal to the present value of the future cash flows it produces. The DCF has three primary parts: 1) Projected cash flows, 2) a future growth rate, and 3) a discount rate. Section 1: Our DCF Approach For our Tier 1 models we use a two-stage DCF approach, projecting five years of cash flows in our first stage, which represents the high-growth stage. Then we calculate a terminal value by assuming the company reaches a constant growth stage in the sixth year. We should point out that this is a rather large assumption for most companies since they will likely go through many business cycles throughout their existence, rather than reaching a flat growth rate held in perpetuity, however, once the model is established and calibrated it does give a comparable valuation over time. Also, since we add an additional year to the forecast every four quarters, the constant growth stage will be pushed out if management is able to continue to execute on growth. Section 2: Stage-One Calculation In our Tier 1 models we calculate the free cash flow at the bottom of the Cash Flow Statement as the cash from operations, less capital expenditures, plus after-tax interest expense. We then discount the free cash flow using the WACC calculated in Chapter 3. This calculation is performed for each of the five stage-one years. The sum of the five discounted cash flows is saved in the DCF section of our model. Apple Model: Stage-One DCF Calculation
Discounted Cash Flow Valuation 3-19 Section 3: Stage-Two Calculation The stage-two calculation estimates the terminal value of the company holding growth constant. The calculation looks daunting (in cell C233 of our Apple Inc model); =((((BF159*(1+C228))-(C229*BF11*(1+C227))+(C223*BF114)))/(C224-C227))/(1+$C$224)^5) However, it is actually a simple perpetuity equation. If you break the equation down, you can see that it represents the Cash Flow for the sixth year, divided by WACC, minus the constant growth rate. Since this represents the terminal value at the end of the fifth year, we discount the result back five years to present value terms. The numerator, which represents the cash flow of year six, is the complex part with the following three parts: Part 1: Cash Flow From Operations (CFO) = CFO of year 5 x (1 + constant CFO growth rate) Part 2: Minus capex = Average capex to sales ratio x [sales x (1 + constant sales growth rate)] Part 3: Plus the after-tax cost of debt = After tax cost of debt x long-term debt Section 4: Final DCF-Based Valuation Now that we have the stage-one and stage-two cash flows in present value terms, all we have to do is add them together with the adjusted net cash per share (the adjustment to cash per share is discussed in Chapter 4). The result is the final DCF-based share valuation. At this point you should be able to recognize how the different inputs impact valuation under different scenarios. As you think about the impact keep the basic equations in mind: Market ERP = Require Return on Equity for the Market Risk-Free Rate, or Constant Sharpe Volatility CAPM = Company Specific Required Return Equity = Risk-Free Rate + Beta Market Risk Premium WACC = Weight of Debt After-Tax Cost of Debt + Weight of Equity Required Return on Equity Using these equations, we can draw the following conclusions about our DCF inputs: Volatility - The higher the VIX, the greater the cost of equity. Increases in volatility will have a greater impact on companies with a greater proportion of their capital structure coming from equity rather than debt. This scenario can tilt if a large debt balance results in a high probability of default, in which case the company s credit spread would widen and the cost of debt and equity would spike. Interest Rates - An increase in market interest rates will increase the required return on equity through the CAPM, and result in lower asset values. If a company has fixed rate liabilities, higher rates will not impact the cost of debt in the WACC when rates change. If the company s debt has caps/floors or adjustable features, then changes in interest rates can have an impact on the cost of debt. Beta - A high beta coefficient will result in greater variability in the cost of equity.
Discounted Cash Flow Valuation 3-20 Section 5: DCF Sensitivity Analysis Now that you understand how the model works you can try changing some of the inputs to see what the impact would be on share price. For example, if you think the Federal Reserve will increase rates over the next year, try increasing the risk-free rate. Or if you think volatility will spike, you can change the VIX assumptions. Keep in mind we have not locked any of the cells in our models so you can change anything you want; However, we suggest sticking to the blue cells to maintain the integrity of the equations. Section 6: Final Note on DCF Valuation You may be thinking I have been using market multiples and missing the risk in my valuation all this time?! That is not necessarily the case. Market multiples are very useful tools, arguably more useful than a discounted cash flow analysis which requires many more assumptions; However, it is important to remember that if you are going to use a multiple approach, you must adjust the multiple during times of increased risk to reflect the greater required return on equity. Regardless of the valuation approach you choose, keeping the fundamental risk/return theory in mind will ultimately lead to better investment decisions. Up next In Chapter 4 we use the forecast from our earnings model to value shares using a market multiple approach.
Market Multiple Valuation 4-21 Chapter 4 Market Multiple Valuation Section 1: Which Multiple to Use Section 2: Separating Cash from the Valuation Section 3: Calculating Share Value Using the Multiple Chapter 4 Overview Most companies can be valued by applying a market multiple to forecasted earnings, however there are a few things we need to consider when deciding which multiple to use. In this chapter we will be review some of the key factors to consider when choosing a multiple, and discuss how to use the earnings forecasted in Chapter 1 to derive a market multiple-based valuation. Section 1: Which Multiple to Use When deciding which multiple to use for valuation we must consider the following factors: Industry/Sector - Each sector has a set of metrics which are widely accepted by analysts and investors including which multiples to use for valuation. For banks it is the Price to Book Value multiple, for energy companies it is the EV to EBITDA multiple, and for developed companies with relatively stable earnings it is the Price to Earnings (PE) ratio. Cyclical vs non-cyclical - If the company s industry is currently in decline, then the company could be operating at a loss. In this case the PE ratio could not be used for valuation. As an alternative it may be appropriate to use a Price to EBITDA ratio or Price to Sales ratio. Another alternative would be to forecast earnings on a normalized basis assuming a return to average market conditions at some point in the future and apply a PE ratio to this later stage in the business cycle. Lifecycle stage - Companies in the development stage have much different earnings profiles compared to those which have reached maturity. Developing companies may not be profitable or may have volatile earnings streams with high growth rates, in which case it may make more sense to apply a multiple to a later stage of earnings rather than using a Next Twelve Month (NTM) PE. For example, Netflix is currently trading at a PE multiple of 647x based on the NTM consensus EPS estimate, while Apple trades at 12x. The reason that investors are willing to pay so much more for Netflix earnings is that the company is currently in a hyper-growth stage. As a result, investors are valuing the company on the ultimate long-term earning capacity which will not be reached until many years from now; Therefore, the NTM earnings are less relevant for valuation purposes. For companies in a hyper-growth stage a growth adjustment will make the PE ratio more meaningful. Continuing with our Apple Inc (NASDAQ:AAPL) Model example, we have selected to use the PE ratio for valuation based on consensus forward earnings expectations. For most of our models we use the average NTM PE multiple. Keep in mind that this will typically result in a value which is close to the current price
Market Multiple Valuation 4-22 due to the nature of the calculation. We do this to isolate the impact of valuation changes to earnings results or other news, and to reflect the baseline scenario for our model users. Other than using a historic average multiple you may want to consider using the multiple of a competitor, a sector average, or a cyclical peak/trough multiple. The multiple is easy to change in our models which gives our users plenty of flexibility to exercise judgment in the valuation section. Section 2: Separating Cash from the Valuation After we have established which multiple to use we must decide if any of the company s assets should be removed and valued separately. For most of our models we subtract the net cash from the share valuation. It is important to note that we are using net cash after deducting debt because we do not want to give a valuation benefit to companies that rack-up large debt balances and let the cash sit on the balance sheet. If cash is generated from foreign operations the company would be subject to a repatriation tax if they chose to bring it back to the United States. Tax laws are complex; we take a simplistic approach for an approximation of the impact by applying the company s effective tax rate to the offshore portion of the cash balance. Section 3: Calculating Share Value Using the Multiple Now that we have the inputs, the calculation is straight forward: the PE multiple, times the sum of the next four quarters of diluted EPS (calculated in Chapter 1), plus adjusted net cash per share = the implied share valuation. For our Tier 1 models we apply a 50% weight to our DCF-based valuation and a 50% weight to our market multiple valuation to arrive at our implied 12-month target share price. Up next We demonstrate how to use regression analysis with leading indicators to predict earnings.
Using Regression Analysis to Predict Earnings 5-23 Chapter 5 Using Regression Analysis to Predict Earnings Section 1: Data Selection Section 4: Analyzing Output Section 2: Running the Regression Section 5: Back Testing Section 3: Model Testing Section 6: Limitations & Improvements Chapter 5 Overview Regression analysis is a mathematical process which estimates the relationship between two or more variables. As investors we must forecast our expectations for future periods. Regression models can be helpful tools when reliable data is available ahead of a company s press release. In this chapter we will demonstrate how we use regression models for earnings projections using a simple linear regression example for Boeing Co (NYSE:BA) and a multiple regression for Starbucks Corp (NASDAQ:SBUX). We will also discuss the limitations associated with using regression analysis to predict results. Section 1: Data Selection The first step is selecting the appropriate variables to use in the model. It can be difficult to find variables with strong explanatory power. Typically, we try to find data which is effective at predicting top-line revenue, since anything below the revenue line can be distorted over time due to fluctuations in profit margins. These fluctuations can impact the regression results. We start by generating a list of potential leading indicators for a company s revenue. Then we test each variable using the steps in this chapter to find the best predictors. For Boeing and Starbucks we found the U.S. Census Bureau s reports to be helpful in providing leading indicators. For Boeing we selected the Aircraft & Parts Shipments section, including defense and nondefense shipments, in the Industrial Production report, which is published on a monthly basis. The final monthly report for each calendar quarter is typically released about a week before Boeing reports quarterly results which makes it a good data point for prediction. The two variables (Boeing s Revenue and the Shipment data) appear to have a strong correlation based on the time series plot below (we will test the correlation in Section 2). In this example Boeing s revenue is what we would like to predict, so it is the dependent variable (Y variable), or the variable which depends on the results of another variable. Aircraft & Parts Shipments from the Industrial Production report is the independent variable (X variable).
2Q09 3Q09 4Q09 1Q10 2Q10 3Q10 4Q10 1Q11 2Q11 3Q11 4Q11 1Q12 2Q12 3Q12 4Q12 1Q13 2Q13 3Q13 4Q13 1Q14 2Q14 3Q14 4Q14 1Q15 2Q15 3Q15 Using Regression Analysis to Predict Earnings 5-24 Boeing Revenue vs Aircraft & Parts Shipments 20% 15% 10% 5% 0% -5% -10% -15% -20% Boeing Revenue (Qtrly chg) U.S. Aircraft & Parts Shipments (Qtrly chg) Source: U.S. Census Bureau, Company reports, and Gutenberg estimates For Starbucks we chose the Food Services & Drinking Places sales data, contained in the Advanced Retail & Food Sales report. Similar to our Boeing example, this report is also available prior to the company s release and shows a strong correlation to Starbucks revenue. In the chart below there is a clear de-coupling between the two variables in the fourth calendar quarter each year. This is because Starbucks fourth calendar quarter sales typically outperform the Food Service & Drinking Places total results. If we do not include an adjustment to account for this, our model will likely have a larger standard error. 1 We will be using a second independent variable to account for seasonality, which is a dummy 2 variable which represents the fourth calendar quarter. Starbucks Revenue vs Food Services & Drinking Places Sales 16% 11% 6% 1% -4% -9% -14% 1 1 1 0 0 0 Calendar 4Q SBUX Revenue Food services sales Source: U.S. Census Bureau, Company reports, and Gutenberg estimates. 1 Standard error refers to the standard deviation of the residuals (residuals are the differences between each observation and the model predicted value for that observation). The smaller the standard error the better the model will be at predicting results. 2 A dummy variable has a value of 0 or 1. In our example a 1 represents the fourth calendar quarter.
Using Regression Analysis to Predict Earnings 5-25 Section 2: Running the Regression Next we must run the regression models for Boeing and Starbucks. We will be using Excel for this analysis since most of our users have access to this program. If you have not installed the Excel Data Analysis addin, please refer to the instructions in Chapter 2, Section 3. Use the following steps to run the regression (starting with the Boeing Model): Step 1: From the Data tab select Data Analysis, then Regression. Select the quarterly percentage change in Boeing s revenue for the Y input range (dependent variable), and the percentage change in shipments for the X input range (independent variable). Step 2: Check the Labels box, which indicates that the Y and X ranges include the data headings. Step 3: Check the Constant is Zero box. For this regression we want to set the constant in the regression equation equal to zero. You can try running the regression with this box checked and unchecked to see which result is better. Step 4: Select the Output Range where you would like the regression results to be populated. Step 5: Click the residual details you would like to analyze (we will discuss this in Section 3). Step 6: Click OK to run the regression. Boeing Regression Model Data Input
Using Regression Analysis to Predict Earnings 5-26 We follow a similar procedure to run the Starbucks multiple regression, except the X range includes two columns of data, and we do not check the Constant is Zero box. Starbucks Regression Model Data Input Section 3: Model Testing Before we can draw any conclusions about the correlation between the variables, we must test the validity of the models. To do this we perform a series of statistical tests, including the following (starting with the Boeing Model): P-value and t-stat review - These two statistics are used to test whether or not the relationship between the variables in the regression is different from zero. If the t-stat is greater than +2.79 3 or less than -2.79, then a statistically significant relationship exists at the 99% confidence interval (also known as the 1% level of significance). In this case the model s t-stat of 12.65 is well above the critical t-value of 2.79, therefore, a statistically significant relationship exists between the variables (pure statisticians would say that we reject the notion that no relationship exists, or we reject the null hypothesis). The P-value represents the lowest level of significance the model can reach while still showing a statistically significant relationship. In this case the P-value is close to zero which means we would reach the same conclusion even at a confidence interval greater than 99%. 3 Critical t-value from a t distribution chart, 0.005 probability in each tail with 25 degrees of freedom.
Using Regression Analysis to Predict Earnings 5-27 Boeing Regression Model Output: P-Value & t-stat Breusche-Pagan test - To make sure the independent variables do not explain variation in the residuals, a situation known as heteroskedasticty, we run the Breusche-Pagan test by regressing the independent variable against the squared residuals. The resulting R-square was relatively low with a high p-value, and a t-stat between the critical-t points, therefore heteroskedasticity is not an issue with this model (correlation between shipments and the squared residuals is not statistically different from zero). Boeing Model Breusche-Pagan Results In addition to the Breusche-Pagan test we can also plot the residual with a linear trend line showing the R Square to determine if the independent variables explain variation in the residuals (this was the box we checked in Section 2, Step 5). In the Boeing example the trend line and R Square are close to zero so the residuals and independent variable are not correlated.
Residuals Using Regression Analysis to Predict Earnings 5-28 Boeing Model: Residual Plot U.S. Aircraft & Parts Shipments Residual Plot 0.060 R² = 0.000 0.040 0.020 0.000-20.00% -15.00% -10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 20.00% -0.020-0.040-0.060-0.080 U.S. Aircraft & Parts Shipments (Qtrly chg) Serial correlation test - Serial correlation is the relationship of a variable with itself over time. If serial correlation is present, past observations will influence future results. To ensure our model does not exhibit signs of serial correlation we ran the Durbin-Watson (DW) test, by calculating the DW statistic 4. Durbin- Watson statistics range in value between 0 and 4, a value near 0 indicates positive serial correlation, a value near 4 indicates negative serial correlation, a value near 2 indicates no significant serial correlation 5. The Boeing model DW statistic is near 2 which indicates that serial correlation is not likely an issue for this model. 4 To calculate the Durbin-Watson statistic first square the residuals from the regression output. Then sum the difference of the actual residuals and the residuals on a one-period lag squared. Next divide the result by the squared residuals. 5 These ranges represent approximations. For exact measures refer to a DW Significance Table.
Using Regression Analysis to Predict Earnings 5-29 Boeing Durbin-Watson Test Results The normal distribution assumption - To test that the data does not violate the assumption of a normal distribution, we calculate the skew 6 and kurtosis 7. Excel has equations for these formulas =SKEW(residuals) and =KURT(residuals). If you feel you need additional evidence, you can also run a Chisq test, and plot the residuals in a histogram to see if they appear to be normally distributed. In our Boeing model the skew (0.02, below +/-1) and kurtosis (-0.53, below 3) show that the sample is approximately normally distributed. Model stability - To test the stability of the model we removed two random observations from the sample and re-ran the regression. The new regression passed all the prior tests with a similar standard error compared to the first model. This proves that the regression model is fairly stable. Other Considerations -Text book examples for regression analysis tend to be relatively straightforward. In the real world data and external conditions will change over time which makes a regression model less powerful, and in some cases ineffective. Even if your model passes all the statistical tests it is important to think qualitatively about whether or not there is a true economic reason for the variables correlation 6 A distribution is considered to be skewed if more observations are found on one side of the mean. A perfect normal distribution would have a skew of 0. A skew of +/-1 can be considered approximately normally distributed. 7 Kurtosis is the measure of the peak of the distribution. A kurtosis of less than 3 can be considered approximately normally distributed.
Using Regression Analysis to Predict Earnings 5-30 and if the direction of the coefficients makes sense. Using our Boeing example, it stands to reason that U.S. Aircraft & Parts Shipments could have predictive power for Boeing s revenue, and the positive regression coefficient makes sense as it implies a direct relationship (when shipments increase Boeing s revenue increases). In addition, it is important to assess whether or not the population has changed over time. If there have been significant changes, for example if Boeing began selling medical devices or hamburgers, then the model could not be used (non-homogenous population through time). Another potential issue is that the Boeing Model uses U.S. Shipment data as a proxy for global revenue. Using a proxy to represent a larger population of data has problems (see limitations in section 6). In addition, if Boeing s global share of revenue shifts significantly this model may fail to provide a reliable estimate. The first five tests are relevant for the both the Boeing and Starbucks regression models; However, since the Starbucks example is a multiple regression, we have a few additional tests to run, including the following: F-stat review - This statistic is similar to the t-stat, except it is used for multiple regressions. If the F-stat is greater than or less than the critical F-values (must look up for the relevant degrees of freedom on a critical F chart), then a statistically significant relationship exists. In our Starbucks model the F-stat of 29.88 is well above the critical F-value of 2.86, therefore, a statistically significant relationship exists between the variables (pure statisticians would say that we reject the notion that no relationship exists, or we reject the null hypothesis). Significance F -The Significance F has the same interpretation as the P-value for a simple linear regression: It represents the lowest level of significance the model can reach while still showing a statistically significant relationship. In this case the Significance F value is close to zero which means we would reach the same conclusion even at a confidence interval greater than 99%. Multicolinearity - To test for multicolinearity we regress the two independent variables against each other to ensure they are not correlated. For our Starbucks regression model the resulting regression between the calendar fourth quarter dummy variable and the percentage change in U.S. Food Service and Drinking Places Sales is not statistically significant at the 95% confidence interval, therefore multicolinearity is not a significant issue. Section 4: Analyzing the Output Now that we have determine that our regression models are valid, we can analyze the results and use them to predict future period revenue, which we can include in our earnings models discussed in Chapter 1. The R Square (also known as the coefficient of determination) represents the amount of variation in the dependent variable explained by the independent variable. For our Boeing example we can conclude that 84.3% of the variation in the percentage change in Boeing s revenue is explained by the percentage change in U.S. Defense and Non-Defense Aircraft & Parts Shipments, based on the R Square in the regression output. Since we ran the Boeing regression without
Using Regression Analysis to Predict Earnings 5-31 an intercept, the regression equation is: Percentage change in Boeing Revenue = 0.883 the percentage change in U.S. Aircraft & Parts Shipments. We can now use this equation to predict Boeing s future quarterly revenue by inputting the quarterly percentage change in Aircraft & Parts Shipments, which is published before Boeing releases quarterly results. Boeing Model Output The R Square in our Starbucks Model is 0.762, which means that 76.2% of the variation in Starbucks revenue is explained by changes in U.S. Food Services & Drinking Places Sales. The Standard error gives us our predicted range of +/- 3.56%. The regression equation is: the percentage change in Starbucks revenue = -0.0156 + 0.8915 percentage change in Food Services Sales + 0.1479 4Q Dummy Variable. Plugging in the new U.S. Census data and dummy variable will result in next quarter s predicted value. Starbucks Model Output
Using Regression Analysis to Predict Earnings 5-32 Section 5: Back Testing Using the regression equation for Boeing we can back test what the model would have predicted based on the shipment data for the last three quarters. The data in the chart shows that the model predicted revenue outperformed the consensus revenue estimate in two of the last three quarters. Boeing Regression Back Testing Results The results for the Starbucks model were not as good as the Boeing model. The regression beat the consensus estimate in only one of the last four quarters. This is due in part to the fact that consensus estimates for Starbucks tend to match management's guidance, and since guidance is generally reliable, earnings surprise is usually low. The regression model would therefore be most useful when sales change sharply after management has already issued guidance. Starbucks Regression Back Testing Results Section 6: Model Limitations & Improvements As with all regression analysis, there are some limitations to our models, including the following: Sample: Regression analysis draws conclusions based on a limited sample of observations. As a result, there is always a degree of error expected. Ahead of an earnings release we quantify the expected error with a range of values, however, actual results can exceed the model s standard error, particularly if the assumptions in the model are not held constant in the actual results. Historic trends: Regression analysis assumes that historic relationships will hold constant in the future and does not consider changes such as market share, or currency rate fluctuations. The residuals from the predicted values show instances in the past where the model predicted revenue differs significantly from the actual result (in both the Boeing and Starbucks examples). Similar instances will likely occur in the future. Revisions: Economic data is often revised after it is released, which will result in impaired predictability.