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The number of units sold is not affected. Answer: 1. In a competitive industry, the pricing decisions of other firms in the industry can affect the market shares of all firms in an industry. A company that is the first to increase prices in response to increased costs will experience a greater decrease in unit sales than a company that increases prices after other firms have already done so.

A firm may decide to delay increasing prices in order to gain market share when other firms increase prices in response to increased costs. Firms that are too quick to increase prices will experience declining sales volumes, though firms that are slow to increase prices will experience declining gross margins.

Other advances in technology will result in either improved substitutes or wholly new products. The introduction of tablets created a substitute for desktop and laptop computers that did not previously exist. Some technological advances can disrupt not only markets but entire industries, as digital photography has done in the camera and film industries. As always, scenario or sensitivity analysis using a variety of scenarios encompassing new product introductions can be informative.

Technological advances have enabled bulb manufacturers to produce a new bulb that is more energy efficient, and Alpha is planning to introduce a bulb next year that uses this new technology. Hence, the forecast horizon should be considered in conjunction with the investment strategy for which the stock is being considered. Highly cyclical companies present difficulties when choosing a forecast horizon. The horizon should be long enough that the effects of the current phase of the economic cycle are not driving above-trend or below-trend earnings effects.

Normalized earnings are expected mid-cycle earnings or, alternatively, expected earnings when the current temporary effects of events or cyclicality are no longer affecting earnings. When there are recent impactful events, such as acquisitions, mergers, or restructurings, these events should be considered temporary, and the forecast horizon should be long enough that the perceived benefits of such events can be realized or not. This terminal value is usually estimated using either a relative valuation i.

When using a discounted cash flow approach to estimate the terminal value, two key inputs are a cash flow or earnings measure and an expected future growth rate. The expected earnings or cash flow should be normalized to a mid-cycle value that is not affected by temporary initiatives and events. Because the terminal value is calculated as the present value of a perpetuity, small changes in the estimated perpetual growth rate of future earnings or cash flows can have large effects on estimated terminal values and, hence, the current stock value.

Assuming that the growth in future profitability will be the same as average profitability growth in the past may not be justified. Inflection points occur due to changes in: Overall economic environment. Business cycle stage. Government regulations. Rather than repeat all of those points here, we present the steps in producing pro forma statements, leaving aside the choice of estimation method and the complexities of estimating the important financial statement items. Do not forget the usual caveats.

Use segment information and create segment forecasts when the subject company has business or geographical segments that differ from each other in important respects. Use sensitivity analysis or scenario analysis to estimate a range of possible outcomes and their probabilities when appropriate.

Steps in developing a sales-based pro forma model: 1. Estimate revenue growth and future expected revenue using market growth plus market share, trend growth rate, or growth relative to GDP growth. Estimate COGS based on a percentage of sales, or on a more detailed method based on business strategy or competitive environment.

Estimate financing costs using interest rates, debt levels, and the effects of any large anticipated increases or decreases in capital expenditures or anticipated changes in financial structure. Estimate income tax expense and cash taxes using historical effective rates and trends, segment information for different tax jurisdictions, and anticipated growth in high- and low-tax segments.

Estimate cash taxes, taking into account changes in deferred tax items. Model the balance sheet based on items that flow from the income statement [working capital accounts i. Use the completed pro forma income statement and balance sheet to construct a pro forma cash flow statement.

Clearly, estimation methods can be simple as when we modeled COGS as a constant percentage of sales or more complex as when we forecast the prices of significant productive inputs based on the competitive environment of input markets. An analyst must always decide when additional or more complex analysis is warranted and when additional complexity in the estimation method provides real benefits in terms of improved forecasts and value estimates.

Jane Larsted, CFA, works as an equity analyst for Rivington Capital where she heads up a team of three analysts covering the retail sector. Larsted is currently reviewing forecasts made by her team for two home improvement retailers in the United States. The first company, Retail, Inc. The second, Midsize, Inc. Financial results for the most recent three years for Retail, Inc. Larsted believes in allowing her team to reach a group conclusion, and she always starts by letting each member of the team choose their own method of forecasting.

The results are then discussed in a team meeting where the team arrives at a common approach. Larsted asked the team to state the assumptions used to forecast revenues. The responses are shown in Exhibit 1. Retail, Inc. My model assumes that Retail, Inc. This is a realistic assumption given the number of new Retail, Inc.

Retail Inc. I expect this growth rate to decline linearly over the next five years until it is equal to the long-term U. GDP growth rate. Revenue Cost of goods sold Selling, general, administrative Operating income Larsted is concerned that the U. She has asked her team to prepare for the meeting by analyzing potential effects of a change in tax rules.

Larsted provides selected information for Retail, Inc. Exhibit 3: Tax Rate for Retail, Inc. Larsted has asked the team to assume the following: 1. This would be repeated each year in the future. Larsted also intends to forecast the amount of debt that would be shown on Retail, Inc. For this task, she makes the assumptions shown in Exhibit 4. There will be no share repurchases. The company expects to see no gains or losses in other comprehensive income for the next three years.

Myers and Conway are using a top-down approach, while Dominguez is using a bottom-up approach. Conway is using a top-down approach, and Myers is using a bottom-up approach. No member of the team is using a strictly bottom-up approach. Using the financial results for shown in Exhibit 2, it would be most appropriate for Larsted to conclude that economies of scale for firms in the home improvements retail sector: A. Under the assumptions given in Exhibit 4, Retail, Inc.

Which of the following statements regarding return on invested capital is most accurate? A company will gain a competitive advantage if it maintains high levels of invested capital by investing in intangible assets. The ownership of a patent on a successful product will often lead to high and persistent levels of return on invested capital. High and persistent levels of return on invested capital are usually an indication that a company has a high percentage of very new assets on its balance sheet.

Use the following information to answer Questions 7 through Stanza is reviewing the ENK annual report that has just been released. The product recall involved an inflatable swimming pool that ENK manufactures and sells for children 4 years and over. Unfortunately, a number of ENK customers have recently reported that an electrical problem in the pump caused injury to their children. Stanza wants to build this possibility into his five forces competitive analysis model by adding government involvement as a sixth force.

There has been a growing trend for customers to prefer traditional hand-crafted toys made and sold by independent retailers. Inputs into the vast majority of products are widely available. Suppliers of game consoles are also reliant on ENK to distribute their product. ENK sells directly to consumers who represent a highly fragmented group.

ENK has established a large distribution network, and the large costs of replicating such a network means the barriers to entry are high. Another significant concern is the near term threat of increased inflation. Although ENK has an exclusive agreement with the maker of the new console, the XTF , Stanza is concerned that the sale of the new console will reduce sales of other consoles that ENK currently sells. Sales of existing consoles to ALFs will remain static.

The new console is being billed as a game changer, coming in at a price point not much higher than existing consoles but with significantly more features. Hoombert is convinced that the introduction of the XTF to the market represents an inflection point in the home console industry. As a result, he is not using his usual approach of using historic price multiples to predict the terminal value of companies in the sector. Hoombert states that he has seen three factors in recent times that have led to inflection points: 1.

The addition of internet capabilities to consoles is causing a rapid shift away from PC gaming. Increased competition in the sector has led to a gradual reduction in the price of gaming consoles. Stanza is most likely wrong regarding the threat to profitability resulting from: A.

Which of the following statements regarding the inflation scenarios in Exhibit 2 is most accurate? Scenario 1 would lead to an increase in gross profit but a decrease in gross margin. Both scenarios would lead to an unchanged gross margin. Only scenario 2 would leave gross profit unchanged. Using the information in Exhibit 3 and 4, total estimated revenue from consoles next year should be closest to: A.

Regarding the choice of forecast horizon for a discounted cash flow model, which of the following statements is least accurate? The forecast horizon: A. Which of the three reasons suggested by Hoombert is least likely to be the cause of an inflection point? Reason 1. Reason 2. Reason 3. Which of the following statements about building a model using pro forma financial statements is least accurate? The cash flow forecast can be automatically generated using the forecasted balance sheet and income statement.

Depreciation is typically forecasted as a decreasing percentage of sales to reflect the ageing assets. Working capital is often forecasted as a constant percentage of sales. Forecast revenue then equals the forecasted market size multiplied by the forecasted market share. Expectations of changes in input prices can be used to improve COGS estimates. The primary determinants of gross interest expense are the amount of debt outstanding gross debt and interest rates.

Net debt is gross debt minus cash, cash equivalents, and shortterm securities. Net interest expense is gross interest expense minus interest income on cash and short-term debt securities owned. The expected effective tax rate times the forecasted pretax income provides a forecast of income tax expense.

Any expected change in the future effective tax rate should be included in the analysis. Working capital items can be forecast based on turnover ratios. In a simple case, items such as inventory, receivables, and payables will all increase proportionately to revenues. Historical depreciation should be increased by the inflation rate when estimating capital expenditure for maintenance because replacement costs can be expected to increase.

Firms with ROIC consistently higher than those of peer companies are likely exploiting some competitive advantage in the production and sale of their products. If suppliers are few, these suppliers may be able to extract a larger portion of any increase in profits. Vertically integrated companies are likely to be less affected by increasing input costs. For highly cyclical companies, the forecast horizon should include the middle of a cycle so that the analyst can forecast normalized earnings i.

When there have been recent impactful events, such as acquisitions, mergers, or restructurings, these events should be considered temporary, and the forecast horizon should be long enough that the perceived benefits of such events can be realized. An analyst will typically estimate a terminal value for a stock at the end of the forecast horizon, using either a price multiple or a discounted cash flow approach.

Because the terminal value using the discounted cash flow approach is calculated as the present value of a perpetuity, small changes in the estimated perpetual growth rate of future profits or cash flows can have large effects on the estimates of the terminal value and thus the current stock value. Estimate revenue growth and future expected revenue. Estimate COGS. Estimate financing costs.

Estimate income tax expense and cash taxes, taking into account changes in deferred tax items. Model the balance sheet based on items that flow from the income statement and estimates for important working capital accounts. Conway is using a market growth and market share approach, which is also top-down. Given that Retail, Inc.

High levels of capital invested will not necessarily result in higher returns. A high level of new assets will increase invested capital but may not generate returns in the short term and, hence, may actually decrease ROIC. Revenue Cost of goods sold Gross profit Gross margin Module Dividend discount models use forecasted dividends as the estimate of cash flow to the shareholder. This material has several important topics that will require careful study.

You should be able to choose the appropriate model for the firm to be valued based on the pattern of expected dividend growth , forecast the future dividends to be discounted, and determine the appropriate discount rate to apply. Dividend discount models DDMs define cash flow as the dividends to be received by the shareholders. The primary advantage of using dividends as the definition of cash flow is that it is theoretically justified.

Even if the investor sells the stock at any time prior to the liquidation of the company, before all the dividends are paid, he will receive from the buyer of the shares the present value of the expected future dividends. An additional advantage of dividends as a measure of cash flow is that dividends are less volatile than other measures earnings or free cash flow , and therefore the value estimates derived from dividend discount models are less volatile and reflect the long-term earning potential of the company.

It is possible to estimate expected future dividends by forecasting the point in the future when the firm is expected to begin paying dividends. The problem with this approach in practice is the uncertainty associated with forecasting the fundamental variables that influence stock price earnings, dividend payout rate, growth rate, and required return so far into the future.

A second disadvantage of measuring cash flow with dividends is that it takes the perspective of an investor who owns a minority stake in the firm and cannot control the dividend policy. Dividends are appropriate as a measure of cash flow in the following cases: The company has a history of dividend payments.

The dividend policy is clear and related to the earnings of the firm. The perspective is that of a minority shareholder. Firms in the mature stage of the industry life cycle are most likely to meet the first two criteria. Free cash flow. Free cash flow to equity FCFE is the cash available to stockholders after funding capital requirements and expenses associated with debt financing. One advantage of free cash flow models is that they can be applied to many firms, regardless of dividend policies or capital structures.

Free cash flow is also useful to minority shareholders because the firm may be acquired for a market price equal to the value to the controlling party. However, there are cases in which the application of a free cash flow model may be very difficult. Firms that have significant capital requirements may have negative free cash flow for many years into the future. This can be caused by a technological revolution in an industry that requires greater investment to remain competitive or by rapid expansion into untapped markets.

This negative free cash flow complicates the cash flow forecast and makes the estimates less reliable. Free cash flow models are most appropriate: For firms that do not have a dividend payment history or have a dividend payment history that is not clearly and appropriately related to earnings. For firms with free cash flow that corresponds with their profitability.

When the valuation perspective is that of a controlling shareholder. Residual income. The theoretical basis for this approach is that the required return is the opportunity cost to the suppliers of capital, and the residual income is the amount that the firm is able to generate in excess of this return. The residual income approach can be applied to firms with negative free cash flow and to dividend- and non-dividend-paying firms. Management discretion in establishing accruals for both income and expense may obscure the true results for a period.

The residual income approach is most appropriate for: Firms that do not have dividend histories. Firms that have negative free cash flow for the foreseeable future usually due to capital demands. Firms with transparent financial reporting and high quality earnings. Calculate the value of the shares today, and determine whether BuyBest is overvalued, undervalued, or properly valued.

Calculate the current value of Machines Unlimited shares. We can use one of several growth models, including the: Gordon constant growth model. Two-stage growth model. Three-stage growth model. With the appropriate model, we can forecast dividends up to the end of the investment horizon where we no longer have confidence in the forecasts and then forecast a terminal value based on some other method, such as a multiple of book value or earnings. Choosing the appropriate growth model is essential to accurate forecasts.

Restoration Software is a growth stock that has never paid a dividend. Restoration has always received an unqualified opinion from its auditors and is generally considered to have high-quality earnings. Which of the following models is most appropriate to value Restoration? Free cash flow to the firm model. Free cash flow to equity model. Residual income model. Dividends grow indefinitely at a constant rate, g which may be less than zero.

The growth rate, g, is less than the required return, r. It is unrealistic to assume that any firm can continue to grow indefinitely at a rate higher than the long-term growth rate in real gross domestic product GDP plus the long-term inflation rate. In practice, we can typically observe the price and current dividend for a publicly traded stock.

Consequently, we are usually interested in either backing out the implied required return, using an assumed growth rate, or the implied growth rate, using an assumed required return. In this example, we calculate the implied growth rate using an estimated return. If the required return on Aurora is 8. The present value of its future investment opportunities PVGO. A substantial portion of the value of growth companies is in their PVGO. In contrast, companies in slow-growth industries e.

Suppose that the shares are properly priced, so price is equal to fundamental value. Dividends are expected to grow at 3. Under this assumption the growth rate would be zero, and the current value of the firm would be equal to the current dividend divided by the required rate of return. This is exactly the same approach used to determine the value of fixed-rate perpetual preferred shares.

Answer: Dividends are not growing because the preferred dividend is based on a fixed rate of 6. The model: Is applicable to stable, mature, dividend-paying firms. Is appropriate for valuing market indices. Is easily communicated and explained because of its straightforward approach. Can be used to determine price-implied growth rates, required rates of return, and value of growth opportunities. Can be used to supplement other, more complex valuation methods. There are also some characteristics that limit the applications of the GGM: Valuations are very sensitive to estimates of growth rates and required rates of return, both of which are difficult to estimate with precision.

The model cannot be easily applied to non-dividend-paying stocks. Unpredictable growth patterns of some firms would make using the model difficult and the resulting valuations unreliable. Next we discuss multistage growth models, which accommodate more realistic growth rate assumptions.

JCI Incorporated pays an annual dividend of 5. The company is expected to continue paying this dividend with no future growth in dividends. The implied required return for MCD is closest to: A. CFCRegs, Inc. The growth rate implied by the Gordon growth model is closest to: A. Video Discs Forever, Inc. For example, many companies experience growth rates in excess of the required rate of return for short periods of time as a result of a competitive advantage they have developed.

We need more realistic multistage growth models to estimate value for companies with several stages of future growth. Over the long term, growth rates tend to revert to a long-run rate approximately equal to the long-term growth rate in real gross domestic product GDP plus the long-term inflation rate. For instance, a firm with a supernormal growth rate is probably more risky should have a higher required return than a stable, mature firm with a slower growth rate.

In most cases on the exam, however, a single required return is applied to all of the stages. Two-Stage DDM: The most basic multistage model is a two-stage DDM in which we assume the company grows at a high rate for a relatively short period of time the first stage and then reverts to a long-run perpetual growth rate the second stage. An example in which the two-stage model would apply is a situation in which a company has a patent that will expire.

Figure The H-model utilizes a more realistic assumption: the growth rate starts out high and then declines linearly over the high-growth stage until it reaches the long-run average growth rate. A three-stage model is a slightly more complex refinement of a two-stage model. Alternatively, in stage 2, the growth rate may also linearly decay to the stage 3 stable, long-run growth rate.

Spreadsheet modeling is applicable to firms about which you have a great deal of information and can project different growth rates for differing periods, such as construction firms and defense contractors with many long-term contracts. A transition phase, in which earnings and dividends are still increasing but at a slower rate as competitive forces reduce profit opportunities and the need for reinvestment. A mature phase, in which earnings grow at a stable but slower rate, and payout ratios are stabilizing as reinvestment matches depreciation and asset maintenance requirements.

The level and pattern of specific fundamental variables during the three phases, as well as the appropriate valuation model to apply in each phase, are shown in Figure Mature firms may develop technology that forms the basis for a whole new product and market. The point is that a multistage model is required in order to value many firms.

Fortunately, the GGM is easily adaptable to multistage growth. There are two ways to do this: using the Gordon growth model and using the market multiple approach. The most common method on the exam is to estimate the terminal value with the Gordon growth model. In other words, at some point in the future, we assume dividends will begin to grow at a constant, long-term rate. Then the terminal value at that point is just the value derived from the Gordon growth model.

Many analysts also use market price multiples to estimate the terminal value rather than use the GGM method of discounting dividends. Calculate the current value per share. However, because we are human beings and not If we were robots instead of humans, this would be fine. However, because we are human beings and not mindless machines , it might be better to actually try to understand what we are doing, limit the need to remember yet another formula, and reduce the possibility of error.

This can be accomplished by drawing a time line and placing the appropriate cash flows on the line, followed by the fairly straightforward computation on our financial calculators that we did earlier in the multiperiod DDM. The forecasted dividends are shown in the following figure. The cash flows that we need to solve the problem are shown in the following figure.

After a bit of practice, you should find that the calculator method is easier than the complicated formula, and, just as importantly, it will be less prone to error. Therefore, the value of the firm is just the present value of the terminal value computed at the point in time at which dividends are projected to start. Calculate the value of Arena shares today. Answer: First forecast the earnings in Year 5. Applying the Gordon growth model to the Year 5 dividend gives us an estimate of the terminal value in Year 4.

The terminal value discounted back four years is the current value of the stock. The H-model approximates the value of a firm assuming that an initially high rate of growth declines linearly over a specified period. The second term is an approximation of the additional value that results from the high-growth period.

Calculate the current value of Omega. Valuation Using the Three-Stage DDM A three-stage model can be used to estimate the value of a firm that is projected to have three stages of growth with a fixed rate of growth for each stage. The approach is the same as the two-stage model, with the projected dividends and the terminal value of the shares discounted to their present value at the required rate of return.

Again, a time line or an equivalent cash flow table will help the intuition. Your speed and accuracy will develop with practice. This question is tedious, but it is not a question to be feared, as long as your calculator batteries hold up. EXAMPLE: Three-stage growth model with linear growth decline in stage 2 As an analyst, you have gathered the following information on a company you are tracking.

Calculate the value of the company. Valuation Models Using Spreadsheets If you have been calculating along with the examples, you already recognize that the use of these models can be computationally intensive, though the formulas are straightforward. These characteristics make DDM models ideally suited to being solved with spreadsheet software.

A spreadsheet allows the analyst to easily calculate values based on models with many stages, growth rates, and required rates of return. The models are just as useful in determining the required rate of return, given the current value and dividends of a stock. Here is an example of how to approach the problem using the two-stage DDM. The only higher value from the multiple choices is The reason for this is the inherent flexibility and computational accuracy of spreadsheet modeling.

When changes in dividends can be predicted, there can obviously be more than two or three stages of change involved. Moreover, there are often idiosyncratic events that, even if they can be predicted, do not fit neatly into any of the patterns required by these models.

Using a spreadsheet is relatively straightforward and can accommodate nearly any pattern that the analyst can imagine. Step 1: Establish the base level of cash flows or dividends. In the case of dividends, this would ordinarily be either the amount paid over the preceding year or some normalized level based upon projected firm earnings. Because the spreadsheet can be programmed in a virtually infinite series of combinations, any dividend pattern desired can be achieved.

Step 3: Because an equity security has an infinite life, the analyst needs to estimate what normalized level of growth will occur at the end of the supernormal growth period. This allows for an estimate of a terminal value, representing the cash flow i. The last step is where the use of the spreadsheet really pays off. The analyst is in position to conduct detailed scenario analyses wherein the model inputs can be altered to see how changes in the pattern of future dividends, interest rates, and firm risk affect firm valuation estimates.

The bottom line is that performing the analysis just listed for a period of 10 or 20 years is relatively easy with a spreadsheet but would be all but impossible with any of the stylized models presented. Calculate its SGR. If the actual growth rate is forecasted to be greater than SGR, the firm will have to issue equity unless the firm increases its retention ratio, profit margin, total asset turnover, or leverage.

However, it is often done with average equity as an approximation. On the exam, use whichever method is specified in the question. Make sure you know how to calculate ROE and SGR given a balance sheet and an income statement, as in the following example.

All values are in millions of USD. Similarly, if the market price is lower than the model price, the stock is considered to be undervalued, and if the model price is equal to the market price, the stock is considered to be fairly valued. Phase A. Transition B. Transition C. Growth Model Gordon growth Multistage Gordon growth 2. The implied required return based on the analyst forecast is closest to: A. Use the following information to answer Questions 3 through 7. Johnson compiled analyst information for the two companies in Table 1.

The sustainable growth rates for each firm are closest to: AAA A. Johnson decides to start by estimating the value of the two stocks using the constant growth dividend discount model and estimating the required rate of returns using the capital asset pricing model CAPM. Both firms are expected to grow at their sustainable growth rates. The estimated values are closest to: AAA A.

After further consideration, Johnson feels the growth rates of AAA and TST are more likely to gradually decline over the next four years and therefore considers the H-model. Use the following information to answer Questions 10 and The current estimated value of Lisa Design using the H-model is closest to: A.

The current estimated value of Lisa Design is closest to: A. Jill Smart is an analyst with Allenton Partners. Jill is reviewing the valuation of three companies P, Q, and R using the dividend discount model DDM and their corresponding current market prices. P is overvalued, Q is undervalued, and R is fairly valued. P is undervalued, Q is fairly valued, and R is overvalued.

P is undervalued, Q is overvalued, and R is fairly valued. Return on equity is 8. The present value of growth opportunities and the value of the stock based on the Gordon growth model are closest to: PVGO A. Dividends are appropriate when: The company has a history of dividend payments. The asset is being valued from the position of a minority shareholder.

Free cash flow is appropriate when: The company does not have a dividend payment history or has a dividend payment history that is not related to earnings. The asset is being valued from the position of a controlling shareholder. Residual income is most appropriate for firms that: Do not have dividend payment histories. Have negative free cash flow for the foreseeable future. Have transparent financial reporting and high-quality earnings.

No matter what the holding period, the stock price is the present value of the forecasted dividends plus the present value of the estimated terminal value, discounted at the required return. Dividend policy is related to earnings. Required rate of return r is greater than the long-term constant growth rate g. Can be applied to indices very easily.

Easily communicated and explained because of its straightforward approach. Useful in determining price-implied growth rates, required rates of return, and value of growth opportunities. Can be added to other more complex valuations. There are also some characteristics that limit the applications of the Gordon model: Valuations are very sensitive to estimates of growth rates and required rates of return, both of which are difficult to estimate with precision. Unpredictable growth patterns of some firms would make using the model difficult.

Strengths: Multiple-stage DDMs are flexible. The models can be used to estimate values given assumptions of growth and required return or to derive required returns and projected growth rates implied by market prices. The models enable the analyst to review all of the assumptions built into the models and to consider the impact of different assumptions.

The models are very easily constructed and computed with the use of spreadsheet software. Limitations: The estimates are only as good as the assumptions and projections used as inputs. A model must be fully understood in order for the analyst to arrive at accurate estimates.

Without a clear understanding of the model, the effects of assumptions cannot be determined. The estimates of value are very sensitive to the assumptions of growth and required return. Formulas and data input can lead to errors that are difficult to identify. The terminal value for multistage models is estimated using the Gordon growth model or market price multiples. The two-stage model has two distinct stages with a stable rate of growth during each stage. The spreadsheet model can incorporate any number of stages with specified rates of growth for each stage.

This is most easily modeled with a computer spreadsheet. A transition stage, in which earnings and dividends are still increasing but at a slower rate as competitive forces reduce profit opportunities and the need for reinvestment. A mature stage, in which earnings grow at a stable but slower rate, and payout ratios are stabilizing as reinvestment matches depreciation and asset maintenance requirements.

The Gordon growth model assumes that in the future, dividends will begin to grow at a constant, long-term rate. Steps include: Establish the base level of cash flows or dividends. Estimate what normalized level of growth will occur at the end of the supernormal growth period, allowing for an estimate of a terminal value.

Discount and sum all projected dividends and the terminal value back to today. Use beginning-of-period balance sheet values unless otherwise instructed. Start by finding the value of the dividends during the high-growth period of five years. Multistage models are most appropriate for firms in the transition phase.

Start by finding the value of the dividends during the high growth period of five years. Assets-to-equity for the industry is calculated as: 0. This approach values the dividend growth at the long-term rate and adds an estimate for the additional value of the supernormal growth during the first stage. Stock Q has model price lower than the market price and hence is overvalued. Stock R has model price equal to the market price and hence is fairly valued. That means it is destroying value!

Make sure you see the parallels between the free cash flow framework and the discounted dividend framework i. This is a very important test topic, as many analysts prefer free cash flow models to dividend discount models. Forget about all the complicated financial statement relationships for a minute and simply picture the firm as a cash processor.

Cash flows into the firm in the form of revenue as it sells its product, and cash flows out as it pays its cash operating expenses e. What does the firm do with its FCFF? First, it takes care of its bondholders because common shareholders are paid after all creditors.

So it makes interest payments to bondholders and borrows more money from them or pays some of it back. However, making interest payments to bondholders has one advantage for common shareholders: it reduces the tax bill. However, the board of directors still has discretion over what to do with that money. It could pay it all out in dividends to its common shareholders, but it might decide to only pay out some of it and put the rest in the bank to save for next year.

So FCFE is the cash available to common shareholders after funding capital requirements, working capital needs, and debt financing requirements. That way if, for example, you happen to forget the FCFE formula on exam day, you still have a chance to reconstruct it by thinking through what FCFE really is. On the other hand, think of FCFE as cash that could be given to shareholders, if management wanted to. Net borrowing increases FCFE. The key to this question on the exam is knowing which cash flows to discount at which rate to estimate which value.

The formula is presented later in this topic review. Significant nonoperating assets, such as excess cash not total cash on the balance sheet , excess marketable securities, or land held for investment should be added to this estimate to calculate total firm value. However, this is an extremely important concept, so memorize it now. The differences between FCFF and FCFE account for differences in capital structure and consequently reflect the perspectives of different capital suppliers.

We can always estimate equity value indirectly by discounting FCFF to find firm value and then subtracting out the market value of debt to arrive at equity value. If investors are willing to pay a premium for control of the firm, there may be a difference between the values of the same firm derived using the two models. Analysts often prefer to use free cash flow rather than dividend-based valuation for the following reasons: Many firms pay no, or low, cash dividends.

Dividends are paid at the discretion of the board of directors. If a company is viewed as an acquisition target, free cash flow is a more appropriate measure because the new owners will have discretion over its distribution control perspective. Free cash flows may be more related to long-run profitability of the firm as compared to dividends.

Chamber Group is analyzing the potential takeover of Outmenu, Inc. Chamber has gathered the following data on Outmenu. All figures are in millions of dollars. The weighted average cost of capital should be substituted for the required return on equity. Calculating FCFF from net income. Noncash charges. The most significant noncash charge is usually depreciation. Here are some other examples of noncash charges that often appear on the cash flow statement: Amortization of intangibles should be added back to net income, much like depreciation.

Provisions for restructuring charges and other noncash losses should be added back to net income. However, if the firm is accruing these costs to cover future cash outflows, then the forecast of future free cash flow should be reduced accordingly. Gains or losses on sale of long-term assets are also removed they would be accounted for under fixed capital investment. Income from restructuring charge reversals and other noncash gains should be subtracted from net income.

For a bond issuer, the amortization of a bond discount should be added back to net income, and the accretion of the bond premium should be subtracted from net income to calculate FCFF. Deferred taxes, which result from differences in the timing of reporting income and expenses for accounting versus tax purposes, must be carefully analyzed. Over time, differences between book and taxable income should offset each other and have no significant effect on overall cash flows.

If, however, the analyst expects deferred tax liabilities to continue to increase i. Increases in deferred tax assets that are not expected to reverse should be subtracted from net income. Fixed capital investment. Investments in fixed capital do not appear on the income statement, but they do represent cash leaving the firm. That means we have to subtract them from net income to estimate FCFF. If there is a loss on sale of assets, add that instead of deducting it.

The long-term assets sold were fully depreciated. The investment in net working capital is equal to the change in working capital, excluding cash, cash equivalents, notes payable, and the current portion of long-term debt. The Anderson Door Co. The gain was classified as unusual. Free cash flow to equity is closest to: A. Suppose an analyst uses the statement of cash flows to calculate free cash flow to the firm FCFF as cash flow from operations less fixed capital investment, and free cash flow to equity FCFE as FCFF calculated as before plus net borrowing.

The firm has short- and long-term debt on its balance sheet. FCFF A. Overstated B. Understated C. Interest expense. Interest was expensed on the income statement, but it represents a financing cash flow to bondholders that is available to the firm before it makes any payments to its capital suppliers.

Therefore, we have to add it back. The net effect on free cash flow is an increase in the after-tax interest cost of 70 cents. However, we can use the statement of cash flows as it is required to be reported under U. GAAP as a framework to provide some intuition concerning the free cash flow formulas and perhaps make it a little easier to remember these formulas.

Free cash flow to the firm is the operating cash flow left after the firm makes working capital and fixed capital investment. Therefore, we can get close to the actual calculation by using the first column in Figure By doing that, we go from our almost definition to the actual formula for FCFF as shown in the second column in Figure We also make the same adjustments as we did before by subtracting out fixed capital and working capital investment.

Even though depreciation is a noncash expense, the firm reduces its tax bill by expensing it, so the free cash flow available is increased by the taxes saved. We have to add back to CFO the after-tax interest expense to get to FCFF because interest expense and the resulting tax shield was reflected on the income statement to arrive at net income. We also have to subtract out fixed capital investment since CFO only includes changes in working capital investment.

I suggest that, at a minimum, you memorize the first one that starts with net income and the last one that starts with cash flow from operations. That way, given either an income statement or a cash flow statement, you can calculate FCFF. Calculating FCFE from net income. We can also calculate FCFE from net income by making some of the usual adjustments.

Finally, we can calculate FCFE from CFO by subtracting out fixed capital investment which reduces cash available to shareholders and adding back net borrowing which increases the cash available to shareholders. The use of preferred stock requires the analyst to revise the FCFF and FCFE formulas to reflect the payment of preferred dividends and any issuance or repurchase of such shares.

Remember to treat preferred stock just like debt, except preferred dividends are not tax deductible. Specifically, any preferred dividends should be added back to the FCFF, just as after-tax interest charges are in the net income approach to generating FCFF. This approach assumes that net income is net income to common shareholders after preferred dividends have been subtracted out. The WACC should also be revised to reflect the percent of total capital raised by preferred stock and the cost of that capital source.

The only adjustment to FCFE would be to modify net borrowing to reflect new debt borrowing and net issuances by the amount of the preferred stock. Keep in mind that relatively few firms issue preferred stock. Use the following information to answer Questions 1 through 3.

He also expects Roth to be profitable for the foreseeable future, so he does not expect the deferred tax liability to reverse. Both items were treated correctly. One item was treated correctly and the other incorrectly. Neither item was treated correctly. He has a 20X6 income statement and balance sheet, as well as 20X7 income statement, balance sheet, and cash flow from operations forecasts as shown in the following tables.

Assume there will be no sales of long-term assets in 20X7. The adjustments to cash flow from operations necessary to obtain free cash flow to the firm FCFF are: A. The first method is to calculate historical free cash flow and apply a growth rate under the assumptions that growth will be constant and fundamental factors will be maintained.

This is the same method we used for dividend discount models. The second method is to forecast the underlying components of free cash flow and calculate each year separately. This is a more realistic, more flexible, and more complicated method because we can assume that each component of free cash flow is growing at a different rate over some short-term horizon. This often ties sales forecasts to future capital expenditures, depreciation expenses, and changes in working capital. Importantly, capital expenditures have two dimensions: outlays that are needed to maintain existing capacity and marginal outlays that are needed to support growth.

Thus, the first type of outlay is related to the current level of sales, and the second type depends on the predicted sales growth. In forecasting FCFE with the second method, it is common to assume that the firm maintains a target debt-to-asset ratio for net new investment in fixed capital and working capital.

Thus, net borrowing may be expressed without having to specifically forecast underlying debt issuance or repayment. The reason is very straightforward. Changes in leverage will have a small effect on FCFE. For example, a decrease in leverage through a repayment of debt will decrease FCFE in the current year and increase forecasted FCFE in future years as interest expense is reduced.

The single-stage FCFF model is useful for stable firms in mature industries. Therefore, analysts usually use target capital structure weights rather than actual weights. On the exam, use target weights if they are given in the problem; otherwise use actual market-value weights. The single-stage FCFE model is often used in international valuation, especially for companies in countries with high inflationary expectations when estimation of nominal growth rates and required returns is difficult.

In those cases, real i. This is where things get a little complicated. If we analyze every possible permutation of multistage free cash flow models that might appear on the exam, you would be overwhelmed. There are at least three important ways that these models can differ. Two-stage versus three-stage models: We can model the future growth pattern in two stages or three. There are several variations of each approach depending on how we model growth within the stages.

There are even variations of this approach in which we start with earnings per share instead of sales. Model Assumptions and Firm Characteristics The assumptions for the two- and three-stage free cash flow models are simply the assumptions we make about the projected pattern of growth in free cash flow. We would use a two-stage model for a firm with two stages of growth: a short-term supernormal growth phase and a long-term stable growth phase.

For example, a firm with a valuable patent that expires in seven years might experience a high growth rate for seven years and then immediately drop to a long-term, lower growth rate beginning in the eighth year. We would use a three-stage model for a firm that we expect to have three distinct stages of growth e.

For now, concentrate on the differences in the assumptions: FCFF versus FCFE, growth pattern in the first stage, and forecasting total free cash flow versus forecasting its components. Given a starting value for sales, we have all we need to forecast FCFE for the first four years. Remember that we also need a terminal value at the end of the first growth stage for each of these examples. The most common method for estimating terminal value is to apply a singlestage free cash flow model at the point in time when growth settles down to its long-run level.

This is the same method we used in the last topic review with dividend discount models. Examples of Three-Stage Models Three-stage models have all the complications of the two-stage models, with an additional growth stage to consider.

Calculate the value of the firm and the value per share of the equity. The target debt-to-equity ratio is 0. There is nothing inconsistent in this example. WACC is usually calculated using target capital weights. The expected growth rate of FCFE is 4. Calculate the value of Ridgeway stock. In the second example we were given FCFE per share, so we could calculate value per share directly.

Read the questions on the exam carefully to make sure you use the correct approach given the information in the problem. Working capital investment equals 7. It is uncommon for growth rates to drop as drastically and quickly from stage 1 to stage 2 as shown in the previous example.

It is more likely to find a gradual decline in the growth rate as a company matures and attracts more competition that will decrease its profit margin and its sustainable growth rate. This next two-stage example is an FCFE model with declining growth rates in stage 1 and constant growth in stage 2. Working capital requirements are 7.

The firm has 1 million shares of common stock outstanding. Answer: Recognize that the target debt-to-asset ratio DR is 0. Growth in the first and third stage is constant, while growth in the second stage is declining. There is one tricky feature to this problem—the required return in each of the three growth stages is different. Its most recent FCFE is 0. Second, due to the changing discount rates, our financial calculator was not as helpful as it was in other multiple cash flow calculations.

It simply cannot handle the changing discount rates in one easy set of calculations. Some variables have a greater impact on valuation results than others. The importance of various forecasting errors can be assessed through comprehensive sensitivity analysis. A representative base year must be chosen, or all of the subsequent analysis and valuation will be flawed.

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