FCF Other Aspects
What you'll learn
- LOS 19.eDescribe approaches for forecasting FCFF and FCFE.
- LOS 19.fExplain how dividends, share repurchases, share issues, and changes in leverage may affect future FCFF and FCFE.
- LOS 19.gCompare the FCFE model and dividend discount models.
- LOS 19.hEvaluate the use of net income and EBITDA as proxies for cash flow in valuation.
- LOS 19.iExplain the use of sensitivity analysis in FCFF and FCFE valuations.
- LOS 19.jExplain the single stage (stable growth), two stage, and three stage FCFF and FCFE models and justify the selection of the appropriate model given a company’s characteristics.
- LOS 19.kEstimate a company’s value using the appropriate free cash flow model(s).
- LOS 19.lDescribe approaches for calculating the terminal value in a multistage valuation model.
- LOS 19.mEvaluate whether a stock is overvalued, fairly valued, or undervalued based on a free cash flow valuation model.
Two approaches are commonly used to forecast future FCFF and FCFE.
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. For example, we could calculate free cash flow in the most recent year and then forecast it to grow at 8% for four years and 4% forever after that. This is the same method we used for dividend discount models.
Note that the growth rate for FCFF is usually different than the growth rate for FCFE.
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. For example, if the target debt ratio is 40% and fixed capital investment is $60 million, $24 million (0.40 multiplied by $60 million) is assumed to be financed with debt and $36 million with equity. Thus, net borrowing may be expressed without having to specifically forecast underlying debt issuance or repayment.
This implies that we can forecast FCFE with the following formula:
This is a deceptively simple LOS. The short answer is that dividends, share repurchases, and share issues have no effect on FCFF and FCFE; changes in leverage have only a minor effect on FCFE and no effect on FCFF.
The reason is very straightforward. FCFF and FCFE represent cash flows available to investors and shareholders, respectively, before any payout decisions. Dividends and share repurchases, on the other hand, represent uses of those cash flows; as such, these financing decisions don’t affect the level of cash flow available.
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.
Figure 19.3: Effect of Financing Decisions on Free Cash Flow
The free cash flow to equity approach takes a control perspective that assumes that recognition of value should be immediate. Dividend discount models take a minority perspective, under which value may not be realized until the dividend policy accurately reflects the firm’s long run profitability.
Net income is a poor proxy for FCFE. We can see that by simply examining the formula for FCFE in terms of NI.
Once again, we have not burdened you with the derivation:
Net income includes noncash charges like depreciation that have to be added back to arrive at FCFE. In addition, it ignores cash flows that don’t appear on the income statement, such as investments in working capital and fixed assets as well as net borrowings.
EBITDA is a poor proxy for FCFF. We can also see this from the formula relating FCFF to EBITDA (which you’ve already seen):
EBITDA doesn’t reflect the cash taxes paid by the firm, and it ignores the cash flow effects of the investments in working capital and fixed capital.
Sensitivity analysis shows how sensitive an analyst’s valuation results are to changes in each of a model’s inputs. Some variables have a greater impact on valuation results than others. The importance of various forecasting errors can be assessed through comprehensive sensitivity analysis.
There are two major sources of error in valuation analysis:
- Estimating the future growth in FCFF and FCFE. Growth forecasts depend on a firm’s future profitability, which in turn depends on sales growth, changes in profit margin, position in the life cycle, its competitive strategy, and the overall profitability of the industry.
- The chosen base years for the FCFF or FCFE growth forecasts. A representative base year must be chosen, or all of the subsequent analysis and valuation will be flawed.
For example, suppose an analyst is conducting a sensitivity analysis on the value of a beverage stock using the FCFE approach. She provides high and low estimates of the following variables consistent with their forecasted ranges in her model: FCFE, beta, risk free rate of return, equity risk premium, and the FCFE growth rate. This produces a series of value estimates that reveal the sensitivity of her valuation estimate to variations in her underlying inputs.
Single Stage FCFF Model
The single stage FCFF model is analogous to the Gordon growth model discussed in the previous topic review on dividend valuation models. The single stage FCFF model is useful for stable firms in mature industries. The model assumes that (1) FCFF grows at a constant rate (g) forever, and (2) the growth rate is less than the weighted average cost of capital (WACC).
The formula should look familiar; it’s the Gordon growth model with FCFF replacing dividends and WACC replacing required return on equity.
The WACC is the weighted average of the rates of return required by each of the capital suppliers (usually just equity and debt) where the weights are the proportions of the firm’s total market value from each capital source:
It is assumed that payments to stockholders are not tax deductible, and payments to debtholders are tax deductible. Thus, the after tax cost of debt is the before tax rate of return on debt multiplied by one minus the firm’s marginal tax rate. WACC will change over time as the firm’s capital structure changes.
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.
Single Stage FCFE Model
The single stage constant growth FCFE valuation model is analogous to the single stage FCFF model, with FCFE instead of FCFF and required return on equity instead of WACC:
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.e., inflation- adjusted) values are estimated for the inputs to the single stage FCFE model: FCFE, the growth rate, and the required return.
Multistage Models: How Many Variations Are There?
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.
Let’s take them one at a time, but keep in mind the basic valuation principle at work here: value is always estimated as the present value of the expected future cash flows discounted at the appropriate discount rate.
FCFF versus FCFE: Remember that the value of the firm is the present value of the FCFF discounted at the WACC; the value of equity is the present value of the FCFE discounted at the required return on equity.
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.
Forecasting growth in total free cash flow (FCFF or FCFE) versus forecasting the growth rates in the components of free cash flow: The simple free cash flow model, in which we forecast total FCFE or FCFF, looks a lot like the multistage dividend discount models. The benefit of using free cash flow models, however, is when we refine our approach by forecasting the values and/or growth rates in the components of free cash flow over the first stage and then calculate free cash flow in each year using one of our formulas. 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.g., a growth phase, a mature phase, and a transition phase).
Let’s discuss some examples of two stage models. We’re going to wait until the next LOS, however, to start doing the number crunching. 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.
We could analyze a:
- Two stage FCFF model in which FCFF is projected to grow at 20% for the first four years and then 4% every year thereafter.
- Two stage FCFE model in which FCFE declines from 20% to 4% over four years and then stays at 4% forever.
- Two stage FCFE model in which sales grow at 20% for four years, the net profit margin is constant at 8%, fixed capital investment is equal to 60% of the dollar increase in sales, working capital investment is equal to 25% of the dollar increase in sales, and the debt ratio is 50%. 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 single stage 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.
Three stage models have all the complications of the two stage models, with an additional growth stage to consider. Keep in mind, however, that what we’re trying to do is forecast FCFF or FCFE over some interim period with three distinct stages of growth, estimate the terminal value, and then estimate the value of the firm or the value of the equity today as the present value of those cash flows discounted at the appropriate required return. For example, we could analyze a:
- Three stage FCFE model in which FCFE grows at 30% for two years (Stage 1), 15% for four years (Stage 2), and then 5% forever (Stage 3).
- Three stage FCFF model in which FCFF grows at 25% for three years (Stage 1), declines to 4% over next the five years (Stage 2), then stays at 4% forever (Stage 3).
- Three stage FCFE model in which we forecast the components of FCFE over three different stages.
We’ve already discussed free cash flow models, so now let’s get to the hard work: actually calculating value using these models. We won’t go through every different possible example, but we will give you a range of examples that cover nearly every important concept.
Single Stage FCFF Model
The first example is a basic single stage FCFF model where we first calculate WACC as the appropriate required return.
Knappa Valley Winery’s (KVW) most recent FCFF is $5,000,000. KVW’s target debt- to equity ratio is 0.25. The market value of the firm’s debt is $10,000,000, and KVW has 2,000,000 shares of common stock outstanding. The firm’s tax rate is 40%, the shareholders require a return of 16% on their investment, the firm’s before tax cost of debt is 8%, and the expected long term growth rate in FCFF is 5%. Calculate the value of the firm and the value per share of the equity.
Solution
Note that the problem gives the FCFF in the most recent year (). Therefore, you need to increase at the growth rate by one year (at the 5% rate) to get .
Let’s calculate the WACC. The target debt to equity ratio is 0.25. This implies that for every $1 of debt, there is $4 of equity, for total capital of $5. Since total assets equals total capital, it follows that the target debt to asset ratio is 1/5, or 20%, and the target equity to asset ratio is 4/5, or 80%. The WACC is:
We can now calculate the value of the firm as:
Given that debt is worth $10,000,000, the implied total value of the equity is:
With 2,000,000 shares outstanding, the value of the equity per share is:
Notice that the actual debt to equity ratio (10,000,000 / 49,931,507 = 0.20) does not equal the target ratio of 0.25. There is nothing inconsistent in this example. WACC is usually calculated using target capital weights.
Single Stage FCFE Model
Ridgeway Construction has an FCFE of 2.50 Canadian dollars (C$) per share and is currently operating at a target debt to equity ratio of 0.4. The expected return on the market is 9%, the risk free rate is 4%, and Ridgeway has a beta of 1.5. The expected growth rate of FCFE is 4.5%. Calculate the value of Ridgeway stock.
Solution
Begin by computing the required return on equity with the CAPM:
Note that the problem gives FCFE in the most recent year (). The model calls for the FCFE next year, which is . Therefore, you need to multiply by one plus the growth rate to get .
The equity value per share is:
Two Stage FCFF Model
The first two stage example requires the FCFF model and a forecast of the components of FCFF during the high growth stage.
The Prentice Paint Company earned a net profit margin of 20% on revenues of $20 million this year. Fixed capital investment was $2 million, and depreciation was $3 million. Working capital investment equals 7.5% of sales every year.
Net income, fixed capital investment, depreciation, interest expense, and sales are expected to grow at 10% per year for the next five years. After five years, the growth in sales, net income, fixed capital investment, depreciation, and interest expense will decline to a stable 5% per year. The tax rate is 40%, and Prentice has 1 million shares of common stock outstanding and long term debt paying 12.5% interest trading at its par value of $32 million.
Calculate the value of the firm and its equity using the FCFF model if the WACC is 17% during the high growth stage and 15% during the stable stage.
Solution
The components of FCFF are calculated in the following table.
FCFF for Years 0 Through 6 (in per share amounts of $)
Let’s demonstrate the calculation of the FCFF in Year 0:
In Year 1, sales grow by 10% to $22.00 per share. Following five years of 10% growth, the growth of each component falls to 5%.
The terminal value (as of Year 5, discounted at the stable WACC of 15%) is:
We can place the cash flows to be evaluated on a time line, such as the one in the following figure, to get a clearer picture of what we need to evaluate.
FCFF Timeline
Notice that the WACC in the high growth stage (17%) is different than the stable stage (15%).
We calculated terminal value in Year 5 using 15%, but we’ll calculate the present value today of the high growth cash flows and the terminal value at 17%. The total of the firm today is:
To perform this calculation quickly and accurately, use the following keystrokes on your financial calculator:
Thus, given that the value of the firm’s debt is $32 per share, the value of equity per share is $70.06 − $32.00 = $38.06.
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.
Consider a rival to the Prentice Paint Company presented in the previous example. Suppose that Sioux Falls Decor also has revenues of $20 million this year. However, we assume that its future performance will be tracked relative to sales as follows:
Sales growth and the net profit margin are projected by year as shown in the following table:
Sales and Net Margin Forecasts
Fixed capital investment net of depreciation is projected to be 30% of the sales increase in each year.
Working capital requirements are 7.0% of the projected dollar increase sales in each year.
Debt will finance 40% of the investments in net capital and working capital.
The company has a 12% required rate of return on equity.
The firm has 1 million shares of common stock outstanding.
Calculate the value of the equity of Sioux Falls using the two stage FCFE model.
Solution
Recognize that the target debt to asset ratio (DR) is 0.40. The following table shows the FCFE for Years 1 through 6 ($ amounts are per share).
Calculating FCFE for Years 1 Through 6
Let’s demonstrate the calculation of the cash flow components in Year 1:
Terminal value (as of Year 5, assuming 5% stable long term growth) is equal to:
Total current value of equity:
As usual, we would rely on the cash flow keys of our financial calculator to perform the previous calculation:
Three Stage FCFE Model
The following example of a three stage FCFE model is a little different than the last two examples because we’re given growth in total FCFE in each of three stages, rather than the growth rates in the components. 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.
Medina Classic Furniture, Inc., is expected to experience growth in three distinct stages in the future. Its most recent FCFE is 0.90 Canadian dollars (C$) per share. The following information has been compiled:
High growth period:
Duration = 3 years.
FCFE growth rate = 30%.
Shareholders’ required return = 20%.
Transitional period:
Duration = 3 years.
FCFE growth will decline by 9% per year down to the indicated stable growth rate.
Shareholders’ required return = 15%.
Stable growth period:
FCFE growth rate = 3%.
Shareholders’ required return = 10%.
Calculate the value of the firm’s equity using the three stage FCFE model.
Solution
The annual FCFE and the associated present value are presented in the table:
FCFE and PV
The transitional present values are computed using a combination of the 20% initial discount rate and the transitional 15% rate. For example, the present value of is computed as:
We can calculate the terminal value of the stock as of Year 6 using the FCFE projected for Year 7. Notice that we use the Stage 3 required return of 10%.
The value of Medina stock is:
The changing discount rates were important here for a couple of reasons. First, the terminal value in Year 6 had to be discounted for three years at 20% and for three years at 15%. 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.
There are two basic approaches for calculating terminal value: using a single stage model or a multiple approach. All of our examples used the first approach, in which we forecasted an FCFF or FCFE at the point in time at which cash flows begin to grow at the long term, stable growth rate, and then we estimated terminal value using a single- stage model.
The other way to do this is to use valuation multiples (like P/E ratios) to estimate terminal value. The terminal value in year n in terms of P/E, for example, would be expressed as:
terminal value in year n = (trailing P/E) × (earnings in year n) terminal value in year n = (leading P/E) × (forecasted earnings in year n + 1)
An analyst estimates the EPS of Polar Technology in five years to be $2.10, the EPS in six years to be $2.32, and the median trailing industry P/E to be 35. Calculate the terminal value in Year 5.
Solution
terminal value in Year 5 = 35 × $2.10 = $73.50
If a stock is trading at a price (market price) higher than the price implied by a free cash flow valuation model (model price), the stock is considered to be overvalued. 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.