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The free cash flow to equity model does not represent a radical departure from the traditional dividend discount model. In fact, one way to describe a free cash flow to equity model is that it represents a model where we discount potential dividends rather than actual dividends. Consequently, the three versions of the FCFE valuation model presented in this section are simple variants on the dividend discount model, with one significant change - free cashflows to equity replace dividends in the models.

When we replace the dividends with FCFE to value equity, we are doing more than substituting one cash flow for another. We are implicitly assuming that the FCFE will be paid out to stockholders. There are two consequences.

1. There will be no future cash build-up in the firm, since the cash that is available after debt payments and reinvestment needs is paid out to stockholders each period.

2. The expected growth in FCFE will include growth in income from operating assets and not growth in income from increases in marketable securities. This follows directly from the last point.

How does discounting free cashflows to equity compare with the modified dividend discount model, where stock buybacks are added back to dividends and discounted? You can consider stock buybacks to be the return of excess cash accumulated largely as a consequence of not paying out their FCFE as dividends. Thus, FCFE represent a smoothed out measure of what companies can return to their stockholders over time in the form of dividends and stock buybacks.

The FCFE model treats the stockholder in a publicly traded firm as the equivalent of the owner in a private business. The latter can lay claim on all cash flows left over in the business after taxes, debt payments and reinvestment needs have been met. Since the free cash flow to equity measures the same for a publicly traded firm, we are assuming that stockholders are entitled to these cash flows, even if managers do not choose to pay them out. In essence, the FCFE model, when used in a publicly traded firm, implicitly assumes that there is a strong corporate governance system in place. Even if stockholders cannot force managers to return free cash flows to equity as dividends, they can put pressure on managers to ensure that the cash that does not get paid out is not wasted.

Free cash flows to equity, like dividends, are cash flows to equity investors and we could use the same approach that we used to estimate the fundamental growth rate in dividends per share.

Expected Growth rate = Retention Ratio * Return on Equity

The use of the retention ratio in this equation implies that whatever is not paid out as dividends is reinvested back into the firm. There is a strong argument to be made, though, that this is not consistent with the assumption that free cash flows to equity are paid out to stockholders which underlies FCFE models. It is far more consistent to replace the retention ratio with the equity reinvestment rate, which measures the percent of net income that is invested back into the firm.

t—' t-> • .l .l t-> .l Net Cap Ex + Change in Working Capital-(New Debt Issues - Repayments)

Net Income

The return on equity may also have to be modified to reflect the fact that the conventional measure of the return includes interest income from cash and marketable securities in the numerator and the book value of equity also includes the value of the cash and marketable securities. In the FCFE model, there is no excess cash left in the firm and the return on equity should measure the return on non-cash investments. You could construct a modified version of the return on equity that measures the non-cash aspects.

, Net Income-After tax income from cash and marketable securities

Book Value of Equity - Cash and Marketable Securities

The product of the equity reinvestment rate and the modified ROE will yield the expected growth rate in FCFE.

Expected Growth in FCFE = Equity Reinvestment Rate * Non-cash ROE This growth rate can then be applied to the non-cash net income to value the equity in the operating assets. Adding cash and marketable securities to this number will yield the total value of equity in the company.

As with the dividend discount model, there are variations on the free cashflow to equity model, revolving around assumptions about future growth and reinvestment needs. In this section, we will examine versions of the FCFE model that parallel our earlier discussion of the dividend discount model.

The constant growth FCFE model is designed to value firms that are growing at a stable rate and are hence in steady state. The value of equity, under the constant growth model, is a function of the expected FCFE in the next period, the stable growth rate and the required rate of return.

P fcfex

P0 = Value of equity today

FCFEl = Expected FCFE next year ke = Cost of equity of the firm gn = Growth rate in FCFE for the firm forever

The model is very similar to the Gordon growth model in its underlying assumptions and works under some of the same constraints. The growth rate used in the model has to be less than or equal to the expected nominal growth rate in the economy in which the firm operates.The assumption that a firm is in steady state also implies that it possesses other characteristics shared by stable firms. This would mean, for instance, that capital expenditures, relative to depreciation, are not disproportionately large and the firm is of 'average' risk. (If the capital asset pricing model is used, the beta of the equity should not significantly different from one.) To estimate the reinvestment for a stable growth firm, you can use one of two approaches.

• You can use the typical reinvestment rates for firms in the industry to which the firm belongs. A simple way to do this is to use the average capital expenditure to depreciation ratio for the industry (or better still, just stable firms in the industry) to estimate a normalized capital expenditure for the firm.

• Alternatively, you can use the relationship between growth and fundamentals developed in Chapter 4 to estimate the required reinvestment. The expected growth in net income can be written as:

Expected growth rate in net income = Equity Reinvestment Rate * Return on equity This allows us to estimate the equity reinvestment rate:

Expected growth rate

Equity reinvestment rate =

To illustrate, a firm with a stable growth rate of 4% and a return on equity of 12% would need to reinvest about a third of its net income back into net capital expenditures and working capital needs. Put another way, the free cash flows to equity should be two thirds of net income.

This model, like the Gordon growth model, is best suited for firms growing at a rate comparable to or lower than the nominal growth in the economy. It is, however, the better model to use for stable firms that pay out dividends that are unsustainably high (because they exceed FCFE by a significant amount) or are significantly lower than the FCFE. Note, though, that if the firm is stable and pays outs its FCFE as dividend, the value obtained from this model will be the same as the one obtained from the Gordon growth model.

Illustration 5.7: FCFE Stable Growth Model: Exxon Mobil

Earlier in this chapter, we valued Exxon Mobil using a modified dividend discount model and found it to be significantly under valued at its current price of $ 60 a share. In this illustration, we will value Exxon Mobil using a stable growth FCFE model instead, with the following assumptions:

- To estimate Exxon's cost of equity, we will continue to use the same parameters we used in the dividend discount model: a beta of 0.80. a riskfree rate of 4.5% and a market risk premium of 4%, resulting in a cost of equity of 7.70%.

- High and rising oil prices have clearly pushed up Exxon's income in 2004 but it is unlikely that oil prices will continue to rise forever at this pace. Rather than use the net income from 2004 of $25.322 billion as our measure of earnings, we will use the average net income of $18.405 billion over the last 5 years as a measure of normalized net income. Netting out the interest income from cash from these earnings yields the non-cash net income value for the base year.

Non-cash Net Income = Net Income - Interest Income from Cash = 18,405 - 321 = $18,086 million

- Based upon the normalized net income of $18.086 billion and the non-cash book value of equity at the end of 2003, we estimated a return on equity of 21.88%.

Non-cash ROE = Non-cash Net Income2004/ (Book value of equity - Cash)2003 = 18086/ (93297 - 10626) = 21.88%

- To estimate the reinvestment rate, we looked at net capital expenditures and working capital investments over the last 5 years and estimated a normalized equity reinvestment rate of 16.98%.7 The expected growth rate in perpetuity can then be computed to be 3.71%:

Expected growth rate in net income = Return on equity * Equity Reinvestment Rate = 21.88% * .1698 = .0371 The value of Exxon Mobil equity can then be estimated as follows: Value of equity in operating assets = Non-cash Net Income (1- Reinvestment Rate) (1+g)/ (Cost of equity -g) = 18086 (1- .1698) (1.0371)/ (.077-.0371) = 390.69 billion Adding the value of cash and marketable securities ($18.5 billion) to this number and dividing by the number of shares yields the value of equity per share: Value of equity per share = (390.69 + 18.5)/ 6.2224 = $65.77

Based upon this model, Exxon is only slightly under valued at $ 60 a share. There are two reasons this valuation is more realistic than the modified dividend discount model valuation. First, the net income is normalized and allows for the cycles that are usually seen in commodity prices. Second, the reinvestment is measured directly in this valuation by looking at capital expenditures and working capital investments rather than indirectly through a retention ratio.

The two-stage FCFE model is designed to value a firm that is expected to grow much faster than a mature firm in the initial period and at a stable rate after that. In this model, the value of any stock is the present value of the FCFE per year for the extraordinary growth period plus the present value of the terminal price at the end of the period.

7 We computed the average of the net capital expenditures each year for the last 5 years and divided this number by the average operating income over the last 5 years. The resulting ratio of 11.83% was then multiplied by the current year's operating income of $35.872 billion to arrive at the normalized net capital expenditure for the current year of $4,243 million. To estimate the normalized non-cash working capital change, we first computed non-cash working capital as a percent of revenues for the last 5 years (0.66%) and multiplied this value by the change in revenues over the last year ($50.79 billion) to arrive at the non-cash working capital change of $336 million. Finally, the normalized change in debt of $ 333 million was estimated using the current book value debt to capital ratio (7.27%) of the total normalized reinvestment (4,243+336). The resulting normalized equity reinvestment is $4246 million (4243+336- 333). Dividing by the non-cash net income in 2004 of $ 25,011 million yields the equity reinvestment rate of 16.98%.

= PV of FCFE + PV of terminal price Value of equity FCFEt + Pn

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