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The discounted cash flow model that uses FCFE can be viewed as an alternative to the dividend discount model. Since the two approaches sometimes provide different estimates of value, it is worth examining when they provide similar estimates of value, when they provide different estimates of value and what the difference tells us about the firm.

a. When they are similar

There are two conditions under which the value from using the FCFE in discounted cashflow valuation will be the same as the value obtained from using the dividend discount model. The first is the obvious one, where the dividends are equal to the FCFE. The second condition is more subtle, where the FCFE is greater than dividends, but the excess cash (FCFE - Dividends) is invested in projects with net present value of zero. (For instance, investing in financial assets which are fairly priced should yield a net present value of zero.)

b. When they are different

There are several cases where the two models will provide different estimates of value. First, when the FCFE is greater than the dividend and the excess cash either earns below-market interest rates or is invested in negative net present value projects, the value from the FCFE model will be greater than the value from the dividend discount model. There is reason to believe that this is not as unusual as it would seem at the outset. There are numerous case studies of firms, which having accumulated large cash balances by paying out low dividends relative to FCFE, have chosen to use this cash to finance unwise takeovers (where the price paid is greater than the value received from the takeover). Second, the payment of dividends less than FCFE lowers debt-equity ratios and may lead the firm to become underlevered, causing a loss in value.

In the cases where dividends are greater than FCFE, the firm will have to issue either new stock to pay these dividends leading to at least three negative consequences for value. One is the flotation cost on these security issues, which can be substantial for equity issues and creates an unnecessary expenditure that decreases value. Second, if the firm borrows the money to pay the dividends, the firm may become overlevered (relative to the optimal) leading to a loss in value. Finally, paying too much in dividends can lead to capital rationing constraints where good projects are rejected, resulting in a loss of value.

There is a third possibility and it reflects different assumptions about reinvestment and growth in the two models. If the same growth rate used in the dividend discount and FCFE models, the FCFE model will give a higher value than the dividend discount model whenever FCFE are higher than dividends and a lower value when dividends exceed FCFE. In reality, the growth rate in FCFE should be different from the growth rate in dividends, because the free cash flow to equity is assumed to be paid out to stockholders. This will affect the reinvestment rate of the firm. In addition, the return on equity used in the FCFE model should reflect the return on equity on non-cash investments, whereas the return on equity used in the dividend discount model should be the overall return on equity. Table 14.7 summarizes the differences in assumptions between the two models.

Dividend Discount Model |
FCFE Model | |

Implicit Assumption |
Only dividends are paid. Remaining portion of earnings are invested back into the firm, some in operating assets and some in cash & marketable securities. |
The FCFE is paid out to stockholders. The remaining earnings are invested only in operating assets. |

Expected Growth |
Measures growth in income from both operating and cash assets. In terms of fundamentals, it is the product of the retention ratio and the return on equity |
Measures growth only in income from operating assets. In terms of fundamentals, it is the product of the equity reinvestment rate and the non-cash return on equity. |

Dealing with cash and marketable securities |
The income from cash and marketable securities is built into earnings and ultimately |
You have two choices: 1. Build in income from cash and marketable securities |

into dividends. Therefore, cash and marketable securities do not need to be added in into projections of income and estimate the value of equity.

2. Ignore income from cash and marketable securities, and add their value to equity value in model

In general, when firms pay out much less in dividends than they have available in FCFE, the expected growth rate and terminal value will be higher in the dividend discount model, but the year-to-year cash flows will be higher in the FCFE model. The net effect on value will vary from company to company.

3. What does it mean when they are different?

When the value using the FCFE model is different from the value using the dividend discount model, with consistent growth assumptions, there are two questions that need to be addressed - What does the difference between the two models tell us? Which of the two models is the appropriate one to use in evaluating the market price?

The more common occurrence is for the value from the FCFE model to exceed the value from the dividend discount model. The difference between the value from the FCFE model and the value using the dividend discount model can be considered one component of the value of controlling a firm - it measures the value of controlling dividend policy. In a hostile takeover, the bidder can expect to control the firm and change the dividend policy (to reflect FCFE), thus capturing the higher FCFE value.

As for which of the two values is the more appropriate one for use in evaluating the market price, the answer lies in the openness of the market for corporate control. If there is a sizable probability that a firm can be taken over or its management changed, the market price will reflect that likelihood and the appropriate benchmark to use is the value from the FCFE model. As changes in corporate control become more difficult, either because of a firm's size and/or legal or market restrictions on takeovers, the value from the dividend discount model will provide the appropriate benchmark for comparison.

Illustration 14.6: Comparing the DDM and FCFE Models: Coca Cola

In Chapter 13, we valued Coca Cola using a three-stage dividend discount model at $42.72 a share. Here, we will value Coca Cola using a three stage free cash flow to equity model.

• Why three stage? Coca Cola's strong brand name will allow it to overcome some of the constraints that may exist on its high growth rate - the saturation of its domestic market and its high market share in the market. However, we believe that this growth will come under assault from competition in future years, leading us to allow for a transition to stable growth.

• Why FCFE? While the firm does have a history of returning cash to stockholders, we wanted to examine the differences in value, if any, estimated with the dividend and FCFE models.

• The firm has used debt a little more liberally in the last few years, but it remains a firm that uses equity for much of its reinvestment needs.

Background Information

Net Income =$3,878

Number of shares outstanding =2487.03

Current Capital Expenditures =$992.00

Current Depreciation =$773.00

Increase in non-cash Working capital in most recent year =$852.00 Net Debt Issued (Paid) during the year =($585.00)

Based upon these values, we can estimate the free cash flows to equity in the most recent year as follows:

Free Cash flow to equity = Net Income - (Cap Expenditures - Depreciation) - Change in non-cash working capital + Net Debt Issued = 3878 - (992- 773) - 852 + (-585) = $2,222 million

The return on equity in the most recent year was estimated to be 23.37% in the dividend discount model. We re-estimated the return on equity excluding the income from cash and marketable securities from net income3 and the value of the cash and marketable securities from book equity:

Modified return on equity = (Net Income - After-tax Interest income from cash)/ (Book

2177-91

Value of Equity - Cash and Marketable Securities) =-= 27.83%

9317-1822

We assume that the cost of equity for Coca Cola will be 9.99% for the five-year high growth period, declining in linear increments to 9.40% in year 10 and stable growth beyond. This cost of equity is slightly higher than the cost of equity used in the dividend discount model to reflect the fact that we are valuing operating assets (not including cash) - the beta used was 0.82, slightly higher than the beta of 0.80 used in the dividend discount model.

The capital expenditures, working capital requirements and the debt ratio for Coca Cola have been volatile over the last five years. To normalize changes over time, we decided to do the following:

• We computed the net capital expenditures as a percent of earnings before interest and taxes each year for the last 5 years.

-5 |
-4 |
-3 |
-2 |
Current |
Average | |

Net Cap Ex |
$1,391.00 |
$1,485.00 |
$1,996.00 |
$2,332.00 |
$219.00 |
$1,484.60 |

EBIT |
$4,833.00 |
$5,001.00 |
$4,967.00 |
$3,982.00 |
$5,134.00 |
$4,783.40 |

31.04% |

Normalized net capital expenditure = Average as % of EBIT over last 5 years * EBIT in most recent year = 0.3104* 5134 = $1,593 million

Normalized net capital expenditure = Average as % of EBIT over last 5 years * EBIT in most recent year = 0.3104* 5134 = $1,593 million

• We estimated non-cash working capital as a percent of revenues in the most recent year and used it to estimate the change in non-cash working capital over the last year.

Non-cash working capital in current year = $223 million Revenues in current year = $20,458 million

3 As in the dividend discount model, we used a normalized net income ($2177 million) just for this computation. The rest of the valuation is based upon the actual net income prior to extraordinary items.

Revenues last year = $19,805 million Normalized change in non-cash working capital last year = 223

20458,

• We normalized the net debt issued by assuming that Coca Cola would continue to fund its reinvestment needs with its market debt to capital ratio. To estimate the market debt to capital ratio, we used the total interest bearing debt outstanding at the end of 2000 and the current market value of equity.

_ Interest bearing debt

„ , . Interest bearing debt + Market value of equity

Debt Ratio s H J

5651 +115125

Normalized debt issued in current year = (Normalized net capital expenditures + Normalized change in non-cash working capital) * Debt Ratio = (1593+7.12)*(0.0468) =$74.89 million The normalized free cash flow to equity can then be computed. Normalized FCFE = Net Income - Normalized Net Cap Ex - Normalized change in working capital + Normalized net debt issued = 3878 - 1593 - 7.12 + 74.89 = $2,353 million

This normalized FCFE also lets us compute the equity reinvestment rate for the firm:

Equity reinvestment rate = 1- —FCFE— _ 1- 2353 _ 39.3%

Net Income 3878

With the current return on equity of 27.83%, this yields an expected growth rate in net income at Coca Cola of 10.94%.

Expected Growth = Equity reinvestment rate * Return on Equity = 0.393*0.2783 = 0.1094

In stable growth, we assume that the return on equity drops to 20% and that the growth rate in perpetuity in net income is 5.5%. The equity reinvestment rate can then be estimated as follows:

Equity Reinvestment rate in stable growth = —— _ £.£% _ 27.5% H J 5 ROE 20%

To value Coca Cola, we will begin by projecting the free cash flows to equity during the high growth and transition phases, using an expected growth rate of 10.94% in non-cash net income and an equity reinvestment rate of 39.3% for the first 5 years. Non-cash Net Income = Net Income - After-tax Interest income from cash and marketable securities = $3,878 million - 89 million = $3,789 million

The next 5 years represent a transition period, where the growth drops in linear increments from 10.94% to 5.5% and the equity reinvestment rate drops from 39.3% to 27.5%. The resulting free cash flows to equity are shown in Table 14.8.

Year |
Expected Growth |
Net Income |
Equity Reinvestment Rate |
FCFE |
Cost of Equity |
Present Value |

High Growth Stage | ||||||

1 |
10.94% |
$4,203.28 |
39.32% |
$2,550.42 |
9.99% |
$2,318.73 |

2 |
10.94% |
$4,663.28 |
39.32% |
$2,829.53 |
9.99% |
$2,338.80 |

3 |
10.94% |
$5,173.61 |
39.32% |
$3,139.18 |
9.99% |
$2,359.03 |

4 |
10.94% |
$5,739.79 |
39.32% |
$3,482.72 |
9.99% |
$2,379.44 |

5 |
10.94% |
$6,367.93 |
39.32% |
$3,863.86 |
9.99% |
$2,400.03 |

Steady Growth Stage | ||||||

ó |
9.85% |
$6,995.48 |
36.96% |
$4,410.06 |
9.87% |
$2,493.13 |

7 |
8.77% |
$7,608.71 |
34.59% |
$4,976.57 |
9.76% |
$2,563.34 |

8 |
7.68% |
$8,192.87 |
32.23% |
$5,552.37 |
9.64% |
$2,608.54 |

9 |
6.59% |
$8,732.68 |
29.86% |
$6,124.69 |
9.52% |
$2,627.34 |

10 |
5.50% |
$9,212.97 |
27.50% |
$6,679.40 |
9.40% |
$2,619.11 |

Sum of the present values of FCFE during high growth = |
$24,707.49 |

To estimate the terminal value of equity, we used the net income in the terminal year (Year 11), reduce it by the equity reinvestment needs in that year and then assume a perpetual growth rate to get to a value. Expected stable growth rate = 5.5%

Equity reinvestment rate in stable growth = 27.5% Cost of equity in stable growth = 9.40% Expected FCFE in year 11

= (Net Income11 )(l - Stable period equity reinvestment rate) = (9212.97)l 055)l - 0.275)= 7,047 million

Stable period cost of equity Stable growth rate

Value of equity in Coca Cola

7,047

To estimate the value of equity today, we sum up the present value of the FCFE over the high growth period and add to it the present value of the terminal value of equity.

= PV of FCFE during the high growth period + PV of terminal value

180,686

(1.0988) (1.0987)(l.0976)(l.0964)(l.0952)(l .0940) = 95,558 million

Adding in the value of the cash and marketable securities that Coca Cola had on hand at the end of 2001, we obtain the total value of equity:

Value of Equity including cash = $95,558 + $1,892 = $97,447 million

= Value of Equity

Value of Equity per share

The FCFE model yields a lower value than the dividend discount model value of $42.72 a share. This may seem surprising since the FCFE each year for the high growth period are greater than the dividends, but this effect is more than offset by the decline in the expected growth rate which is generated by the equity reinvestment rate being lower than the retention ratio. We would argue that this valuation is probably more realistic than the dividend discount model because it keeps investments in cash and marketable securities separate from investments in operating assets. The dividend discount model overstates the expected growth rate because it does not consider the fact that the low return earned by cash investments will bring the return on equity down over time (and the growth rate down with it).

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