Allied Academies International Conference page 11

APPLYING THE FREE CASH FLOW TO EQUITY

VALUATION MODEL TO COCA-COLA
John C. Gardner, University of New Orleans
Carl B. McGowan, Jr., Norfolk State University
Susan E. Moeller, Eastern Michigan University

ABSTRACT

In this paper we provide a detailed example of applying the free cash flow to equity valuation
model proposed in Damodaran (2006). Damodaran (2006) argues that the value of a stock is the
discounted present value of the future free cash flow to equity discounted at the cost of equity. We
combine the free cash flow to equity model with the super-normal growth model to determine the
current value of Coca-Cola. In addition to computing free cash flow to equity, we show how to
calculate the sustainable growth rate, the long term growth rate, beta, and the cost of equity.

Free Cash Flow to Equity

In this paper, we combine the concept of the super-normal growth rate model of stock
valuation with the Free Cash Flow to Equity model from Damodaran (2006, pp. 491-493) (See
Damodaran, Aswath. “Applied Corporate Finance,” Second Edition, John Wiley& Sons, Inc.,
2006). The FCFE model defines FCFE as net income minus net capital expenditures minus the
change is working capital and plus net changes in the long-term debt position. Net income is taken
from the income statement. Net capital expenditure equals capital expenditures minus depreciation
both taken from the statement of cash flows. The change in working capital is the difference of
accounts receivable plus inventory from one year to the next less the difference in accounts payable
from one year to the next.
FCFE = NI – (CE-D) – (∆WC) + (NDI-DR)
FCFE = Free Cash Flow to Equity
(CE-D) = Net Capital Expenditures
(∆WC) = Changes in non-cash working capital accounts: accounts receivable, inventory,
payables
(NDI-DR) = new debt issues are a cash inflow while the repayment of outstanding debt is a cash
outflow. The difference is the net effect of debt financing on cash flow.
NI – Net Income
CE – Capital Expenditure
D - Depreciation
∆WC – Change in Working Capital
NDI – New Debt Issued
DR – Debt Retired

Proceedings of the Academy of Accounting and Financial Studies, Volume 14, Number 1 New Orleans, 2009
page 12 Allied Academies International Conference

Computing Free Cash Flow to Equity for Coca-Cola for 2000 to 2007

The following table shows the computation of FCFE for Coca-Cola for the period from 2000
to 2007. Net income is taken from the income statement and depreciation is taken from the
Statement of Cash Flows. Capital expenditure is the difference between purchases of Property,
Plant, and Equipment and depreciation. The change is working capital for each year is calculated
by taking the difference in each of the working capital accounts for each year from 1999 to 2007.
The working capital accounts are accounts receivable, inventory, and accounts payable and the
change in working capital is defined at the net change in accounts receivable plus inventory minus
accounts payable. When net income, depreciation, capital expenditure and the change in working
capital are combined we have FCFE before changes in debt. Net cash flow from debt equals new
debt financing minus old debt retirement which is added to FCFE before debt to compute FCFE after
debt.

Year NI Depr Cap Exp ∆WC FCFE(BD) NCFFD FCFE(AD)

2000 2177 773 -678 242 2514 -1939 575
2001 3969 803 -678 -340 3754 -1039 2715
2002 3050 806 -782 -441 2633 -1340 1293
2003 4347 850 -725 414 4886 -1435 3451
2004 4847 893 -414 24 5350 168 5518
2005 4872 932 -811 49 5042 -4107 935
2006 5080 938 -1295 39 4762 -3672 1090
2007 5981 1163 -1409 551 6286 4122 10408

The Free Cash Flow to Equity for 2007 is $10,408 million. However, because Free Cash Flow to
Equity for Coca-Cola over the period from 2000 to 2007 is volatile, we use the average value for
the period from 2000 to 2007 of $3,248 million to estimate the future values of Free Cash Flow to
Equity for the five year super-normal growth period assumed in the following table.

Year FCFE PV(FCFE)

2008 3684 3347
2009 4179 3449
2010 4740 3554
2011 5377 3662
2012 6099 3773
Column 1 Year
Column 2 Projected Free Cash Flow to Equity for Years 2008 to 2012, assuming a growth rate of 13.43%.
Column 3 Present value of FCFE for years 2008 to 2012 discounted at the required rate of return for equity for
Coca-Cola.

New Orleans, 2009 Proceedings of the Academy of Accounting and Financial Studies, Volume 14, Number 1
Allied Academies International Conference page 13

The projected Free Cash Flow to Equity for year 2013 is $6,504 million. The terminal value
for year 2012 is $188,509 million which is equal to $6,504 million divided by the required rate of
return, 10.08% minus the anticipated growth rate of 6.63% and equals $116,625 million.

Year FCFE P5 PV(FCFE)

2013 $6,504 $188,509 $116,625

Thus, the current value of Coca-Cola is the sum of the five anticipate Free Cash Flow to
Equity plus the present value of the value of the firm at time t=5. The discounted present value of
the Free Cash Flow to Equity for the super-normal growth period for the five years from 2008 to
2012 is $ 21,502 million and the present value of the terminal value is $106,165. The total value
of Coca-Cola is $129,643 million.

$17,875 PV(FCFE)

$116,625 PV(terminal value)

$134,410 Total value

When we value a stock that has a period of super-normal growth, that value of the equity is
the discounted present value of the expected free cash flow to equity during the super-normal growth
period plus the terminal value of the stock at the end of the super-normal growth period. In the case
of the KO valuation, I assume that the super-normal growth period will last five years. This is
standard in the valuation industry. Projections beyond five years are very uncertain. The value of
the stock at the end of the super-normal growth period is the discounted present value of all of the
future free cash flow to equity and is computed from the P0 = FCFE1/(k-g). The difference is that
the present value of a share of stock at time=t is equal to the anticipated free cash flow to equity at
time=(t+1). Beginning with time=(t+1), the investment returns to the long-term growth rate with
both k and g becoming constant and k being strictly greater than b. Since we are using a super-
normal growth period of five years, the terminal value of the stock is P5 = FCFE6/(k-g). The value
of P5 is five years into the future and must be discounted to the present using the cost of equity.

FCFE6 = FCFE5(1+g)1
= $6,504 (1+.0663)1
= $6,504
P5 = FCFE6/(k-g)
= $6,504/(0.1208-0.0663)
= $6,504/(0.0345)
= $134,410
PV(P5) = P5/(1+k)5
= $134,410/(1+.1008)5
= $116,625

Proceedings of the Academy of Accounting and Financial Studies, Volume 14, Number 1 New Orleans, 2009
page 14 Allied Academies International Conference

Summary and Conclusions

In this paper, we have combined the concepts of equity valuation, super-normal growth,
required rate of return on equity, and sustainable growth to determine the long-term value of Coca-
Cola Corporation (KO). The value of the equity of a firm is defined as the present value of all future
cash flows from the firm to the shareholders. The value of the firm is FCFE divided by the sum of
the required rate of return for equity minus the growth rate of the firm’s earnings. Free Cash Flow
to Equity is defined as net income minus net capital expenditures minus the change in net working
capital plus the net change in long-term debt financing. The required rate of return for equity is
computed using the CAPM using a five-year monthly rate of return beta relative to the S&P500
index. Sustainable growth for the super-normal growth period is computed with the extended
DuPont model. The long-term growth rate is assumed to be the same as the growth rate of the
economy. The table in Appendix C shows the results of this analysis.

REFERENCES

Brigham, Eugene F. and Michael C. Ehrhardt. Financial Management, Theory and Practice, Twelth Edition,
Thomson/Southwestern, Mason, OH, 2008.

Damodaran, Aswath. “Applied Corporate Finance,” Second Edition, John Wiley& Sons, Inc., 2006.

Graham, John R. and Campbell R. Harvey. “The Theory and Practice of Corporate Finance: Evidence form the Field,”
Journal of Financial Economics, 2002, pp. 187-243.

http://nobelprize.org/nobel_prizes/economics/laureates/1990/press.html

Ross, Stephen A., Randolph W. Westerfield, and Bradford D. Jordan. Fundamentals of Corporate Finance, Eighth
Edition, McGraw-Hill Irwin, New York, 2008.

William R. Sharpe, Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk, The Journal of
Finance, September 1964, pp. 425-552.

Stocks, Bonds, Bills, and Inflation, Market Results for 1926 -2006, 2007 Yearbook, Classic Edition, Morningstar, 2007.

New Orleans, 2009 Proceedings of the Academy of Accounting and Financial Studies, Volume 14, Number 1
Allied Academies International Conference page 15

Appendix 1
Calculating the Present Value of Free Cash Flow to Equity for Coca-Cola

FCFE0 $3,914

RROR 9.96%

g 5.50%

g* 13.43%

Years 5

Year FCFEt PV(FCFEt)

0 $3,914

1 4,440 4,037

2 5,036 4,165

3 5,712 4,296

4 6,479 4,432

5 7,349 4,572

6 7,754

PV5 169,291

PV(P5) 104,735

PV0 $126,165
FCFE0 Free cash flow to equity at time zero.
FCFE is used as the initial cash flow, FCFE0.
FCFEt The Free Cash Flow to Equity at each year in the future.
FCFE1 to FCFE5 grow at the super-normal growth rate.
We use a super-normal growth rate of 13.43% which is the average growth rate for Coca-Cola over
the company’s life.
FCFE6 The Free Cash Flow to Equity in the sixth year grows over the Free Cash Flow to Equity in year five
by the long-term real growth rate of GDP, 3.6%. Assume that in the long-term, all large firms grow
at the GDP growth rate.

RROR The required rate of return is derived from the CAPM and is 10.08%.

Proceedings of the Academy of Accounting and Financial Studies, Volume 14, Number 1 New Orleans, 2009