the weighted average cost of capital;

(4) Abnormal earnings is net income less shareholders™ equity at the beginning of the

year times cost of equity;

(5) Free cash ¬‚ows to debt and equity are NOPAT less the increase in operating working

capital less the increase in net long-term assets; and

(6) Free cash ¬‚ow to equity is net income less the increase in operating working capital

less the increase in net long-term assets plus the increase in net debt.

The weighted average cost of capital (WACC) used is 9.2 percent based on an as-

sumed equity cost of capital of 12 percent, a 5 percent after-tax net interest rate on debt,

and a 40 percent ratio of debt to net capital. Recall that the net interest rate and capital

structure assumptions are among the six assumptions made earlier for forecasting

income statements and balance sheets. Here we needed to make an additional assump-

tion about the ¬rm™s cost of equity capital. We will discuss later in the chapter how to

make assumptions regarding a company™s equity capital.

Recall that the balance sheet at the beginning of 2004 shown in Table 12-2 is based

on the assumption that sales in 2004 will grow at 3.5 percent. If we assume a low growth

in sales, the assumed incremental investments in working capital and long-term assets

in 2003 will also be low. As a result, cash ¬‚ows to debt and equity and cash ¬‚ows to

equity shown in 2003 will show a signi¬cant jump in 2003, as shown in Table 12-3. If

we assumed a larger growth rate in 2004 and beyond, free cash ¬‚ows in 2003 will jump

by a smaller amount. As discussed in Chapter 11, the performance variables forecasted

in Table 12-3 are key inputs into the valuation process. Operating ROA, abnormal

NOPAT, and free cash ¬‚ow to debt and equity can be used to value Sigma™s net capital

Table 12-3 Performance Forecasts for Sigma, Inc.

1999 2000 2001 2002 2003

.............................................................................................................................................

Abnormal operating ROA 7.7% 6.2% 4.6% 3.1% 1.6%

Abnormal ROE 12.9% 10.3% 7.7% 5.2% 2.6%

Abnormal NOPAT (millions) $55.2 $48.6 $40.2 $29.2 $16.4

Abnormal earnings (millions) $55.2 $48.6 $40.2 $29.6 $16.4

Free cash ¬‚ow to debt and equity

(millions) $49.5 $42.4 $33.3 $22 $76.1

Free cash ¬‚ow to equity (millions) $63.8 $58.1 $50.6 $41 $69.8

.............................................................................................................................................

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Prospective Analysis: Valuation Implementation

12-5 Part 2 Business Analysis and Valuation Tools

(or net assets); ROE, abnormal earnings, and free cash ¬‚ow to equity can be used in val-

uing Sigma™s equity.

Table 12-4 shows present values of the performance variables by year. Present values

of abnormal NOPAT and free cash ¬‚ow to debt and equity are computed using a WACC

of 9.2 percent; present values of abnormal earnings and free cash ¬‚ow to equity are com-

puted using a cost of equity of 12 percent. To calculate the present values of abnormal

operating ROA and abnormal ROE, the values for each year are ¬rst multiplied by the

corresponding growth factor, as shown in the formulae in Chapter 11, and then they are

discounted using a WACC of 9.2 percent and cost of equity of 12 percent, respectively.

To complete the valuation task, however, we also need to estimate the terminal value

of Sigma at the end of the detailed forecasting horizon, the end of year 2003. We will,

therefore, turn to the discussion of how to estimate terminal values next.

Table 12-4 Present Values of Performance Forecasts for Sigma, Inc.

Total for

1999 2000 2001 2002 2003 1999“2000

............................................................................................................................................................

Discount factor for asset ¬‚ows 0.916 0.839 0.768 0.703 0.644 N/A

Discount factor for equity ¬‚ows 0.893 0.797 0.712 0.636 0.567 N/A

Growth factor 1.000 1.100 1.210 1.331 1.464 N/A

PV of abnormal operating ROA 0.071 0.057 0.043 0.029 0.015 0.215

PV of abnormal ROE 0.115 0.090 0.067 0.044 0.022 0.338

PV of abnormal NOPAT (millions) $50.6 $40.8 $30.9 $20.8 $10.6 $153.7

PV of abnormal earnings (millions) $49.3 $38.8 $28.6 $18.8 $9.3 $144.8

PV of free cash ¬‚ow to debt and

equity (millions) $45.3 $35.5 $25.6 $15.4 $49.0 $170.8

PV of free cash ¬‚ow to equity

(millions) $57.0 $46.3 $36.0 $26.1 $39.6 $205

............................................................................................................................................................

Notes:

1. Discount factor for asset flows and equity flows are computed using WACC (9.2 percent) and cost of equity (12 per-

cent). The value for year t is equal to 1/(1 + r) t where r is the appropriate discount rate.

2. Growth factor is computed using the assumed sales growth rate of 10 percent in all the years. The value for year t is

equal to (1 + g) t - 1.

3. Present values of abnormal operating ROA and abnormal ROE are equal to their respective values in each year

times the growth factor times the appropriate discount factor.

4. Present values of abnormal NOPAT, abnormal earnings, free cash flow to debt and equity, and free cash flow to

equity are equal to their respective values in each year times the appropriate discount factor.

TERMINAL VALUES

The forecasts in Table 12-2 extend only through the year 2003, and thus we label 2003

the “terminal year.” (Selection of an appropriate terminal year is discussed later.) Termi-

nal value is essentially the present value of either abnormal earnings or free cash ¬‚ows

466 Prospective Analysis: Valuation Implementation

12-6

Prospective Analysis: Valuation Implementation

occurring beyond the terminal year. Since this involves forecasting performance over the

remainder of the ¬rm™s life, the analyst must adopt some assumption that simpli¬es the

process of forecasting. Below, we discuss a variety of alternative approaches to this task.

Terminal Values with the Competitive Equilibrium Assumption

Table 12-2 projects that until the year 2003, Sigma™s sales, earnings, and cash ¬‚ows from

operations will all grow at an annual rate of 10 percent. What should we assume beyond

2003? Is it reasonable to assume a continuation of the 10 percent growth rate? Is some

other pattern more reasonable?

One thing that seems clear is that continuation of a 10 percent sales growth rate is un-

realistic over a very long horizon. That rate would likely outstrip in¬‚ation in the dollar

and the real growth rate of the world economy. Over many years, it would imply that

Sigma would grow to a size greater than that of all other ¬rms in the world combined.

But what would be a suitable alternative assumption? Should we expect the ¬rm™s sales

growth rate to ultimately settle down to the rate of in¬‚ation? Or to a higher rate, such as

the nominal GNP growth rate? Or to something else?

Ultimately, to answer these questions, one must consider how much longer the rate

of growth in industry sales can outstrip the general growth in the world economy, and

how long Sigma™s competitive advantages can enable it to grow faster than the overall

industry. Clearly, looking six or more years into the future, any forecasts of sales growth

rates are likely to be subject to considerable error.

Fortunately, in many if not most situations, how we deal with the seemingly impon-

derable questions about long-range growth in sales simply does not matter very much!

In fact, under plausible economic assumptions, there is no practical need to consider

sales growth beyond the terminal year. Such growth may be irrelevant, so far as the

¬rm™s current value is concerned!

How can long-range growth in sales not matter? The reasoning revolves around the

forces of competition. Competition tends to constrain a ¬rm™s ability to identify, on a

consistent basis, growth opportunities that generate supernormal pro¬ts. (Recall the ev-

idence in Chapter 10 concerning the reversion of ROEs to normal levels over horizons

of ¬ve to ten years.) Certainly, a ¬rm may at a point in time maintain a competitive ad-

vantage that permits it to achieve returns in excess of the cost of capital. When that ad-

vantage is protected with patents or a strong brand name, the ¬rm may even be able to

maintain it for many years, perhaps inde¬nitely. With hindsight, we know that some such

¬rms”like Coca-Cola and Wal-Mart”were able not only to maintain their competitive

edge, but to expand it across dramatically increasing investment bases. But in the face

of competition, one would typically not expect a ¬rm to extend its supernormal pro¬t-

ability to new additional projects year after year. Ultimately, we would expect high

pro¬ts to attract enough competition to drive the ¬rm™s return down to a normal level.

Each new project would generate cash ¬‚ows with a present value no greater than the cost

of the investment”the investment would be a “zero net present value” project. Since the

467

Prospective Analysis: Valuation Implementation

12-7 Part 2 Business Analysis and Valuation Tools

bene¬ts of the project are offset by its costs, it does nothing to enhance the current value

of the ¬rm, and the associated growth can be ignored.

Table 12-5 presents a simple illustration to clarify the point. In it we consider a wide

range of growth in sales for the year 2004: no growth at all, 5 percent growth, and 10

percent growth. The NOPAT margin is assumed to drop to 5.98 percent; all other assump-

tions (including the cost of equity) are expected to remain the same as in the years 1999

to 2003. Under these assumptions, the table shows that the sales growth”whether zero,

5 percent, or 10 percent”does nothing to enhance the current value of the ¬rm.

The key assumption is that the NOPAT margin is 5.98 percent of sales. Under that as-

sumption, Sigma™s operating ROA is equal to its weighted average cost of capital, its

ROE is equal to its cost of equity, and the ¬rm earns no abnormal NOPAT or abnormal

earnings. While the ¬rm generates positive free cash ¬‚ows, they are just suf¬cient to

cover the capital charge on the investments in working capital and long-term assets re-

quired to generate the incremental sales. These conclusions remain unchanged whatever

is the growth rate in sales.

The assumption about the NOPAT margin is not arbitrary, but based on the notion that

over the long run, competitive forces drive margins to the point of costs. Margins any

higher than this attract competition and force margins down. Margins below this level

drive investment away until margins recover.

When we invoke the competitive equilibrium assumption during the terminal years,

it is straightforward to determine what the terminal values will be. These are shown in

Table 12-6, assuming a sales growth of 3.5 percent in 2004 and beyond. Since abnormal

NOPAT and abnormal earnings are zero in years beyond 2003, terminal values for these

Table 12-5 Sigma™s Financial Forecasts Beyond the Terminal Year

Under Alternative Growth Assumptions and No Abnormal Earnings

Forecasted Financial Performance in 2004 and Beyond

...............................................................................................................................................

Assumed sales growth 0% 5% 10%

Assumed NOPAT margin 5.98% 5.98% 5.98%

Sales (millions) $1,611 $1,691 $1,772

NOPAT (millions) $96 $101 $106

Net income (millions) $75 $79 $83

Assets at the beginning of the year (millions) $1,047 $1,099 $1,152

Equity at the beginning of the year (millions) $628 $660 $691

Abnormal operating ROA 0% 0% 0%

Abnormal ROE 0% 0% 0%

Abnormal NOPAT $0 $0 $0

Abnormal earnings $0 $0 $0

...............................................................................................................................................

468 Prospective Analysis: Valuation Implementation

12-8

Prospective Analysis: Valuation Implementation

two variables are zero. Since free cash ¬‚ows are essentially equal to the capital charge,

terminal values for free cash ¬‚ow to capital and free cash ¬‚ow to equity are the same as

the book values of capital and equity in Table 12-2, respectively.

Terminal value estimation does not require this “competitive equilibrium assump-

tion.” If the analyst expects that supernormal margins can be extended to new markets

for many years, it can be accommodated within the context of a valuation analysis. At a

minimum, as we will discuss in the next section, the analyst may expect that supernor-

mal margins can be maintained on the existing sales base, or on markets that grow at the

rate of in¬‚ation. However, the important lesson here is that the rate of growth in sales

beyond the forecast horizon is not a relevant consideration unless the analyst believes

that the growth can be achieved while generating supernormal margins”and competi-

tion may make that a dif¬cult trick to pull off.

Table 12-6 Sigma™s Terminal Values with No Abnormal Earnings Beyond

the Terminal Year

Present value of ¬‚ows

beyond 2003 (at the

Present value of ¬‚ows beginning of 1999),

beyond 2003 (at the or

Valuation attribute beginning of 2004) Terminal value

.......................................................................................................................................

Abnormal operating ROA 0 0

Abnormal ROE 0 0

Abnormal NOPAT 0 0

Abnormal earnings 0 0

Free cash ¬‚ow to debt and Book value of net assets at the

1083 / (1.092)5 = $697.8

equity (millions) beginning of 2004 = $1,083

Free cash ¬‚ow to equity Book value of equity at the

650/ (1.12)5 = $368.9

(millions) beginning of 2004 = $650

.......................................................................................................................................

Terminal Values with Competitive Equilibrium

Assumption Only on Incremental Sales

An alternative version of the competitive equilibrium assumption is to assume that Sig-

ma will continue to earn abnormal earnings forever on the sales it had in 2003, but there

will be no abnormal earnings on any incremental sales beyond that level. That is, the

NOPAT margin in 2004 and beyond will remain at 7 percent on the sales level achieved

in 2003; the NOPAT margin on any incremental sales will be 5.98 percent, leading to zero

incremental value from these sales.

If we invoke the competitive equilibrium assumption on incremental sales for years

beyond 2004, then it does not matter what sales growth rate we use beyond that year, and

469

Prospective Analysis: Valuation Implementation

12-9 Part 2 Business Analysis and Valuation Tools

we may as well simplify our arithmetic by treating sales as if they will be constant at the