Earnings and cash flow
Cash flow and cash flow
Valuation with the WACC model: Overview
Valuation with the WACC model: An example
The big picture
Excel section
Challenge section
T
here is little question that the technically correct way of valuing a company is with the discounted cash flow (DCF) model. As we discussed in the previous chapter, this model has many variations depending on the definition of cash flow and the discount rate used. In this chapter we’ll discuss the weighted-average cost of capital (WACC) model, the most widely used version of the DCF model.Earnings and cash flow
It is often said that earnings are an opinion and cash flows are a fact. And it is largely true. As a matter of fact, the accounting scandals of the past few years did nothing but reinforce this idea. Regardless of what accountants report, at the end of the day investors care about the ability of companies to generate cash. And that is the ultimate goal of all DCF models: to forecast the generation of cash, to account for the risk of that cash, and to bring both together into the estimation of an intrinsic value.
But before we go any further, a fair warning. We’ll be giving names to several concepts, and you may have seen the same or similar concepts named differently elsewhere. In fact, it would be surprising if you had not. Accountants agree on names just as much as traders do on whether the market will be up or down tomorrow. That’s one reason for trying to keep the discussion down to the essentials.
Let’s start by considering Table 14.1. The left column shows a simplified income statement. Beginning from the revenues generated by the company, we subtract all operating costs (cost of goods sold; selling, general, and administrative expenses; and so on), depreciation and amortization, the interest expense (if any), and taxes to arrive at the company’s net income. That is what accountants usually refer to as the company’s earnings.
TABLE 14.1
Revenue Net income
– Operating costs + Depreciation and amortization – Depreciation and amortization – Net capital expense
= Earnings before interest and taxes (EBIT) – Increase in net working capital
– Interest = Equity Free Cash Flow (EFCF)
= Earnings before taxes + After-tax interest
– Taxes = Capital free cash flow (CFCF)
= Net income
However, there are many reasons why this net income is not a proper measure of cash generation. Recall, first, that depreciation and amortization are non-cash charges, that is, they reduce earnings but do not affect cash flows.
Recall, also, that the net income does not reflect changes in working capital or in fixed capital, both of which do affect cash flows.
In order to properly account for the inflows and outflows of cash, we start by adding back to the net income the non-cash charge of depreciation and amortization. Then we subtract the net capital expense, which is the difference between investments on and sales of fixed assets. And then we subtract the increasein net working capital, which consists of the cash contribution to the day-to-day operations of the company. The end result of this is what we’ll call the equity free cash flow (EFCF), also called free cash flow to equity or levered free cash flow, which is given by
EFCF = Net income + Depreciation and amortization – Net capital expense
– Increase in net working capital (14.1)
Finally, if we add the after-tax interest payments we get the capital free cash flow (CFCF), also called free cash flow to the firm or unlevered free cash flow, which is given by
CFCF = Net income + Depreciation and amortization – Net capital expense – Increase in net working capital + After-tax interest (14.2)
Cash flow and cash flow
Let’s think a bit about these two definitions of cash flow. We can think of the EFCF as the cash available to the shareholders of a company. More precisely, this is the cash available to the shareholders after the company has paid interest to the debt holders and taken care of fixed capital and working capital requirements. We can also think of the EFCF as the highest dividend the company could afford to pay with the cash generated in any given period.
The CFCF, on the other hand, is the cash available to all the providers of capital after taking into account fixed capital and working capital requirements.
In our somewhat-simplified discussion, this is the cash available to shareholders
and debt holders. If the company had raised capital through additional sources of financing, such as preferred stock, then the CFCF would also include the cash available to preferred shareholders (in which case we would have to add a line between EFCF and CFCF in Table 14.1 with the preferred dividends). Note, then, that the main difference between CFCF and EFCF arises from claims to cash from non-equity holders.
There is another way of thinking of the difference between CFCF and EFCF and it is related to the impact of leverage on cash flows. The argument, in a nutshell, is this: the EFCF depends on the company’s capital structure (that is, on its combination of debt and equity) whereas the CFCF does not. To see this, take a look at Table 14.2, which displays the calculation of the EFCF and the CFCF for a company under three different capital structures. This company borrows at 5% and pays taxes at the corporate tax rate of 35%.
TABLE 14.2
0% Debt 20% Debt 40% Debt
$ $ $
Debt 0 2,000 4,000
Equity 10,000 8,000 6,000
Capital 10,000 10,000 10,000
Income Statement
$ $ $
Revenues 10,000 10,000 10,000
Operating costs –6,000 –6,000 –6,000
Depreciation –1,000 –1,000 –1,000
EBIT 3,000 3,000 3,000
Interest 0 –100 –200
Earnings before taxes 3,000 2,900 2,800
Taxes –1,050 –1,015 –980
Net Income 1,950 1,885 1,820
FCF calculation
$ $ $
Net income 1,950 1,885 1,820
Depreciation 1,000 1,000 1,000
Net capital expense –1,000 –1,000 –1,000
Increase in NWC –500 –500 –500
EFCF 1,450 1,385 1,320
After-tax interest 0 65 130
CFCF 1,450 1,450 1,450
Note that the more the company borrows, the higher the interest expense, and the lower that both the net income and the EFCF are. (In this example, the only difference between net income and EFCF stems from the $500 increase in net working capital, because depreciation and the net capital expense cancel each other out.) But note that the decrease in both net income and EFCF is not equal to the full amount of the interest payment; rather, it is equal to the after- taxinterest payment, which accounts for the tax shield provided by debt. This after-tax payment is calculated simply as (1 – tc) · (Interest), where tc is the corporate tax rate.
Finally, the last line shows that the CFCF, the cash available to all the providers of capital, remains unchanged in the presence of leverage. Therefore, we can think of the CFCF as the free cash flow delivered by the company independently from its capital structure, or, alternatively, as the free cash flow of the unlevered company.
Valuation with the WACC model: Overview
As we discussed in the previous chapter, the underlying idea behind all DCF models is to discount cash flows at a rate consistent with their risk, which means that given the definition of cash flow the appropriate discount rate follows. The dividend discount model (DDM) we discussed in the previous chapter discounts expected dividends at the cost of equity. The WACC model we discuss in this chapter discounts expected capital free cash flowsat the cost of capital (or, more precisely, at the weighted-average cost of capital, which is where the name of this method comes from).
Formally, the WACC model can be expressed as
(14.3)
where Vdenotes the value of the company, E(CFCFt) the expected capital free cash flow in period t, TVa terminal value, RWACCthe (weighted-average) cost of capital, and T the number of periods for which cash flows are forecasted. The cost of capital, in turn, is given by
RWACC= (1 – tc) · xD· RD+ xE· RE (14.4) V= E(CFCF1)
+ E(CFCF2)
+ . . . + E(CFCFT) + TV (1 + RWACC) (1 + RWACC)2 (1 + RWACC)T
where RDand REdenote the required return on debt and the required return on equity, xD and xE denote the proportions of debt and equity (measured at market value) in the company’s capital structure, and tc denotes the corporate tax rate. The debt considered for the estimation of the cost of capital is interest- bearing (usually long-term) debt. Both the CAPM (the model most widely used to estimate the required return on equity) and the cost of capital are discussed in more detail in Chapter 7.
Before we apply this model to the valuation of a company, several issues are worth discussing. First, the terminal value (TV) is the last cash flow to be discounted and attempts to summarize in a single number all the cash flows from that point on. It can be estimated in different ways, although a growing perpetuity or a multiple of some fundamental variable are the two most widely used alternatives.
Second, the standard implementation of the WACC model consists of estimating one or more short-term rates of growth for the cash flows as well as a terminal value. Although short-term growth rates can be as high as it may be plausible to assume given the characteristics of the company, if the terminal value is estimated as a growing perpetuity the ‘6% restriction’ applies. That is, in the long term, it doesn’t make sense to assume a rate of growth in cash flows beyond the growth rate of the overall economy.
Third, it is essential to note that equation (14.3) does not yield the value of the company’s equity but the value of the equity plus debt. Note that the CFCFs we’re discounting are those to be distributed to shareholders and debt holders; therefore, the present value we’re calculating is that of equity and debt. The important implication of this fact is that after arriving at an estimate of the value of the company using equation (14.3), in order to estimate the value of the company’s equity we need to subtract the market value of long- term debt outstanding. (If you buy a house valued at $100,000 for which the owner has a mortgage and still owes $40,000, you would only pay $60,000. The remaining $40,000 is the debt you will be assuming.)
Finally, although the DDM is typically used in a way that yields the value of a company’s share, the WACC model is typically used in a way that yields the value of the company’s equity. Therefore, in order to estimate the intrinsic value of an individual share, we need to divide the resulting value of the equity by the number of shares outstanding.
Valuation with the WACC model: An example
In 2003, Dell delivered a profit of $2.6 billion on revenues of $41.4 billion. On January 30, 2004, when Dell’s fiscal year 2003 concluded, the company’s market cap was $85.5 billion and its stock price $33.44. At the same time, Dell’s earnings per share (EPS) and price/earnings (P/E) ratio were $1.01 and 33, respectively. Our goal is to use the WACC model to assess the value of Dell at the end of January 2004.
Before we get to the numbers, bear this in mind: our goal is to illustrate the use of the WACC model, not to make a strong statement about Dell’s intrinsic value. For the latter we would have to think long and hard about the most appropriate assumptions for the analysis. The assumptions we’ll discuss below are plausible, but not necessarily those that a more thorough analysis of the company would yield. Having said that, take a look at the most relevant items of Dell’s balance sheet, income statement, and cash flow statement for fiscal year 2003, displayed in Table 14.3.
TABLE 14.3
Balance sheet ($m) Income statement ($m)
Cash and equivalents 4,317 Revenue 41,444
Other current assets 6,316 Cost of goods sold –33,629 Total current assets 10,633 Selling, general, and administrative –3,544
Net fixed assets 1,517 R&D –464
Other non-current assets 7,161 Depreciation and amortization –263
Total assets 19,311 EBIT 3,544
Accounts payable 7,316 Net interest 180
Other current liabilities 3,580 Earnings before taxes 3,724
Total current liabilities 10,896 Taxes –1,079
Long-term debt 505 Net Income 2,645
Other non-current liabilities 1,630
Total liabilities 13,031 Cash flow statement (excerpt, $m)
Equity 6,280 Net capital expense –329
Total liabilities and equity 19,311 Change in net working capital –872
Other –110
Free cash flow estimation
Our first step is to estimate Dell’s CFCF based on the company’s financial statements. The calculation and final result are displayed in Table 14.4, where all numbers are in millions.
TABLE 14.4
$m
Net income 2,645
+ Depreciation and amortization 263
– Net capital expense –329
– Increase in net working capital 872
– Other –110
EFCF 3,341
+ After-tax interest 10
CFCF 3,351
A few things are worth mentioning. First, Dell actually decreasedits working capital by $872 million, which has a positive impact on its CFCF. Second, the
‘Other’ item consists of several adjustments (such as exchange rate effects) that had a negative impact on Dell’s cash flow. Third, of the positive $180 million of net interest in Dell’s income statement, $14 million were interest payments.
Therefore, the after-tax interest payment is (1 – 0.29) · ($14m) = $9.94m ≈
$10m. (For a variety of reasons, Dell pays taxes at the rate of 29%, lower than the statutory rate of 35%.)
We now have to make some assumptions about how the CFCFs are going to evolve over time. Let’s assume first that over the next five years (2004 to 2008), Dell’s CFCFs will increase at the annual rate of 17%; this is actually the rate at which analysts expect Dell to increase its earnings during the same period. Let’s also assume that over the following five years (2009 to 2013), Dell’s CFCFs will slow down and increase at the annual rate of 10%. And let’s finally assume that, from that point on, Dell’s CFCFs will grow along with the economy at the annual rate of 6%. The expected CFCFs that follow from these assumptions are displayed in Table 14.5.
TABLE 14.5
Year CFCF Year CFCF
($) ($)
2004 3,921 2010 8,890
2005 4,587 2011 9,779
2006 5,367 2012 10,756
2007 6,279 2013 11,832
2008 7,347 TV 161,956
2009 8,081
Note that the last number in the table, roughly $162 billion, is the terminal value (TV) and is calculated as the present value of CFCFs growing at 6% in perpetuity from 2013 on. (If you have read the previous chapter, after estimating Dell’s cost of capital below, you should have no difficulty in calculating this number yourself.)
Cost of capital estimation
Having an estimate of the expected CFCFs we now have to estimate the discount rate that captures their risk, that is, Dell’s cost of capital. All the magnitudes relevant for its calculation are displayed in Table 14.6.
TABLE 14.6
(Long-term) debt Equity
6.55% Fixed-rate senior notes CAPM-related magnitudes
Book value $200m Risk-free rate 4.1%
Interest rate 6.55% Market risk premium 5.5%
Market value $227.6m Beta: 1.8
Yield 3.50%
Due April 15, 2008 Other equity-related magnitudes 7.10% Fixed-rate senior debentures Stock price $33.44
Book value $300m Shares outstanding 2,556,000
Interest rate 7.10% Market value $85.5bn
Market value $358.1m
Yield: 5.77%
Due: April 15, 2028
Let’s start with the debt. Dell has two types of interest-bearing (long-term) debt relevant for the calculation of the cost of capital; their book value, market value, interest rate, yield, and maturity date are all displayed in Table 14.6. Note that both bonds have a yield lower than their respective interest rate. (The difference between these two concepts is discussed in Chapter 18.) The total amount of long-term debt at market value is $585.7 million. We can estimate the required return on debt (RD) as the weighted average of the return required on these two types of debt. That is,
RD= ($227.6m/$585.7m) · (0.0350) + ($358.1m/$585.7m) · (0.0577) = 4.9%
Now to the required return on equity, which we can estimate with the CAPM.
Given the 4.1% yield on ten-year US Treasury notes, the historical market risk premium of 5.5%, and the beta of 1.8, Dell’s required return on equity (RE) is
RE= (0.041) + (0.055) · (1.8) = 13.8% .
Finally, we need to calculate the proportions of debt and equity at market value. The total amount of long-term debt is $585.7 million. Given Dell’s share price of $33.44 and the 2,556,000 shares outstanding, the market value of equity is $85,472.6 million. Therefore, the total amount of capital is equal to $86,058.3 million. The proportions of debt and equity follow directly and are calculated as
$585.7m/$86,058.3m = 0.7% and $85,472.6m/$86,058.3m = 99.3%. Essentially, Dell is an unlevered company fully financed by equity.
Putting together the required returns on debt and equity, the proportions of debt and equity, and Dell’s corporate tax rate (29%), we get that the company’s cost of capital is
RWACC= (1 – 0.29) · (0.007) · (0.049) + (0.993) · (0.138) = 13.7%
Discounting the CFCFs in Table 14.5 at this cost of capital, we get
Recall, however, that this is the value of bothDell’s equity and debt. Therefore, to get an estimate of the value of Dell’s equity, we need to subtract from this figure the market value of long-term debt. After doing so, we get $80,399.6m –
$585.7m = $79,813.9m.
Finally, dividing this number by the number of shares outstanding we get
$79,813.9m/2,556m = $31.2. If we believe our assumptions, then, we should conclude that at $33.44 Dell is slightly overpriced. (However, note that Dell’s EPS between 1994 and 2003 grew at an annual rate of over 47%. Perhaps the market is reasonably expecting from Dell a higher short-term growth than we assumed. Again, you should interpret our valuation more as an illustration of the WACC model than as a strong statement on Dell’s valuation.)
V= $3,921m
+ $4,587m
+ . . . + $11,832m + $161,956m
= $80,399.6m (1.0137) (1.0137)2 (1.0137)10
The big picture
The WACC model is the most widely used version of the DCF model, and for good reason. Unlike the DDM, the WACC model enables analysts to perform a detailed analysis and prediction of different components of a company’s financial statements, and to assess their impact on both free cash flows and intrinsic value. In this regard, spreadsheets have become an inseparable component of valuation with the WACC model.
All versions of the DCF model discount cash flows at a rate that appropriately captures their risk. The WACC model, in particular, discounts CFCFs at the cost of capital. It therefore yields the value of the whole company, not just the value of the equity. This means that the market value of the claims of non-equity holders must be subtracted from the present value of CFCFs in order to find the intrinsic value of the company’s equity.
Although, in theory, all versions of the DCF model should yield the same value of a company’s equity, in practice there are situations in which implementing one version is easier than implementing some other. That’s why it pays to discuss two other versions of the DCF model, and that is exactly what we’ll do in the next chapter.
Excel section
There is no new Excel material in this chapter.
Challenge section
1 In 2003, Oracle delivered a profit of $2.7 billion on revenues of $10.2 billion. On May 30, 2004, when Oracles’s fiscal year 2003 concluded, the company’s market cap was $58.9 billion and its stock price $11.40.
At the same time, Oracle’s earnings per share (EPS) and price/earnings (P/E) ratio were $0.50 and 23, respectively. Tables 14.7 and 14.8 display information relevant for the valuation of Oracle at the end of May 2004.
TABLE 14.7
Balance Sheet ($m) Income statement ($m)
Cash and equivalents 4,138 Revenue 10,156
Other current assets 7,198 Cost of goods sold –2,083 Total current assets 11,336 Selling, general, and administrative –3,975 Net fixed assets 1,068 Depreciation and amortization –234
Other non-current assets 359 EBIT 3,864
Total assets 12,763 Interest income 102
Accounts payable 191 Interest expense 21
Other current liabilities 4,081 Earnings before taxes 3,945
Total current liabilities 4,272 Taxes –1,264
Long-term debt 163 Net Income 2,681
Other non-current liabilities 333 Cash flow statement (excerpt, $m) Total liabilities 4,768 Net capital expense –189 Equity 7,995 Change in net working capital –60
Total liabilities and equity 12,763 Other –202
TABLE 14.8
(Long-term) debt Equity
6.91% Senior notes CAPM-related magnitudes
Book value $163m Risk-free rate: 4.7%
Interest rate 6.91% Market risk premium: 5.5%
Market value $165.5m Beta: 1.7
Yield 3.66%
Due: February 2007 Other equity-related magnitudes
Stock Price $11.40
Shares outstanding 5,171,000
Market value $58.9bn
Using the information provided in Tables 14.7 and 14.8, and a corporate tax rate of 35%, calculate Oracle’s EFCF and CFCF for the fiscal year 2003. (Note that during fiscal year 2003 Oracle decreased its net working capital by $60 million.)
2 Assuming that Oracles’s CFCF will increase at the annual rate of 10%
over the next five years, at the annual rate of 8% over the following five years, and at 6% a year from that point on, calculate Oracle’s expected CFCFs.