# Valuation 101: How to do a discounted cashflow analysis

Sunday, Jan 22 2012 by

## What is a DCF Valuation?

Discounted cash flow (DCF) analysis is a method of valuing the intrinsic value of a company (or asset). In simple terms, discounted cash flow tries to work out the value today, based on projections of all of the cash that it could make available to investors in the future. It is described as "discounted" cash flow because of the principle of "time value of money" (i.e. cash in the future is worth less than cash today).

The advantage of DCF analysis is that it produces the closest thing to an intrinsic stock value - relative valuation metrics such as price-earnings (P/E) or EV/EBITDA ratios aren't very useful if an entire sector or market is overvalued. In addition, the DCF method is forward-looking and depends more on future expectations than historical results. The method is also based on free cash flow (FCF), which is less subject to manipulatio than some other figures and ratios calculated out of the income statement or balance sheet.

DCF does however have its weaknesses as an approach. As it is a mechanical valuation tool, it is subject to the principle of "garbage in, garbage out". In particular, small changes in inputs can result in large changes in the value of a company, given the need to project cash-flow to infinity.  James Montier argues that, "while the algebra of DCF is simple, neat and compelling, the implementation becomes a  minefield of problems" (he cites, in particular, problems with  estimating cash flows and estimating discount rates). Despite the issues, DCF analysis is very widely used and is perhaps the primary valuation tool amongst the financial analyst community. As part of Stockopedia PRO, we provide pre-baked DCF valuation models for all stocks, which you can then modify with your own assumptions.

## So how does it work?

In summary, the key steps in a DCF analysis are as follows:

1. Estimate Cashflows
2. Estimate Growth Profile (1 stage, 2 stage, 3 stage etc) & Growth Rates
3. Calculate Discount Rate
4. Calculate the Terminal Value
5. Calculate fair value of company and its equity

We explain each of these steps in more detail below.

## 1. How do we estimate base cashflow for a DCF?

In a DCF model, the first step is to estimate how much cash that the business will generate and could be paid to the investors.  In the strictest sense, the only cash flow that an investor will receive from an equity investment is the dividend. Actual dividends, however, may be much lower than the potential dividends because i) managers are conservative and like to hold on to cash to meet unforeseen future contingencies and investment opportunities. When actual dividends are less than potential dividends, using a model that focuses only on dividends will understate the true value of the equity in a firm. Some analysts assume that the earnings of a firm represent its potential dividends but this will typically over estimate the value of the equity in the firm. Earnings are not cash flows, since there are both non-cash revenues and expenses in the earnings calculation. This also fails to take into account the need for a firm to invest in new assets in order to grow.

For that reason, the best option is to focus on free cash flow - there are two main such definitions

i) Free Cash Flow to the Firm (FCFF). This is the cash available to bond holders and stock holders after all expense and investments have taken place. It is defined as:

EBIT  * ( 1 - tax rate) - (Capital Expenditures - Depreciation) -  Change in Working Capital.

ii) Free Cash Flow to the Equity (FCFE). This is the cash is available to pay to a company's equity shareholders after accounting for all expenses, reinvestment, and debt repayment. It is defined as:

Net Income - (Capital Expenditures - Depreciation) - Changes in non-cash Working Capital - (Principal Repayments - New Debt Issues) OR alternatively Cash From Operations - (Capital Expenditures - Depreciation)  +  Net Borrowing.

If we are looking to value the equity, then the most obvious option is to use FCFE. FCFF is preferred if the company is unstable or has huge amount of debt because the FCFE might be very low or negative in this case. Basically, the drawback of FCFE is that it will change if the capital structure changes. That is, FCFE will go up if the company replaces debt with equity (an action that reduces interest paid and therefore increases CFO) and vice versa.

## 2. How do we forecast a company's cash-flow growth profile?

The next step is to estimate how fast will the company grow its free cash flow. This is a critical part of any valuation and is typically where the biggest errors creep in. People tend to overestimate how fast a company can grow. First, we need to decide whether how many different stages of growth the DCF will have. A 1 stage DCF model would be used for a company expected to see consistent stable growth. The prevalent form of the DCF model in practice is the two-stage DCF model - this involves  an explicit projection of free cash flows generally for 5-10 years, following which a terminal terminal value is calculated to account for all the cash flows beyond the forecast period - but a more involved 3+ stage DCF model could also be used.

Once this is decided, there are three basic ways of estimating growth for any firm:

i) Extrapolate from historic growth - One option is to use historic growth rates, but unfortunately these rates tend to have considerable noise associated with them. In an study of the relationship between past growth rates and future growth rates, Little (1960) coined the term 'Higgledy Piggledy Growth" because he found little evidence that firms that grew fast in one period continued to grow fast in the next period. In addition, measurement is not straightforward - growth rates can be different depending the period selected or they may be complicated by the presence of negative earnings.

ii) Trust the Analysts - The second approach is to trust the equity research analysts that follow the firm to come up with the right estimate of growth for the firm, and to use that growth rate in valuation. However, the evidence suggests that analysts are very poor forecasters, especially over the long-term. Work by James Montier found that the average 24-month forecast error is around 94%, and the average 12-month forecast error is around 45%.

iii) Fundamental Determinants - With both historical and analyst estimates, growth is treated as an exogenous variable that affects value but  is  divorced  from  the  operating  details  of  the  firm.  As Professor Damodaran notes, the alternative way of incorporating growth into value is to make it endogenous, i.e., to make it a function of how much a firm reinvests for future growth and the quality of its reinvestment. When a firm has a stable return on capital, its expected growth in operating income (and therefore cashflow) is a product of the reinvestment rate, i.e., the proportion of the after-tax operating income that is invested in net capital expenditures and non-cash working capital, and the quality of these reinvestments, measured as the return on the capital invested. The formula is:

Reinvestment Rate * Return on Capital where Reinvestment Rate = Capital Expenditure  - Depreciation  +  Change in Non-cash WC and Return on Capital = EBIT (1-t) / Capital Invested

Option iii) is probably the best option but may feel a bit involved. A simpler approach would be to look at historic growth over the past several years, take an average, and then reduce that in stages. A three-stage model might take the last 3-years' growth rate, apply it to the next five years, chop it in half for the next five years, and then reduce it to 3% (the long term rate of inflation, e.g. no "real" growth) from then on.

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## 3. How do we choose a discount rate?

Having projected the company's free cash flow for the next X years, we need an appropriate discount rate which we can use to calculate the net present value (NPV) of the cash flows. This is a critical ingredient in discounted cashflow valuation. Errors in estimating the discount rate or mismatching cashflows and discount rates can lead to serious errors in valuation. It is important that the Discount Rate should be consistent with the cash flow being discounted. If the cash flows being discounted are cash flows to equity, the appropriate discount rate is a cost of equity. If the cash flows are cash flows to the firm, the appropriate discount rate is the cost of capital (or WACC - the weighted average cost of capital).

### Cost of Equity

Equity shareholders expect to obtain a certain return on their equity investment in a company. From the company's perspective, the equity holders' required rate of return is a cost. However, unlike the cost of debt which is relatively easy to determine from observation of interest rates in the capital markets, a company's current cost of equity is unobservable and must be estimated.

### CAPM

There are various models for doing so, the most commonly accepted of which is the Capital Asset Pricing Model, or CAPM where:

Cost of Equity (Re) = Risk Free Rate (Rf) + Beta * Equity Risk Premium.

To explain these terms:

i) Risk-Free Rate - This is the amount obtained from investing in securities considered free from credit risk, such as US government bonds.

ii) ß - Beta - This measures how much a company's share price moves against the market as a whole. A beta of one, for instance, indicates that the company moves in line with the market. If the beta is in excess of one, the share is amplifying the market's movements; less than one means the share is more stable.

iii) Equity Market Risk Premium - The equity market risk premium represents the returns investors expect, over and above the risk-free rate, to compensate them for taking extra risk by investing in the stock market. In other words, it is the difference between the risk-free rate and the market rate. Practitioners never seem to agree on the premium; it is sensitive to how far back you go in history, what bonds you use as a reference point, and whether you use geometric or arithmetic averages.

While widely used, CAPM has been widely criticised as being empirically flawed - according to Montier, "CAPM woefully under predicts the returns to low beta stocks, and massively overestimates the returns to high beta stocks. Over the long run there has been essentially no relationship between beta and return" - as well as being based on a highly unrealistic set of assumptions. For that reason, it may be better to just adopt a discount rate that seems intuitively consistent with both the riskiness and the type of cashflow being discounted.

Interestingly, Buffett uses something like the thirty-year U.S. treasury bond rate but without a risk premium on the basis that he avoids risks. "I put a heavy weight on certainty.  If you do that, the whole idea of a risk factor doesn't make any sense to me. Risk comes from not knowing what you're doing." (although, presumably, as a value investor, he builds a significant margin of safety elsewhere).

## 4. How do we calculate the Terminal Value?

Instead of trying to project the cash flows to infinity, terminal value techniques are used. One way of calculating the terminal value (TV) is by using the Gordon Growth Model, which essentially assumes that company's cash flow will stabilize after last projected year and will continue at the same rate forever. Here is the formula:

Final Projected Year Cash Flow X (1+Long-Term Cash Flow Growth Rate) / (Discount Rate – Long-Term Cash Flow Growth Rate).

Another possibility of determining terminal value of the company is to use multipliers of income or cash flow measures (net income, net operating profit, EBITDA, operating cash flow or FCF), which are determined with reference to comparable companies on the market.

The TV often represents a large percentage of the total DCF valuation. As Montier notes:

"If  we assume a perpetual growth rate of 5% and a cost of capital of 9% then the terminal  multiple is 25x. However, if we are off by one percent on either or both of our inputs, then  the terminal multiple can range from 16x to 50x!".

Valuation, in such cases, can unfortunately become largely dependent on TV assumptions rather than operating assumptions for the business or the asset.

## Calculate Fair Value of Company & Equity

To arrive at a total company value, or enterprise value (EV), we simply have to take the present value of the cash flows and the Terminal value, divide them by the discount rate and, finally, add up the results. If we are discounting FCFE at the cost of equity, this will give the value of the equity. If we are discounting FCFF at the weighted average cost of capital, this would give the value of the firm, so it would be necessary to deduct net debt in order to arrive at the equity value.

## Conclusions

Although Montier argues that DCF "should be consigned to the dustbin of theory, alongside the efficient markets hypothesis, and CAPM", this seem a little harsh. It is a useful tool, provided that its constraints are clearly understood (e.g. the sensitivity to inputs), and it is best used with other tools such as Earnings Power Value and Relative Value techniques as a sense check. In order to use DCF most effectively, the target company should generally have positive and predictable free cash flows (i.e. typically it's best with mature firms that are past the growth stages). DCF works less well when a company's operations lack "visibility" - i.e, when it's difficult to predict revenue and cost trends with much certainty. DCF analysis also demands vigilance so if Company X delivers disappointing quarterly results, or if interest rates change dramatically, you may need to adjust your assumptions.

Filed Under: Valuation,
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