Valuation: Discounted Cash Flow Analysis

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If there are simpler valuation methods out there that give accurate estimates for the value of a company, why do we need to use a discounted cash flow analysis (DCF)? In short, a DCF analysis can be adjusted to a very specific situation, whereas comparable companies and other forms of valuation are more generic.

For example, a private equity firm that is looking to purchase a company may place a lower value on it than would another company within the specific industry. Another company — or strategic acquirer — may be able to realize significant cost savings in a merger and thus be willing to pay more than a PE firm that cannot realize such savings.

Cost savings such as these can be incorporated into a DCF analysis in a way that other forms of valuation cannot. Thus, a DCF model can be used to determine the upper end of a negotiation range for acquiring a company.

The Big Picture

So how do we get started with a DCF analysis? The concept is simple: we forecast the company’s free cash flows and then discount them to the present value using the company’s weighted-average cost of capital (WACC).

Forecasting free cash flows and calculating WACC, however, can be a bit more complicated. To illustrate a DCF analysis, let’s look at a hypothetical private discount retail company. We’ll forecast its free cash flow, calculate its WACC and determine its valuation.

Forecasting Free Cash Flow

Forecasting free cash flows is an art. There are many things that can impact cash flows and as many as possible should be taken into account when making a forecast:

What is the outlook for the company and its industry?
What is the outlook for the economy as a whole?
Is there any factors that make the company more or less competitive within its industry?

The answers to these questions will help you to adjust revenue growth rates and EBIT margins for the company. For our hypothetical company, let’s assume a normal economic outlook for the future, a positive outlook for the industry and an average outlook for our company.

Given these assumptions, we can simply look at our company’s historical performance and continue this performance out into the future. Looking at our company’s revenues for the past three years, we can calculate the compound annual growth rate (CAGR) and use it to forecast revenue for the next five years. The formula for calculating CAGR is:

(Year 3 Revenue/Year 1 Revenue)^(1/2 Years of Growth)-1

Next, let’s calculate the company’s EBIT margin so that we can forecast earnings before interest and taxes. The formula for EBIT margin is simply EBIT over Revenues. To forecast EBIT we simply multiply our forecasted revenues by our EBIT margin.

The Taxman Cometh

To get to free cash flows, we now need to forecast taxes and make certain assumptions about the company’s needs for working capital and capital expenditures. We calculate our company’s tax rate by dividing the company’s historical tax expenses by its historical earnings before taxes (EBIT less interest expense). We can then forecast tax expenses by multiplying the tax rate by our forecasted EBIT for each year.

Once we have after-tax income forecasted (EBIT – taxes), we need to add back depreciation and amortization, subtract capital expenditures and subtract working capital investments. We can forecast depreciation and amortization expenses by calculated their percentage of historical revenues and multiplying that percentage by forecasted revenues.

Capital expenditures are made to upgrade depreciating equipment and invest in new assets and equipment for growth. Although capital expenditure is typically higher than depreciation and amortization for growing companies, we will make the simple assumption that capital expenditure is equal to depreciation and amortization in order to forecast capital expenditures in the future.

Finally, we need to forecast working capital investments. In order to grow the business, we would need a growing amount of working capital on the balance sheet in order to achieve higher revenues. This addition of capital to the balance sheet would result in a negative cash flow. For our model we will assume that working capital needs to grow by 1% of revenue, therefore our working capital investment forecast would simply be 1% multiplied by our forecasted revenues.

We can now get to free cash flow by adding depreciation and amortization to after-tax income and subtracting capital expenditure and working capital investment.

Terminal Value

If we were to take the net present value of these cash flows, we would be grossly understating the value of the company. We would be leaving out the value of the company’s cash flows beyond five years. In order to capture this value, we need to calculate the company’s terminal value (the value of the company in year five or the last year in our DCF analysis).

Terminal value can be calculated a couple of ways — with a perpetuity calculation or an exit multiple calculation. The perpetuity calculation is like a mini DCF analysis of the company’s cash flows off into infinity. The calculation of the perpetuity value is as follows:

Cash Flow in Terminal Year / (WACC – Long-Term Growth)

The exit multiple method is similar to a comparable companies analysis. You pick a valuation multiple for data point you have forecasted and multiply it by the data point to get the company’s valuation at that point in time.

Since we haven’t yet calculated our company’s WACC, we’ll use the exit multiple method and simply multiply our EBIT value in year five by a multiple of seven to calculate our terminal value. We can get an accurate multiple for our company by pulling a few public comps and seeing where the range of multiples currently falls in today’s marketplace.

Finally, we add this terminal value to our cash flow in year five to get our five years of free cash flows. Now all we need to do is discount these cash flows by the company’s WACC to determine the enterprise value.

Taking a WACC

The weighted average cost of capital or WACC represents weighted average price a company must pay for debt or equity capital. The formula for WACC is straightforward:

WACC = Cost of Debt * Debt / (Debt + Equity) + Cost of Equity * Equity / (Debt + Equity)

The weightings of capital in this equation are very easy to calculate based on the company’s current balance sheet. The cost of debt is a little more involved, but pretty straightforward, but the cost of equity calculation can be difficult.

For a company with publicly traded debt, you would need to look up the current yield to maturity for each piece of debt that it has outstanding. You would also need to look at the rate paid on each piece private debt on the company’s balance sheet. You then take the weighted average of all these yields and rates to come up with company’s cost of debt.

Since our hypothetical discount retail company only has private debt, we can calculate it’s cost of debt by dividing its last year of interest expenses by the average of its debt balances from the current year and the previous year.

Cost of Equity

The cost of equity in our WACC computation can be represented by the capital asset pricing model (CAPM):

Ke = Rf + Beta (market risk premium) + (other company-specific premiums)

In this equation, Ke is the cost of equity and Beta is a measure of how the value of a company moves with respect to the value of the overall market. The market risk premium is the premium that investors demand to invest in the stock market versus the U.S. treasury market. Other premiums might include a “small cap premium” or a “private company premium.”

The market risk premium as well as other premiums are often taken from a source such as Ibbotson. In general the market risk premium is usually somewhere between 7 and 8%. The risk free rate is usually assumed to be a medium-term U.S. treasury yield (1-10 years).

Calculating Beta is the fun part. Since Beta is a measure of how a stock moves with the overall market, you would calculate it by doing a regression analysis of the stocks performance against a broad index such as the S&P 500. Fortunately, many stock information services such as Bloomberg or Yahoo Finance have already calculated Beta for stocks.

The problem with these Betas is that they are levered Betas. We need an unlevered Beta for our cost of equity calculation. The reason we need an unlevered Beta is that the amount of debt or leverage that a company has can affect its Beta. And since a potential acquirer of a company could choose to significantly alter its capital structure, we should take out the effect of leverage to have a better sense of the company’s value.

Unlevering a Beta

Unlevering a Beta can be a tricky process. The formula for an unlevered Beta is as follows:

Unlevered Beta = Equity Beta / [ 1 + (1 – tax rate) * Debt / Equity]

The equity Beta would be the Beta you get from Yahoo Finance on the Key Statistics page. You can calculate the company’s tax rate by dividing tax expenses by before tax income on the company’s income statement. Debt is the company’s total debt. Equity in this case is the market value of the company’s equity — its market capitalization.

Beta Comps

As if calculating an unlevered Beta were not tricky enough, our hypothetical company is private, and therefore, we can’t calculate a Beta since it is not publicly traded. Instead, we must analyze industry comparables to find and average or median unlevered Beta as an approximation for our company’s Beta.

What this means is that we need to look up public comps for our company, calculate each of their unlevered Betas and take an average. Since our company is a discount retailer, we’ll use Wal-mart, Target, CostCo and BJ’s as our comps.

Now that we have an approximation for our company’s Beta, we can plug all our variables into capital asset pricing model to calculate our cost of equity. We can now take the weighted average of our cost of equity and cost of debt using our WACC formula to calculate our company’s weighted average cost of capital.

Net Present Value

Now that we have our free cash flows forecasted and our WACC calculated, we can calculate the net present value of these cash flows using WACC to get our company’s enterprise value. The net present value is the sum of the present values of each of the cash flows. The formula for present value is as follows:

Present Value = Future Value / (1 + Discount Rate) ^ Number of periods

For our cash flows, the future value will be the free cash flow that we projected for each year. The discount rate will be equal to WACC. And the number of periods will correspond to the year of each cash flow (year five cash flow equals five).

Fortunately, Excel has an NPV function we can use in which we can simply reference our rate (WACC) and the cells for our free cash flows in order to calculate the net present value.

Although the net present value of free cash flows will determine a company’s enterprise value, people often want to determine the equity value of a company because that is the value to which owners can lay claim. The equity value is simply the enterprise value less total debt (including preferred and minority interests) plus cash. In other words, the owners would have to pay off any debt owed on the company and would be able to keep any cash left in the event of the company’s sale.

As you may guess, a discounted cash flow analysis can be highly sensitive to the assumptions that you make. You may want to include a sensitivity table at the end of your analysis that looks at changes in WACC and perhaps revenue growth or your terminal value multiple to see how the valuation changes if these values are different.

Again, a DCF analysis is one method of valuing a company that has its advantages and disadvantages. In most cases you should attempt to perform a variety of valuation methods — comparable companies, precedent transactions or DCF — to make an informed determination of a company’s value.