The challenge of using a DCF methodology for corporations is determining what constitutes cash flow, what the company is worth beyond the forecast period, and what discount rate(s) to use to determine the present value. Relevant cash flow calculations can be confusing because there are many sources and uses of funds. Also, perspective matters. Cash available for a debt holder is most likely different from that of an equity holder. The number of periods of cash flow we count in a forecast is also of major concern. Many company owners would suggest that their company is worth more than just the cash flows that can be spun out of the firm during the forecast period. They would suggest that there is a terminal value to a firm, since after the forecast period the firm could be liquidated, run without capital investment, or operated in perpetuity. Finally, once we understand what cash flow to count and for how long, we then need to figure out the proper rate or rates to discount the cash flows in order to obtain a present value. Figure 9.1 depicts the overall process.

So, what is value? For the firm as a whole, meaning from the perspective of both debt and equity holders, it is any cash that is left over after meeting operating expenses, working capital needs, capital reinvestment, and taxes. Formally, this is known as free cash flow to the firm (FCFF). While there are a number of methods to derive FCFF, the easiest is to use the following formula, which is also represented in Figure 9.2:

The FCFF formula often causes confusion as to what each term means, so we should go through the terminology. We start the formula with earnings before interest and taxes (EBIT). Some prefer to start with net income, but since FCFF also includes the perspective of debt holders it is easier to begin with EBIT. The reason it is easier is because interest payments are value to debt holders. If we start with net income, we would have to calculate and add back the after-tax interest. Instead, we could just start with EBIT and remove tax, since tax is an actual cash flow out.

The next part of the formula, non-cash items, is actually an addition to FCFF. This is because non-cash items are just as their name implies: not actual cash. Amounts from concepts such as depreciation, amortization, deferred taxes, and so on have been removed from EBIT and therefore should be added back. We have to go through this add-back process because these items have tax effects that need to be included in the EBIT calculation in order to determine the proper tax amount. Once tax is calculated, we then add back the non-cash items since they are not real cash flow.

After adding back non-cash items, we can move on to capital expenditure, which is clearly a real cash outlay. Capital expenditures are typically a necessity to keep the business generating income and therefore must be removed from any “free” cash. Similarly, if a company’s business is oriented around intangibles, such as a film company, then intangible investment would be included here.

Finally, we have working capital needs, which is one of the most confused parts of the FCFF formula. In Chapter 8, we defined working capital as current assets less current liabilities. Working capital is critical to a business because the current assets and liabilities keep operations running on a day-to-day basis. Therefore, there should always be enough funding from current liabilities to cover the assets that are created; otherwise, we need to fund working capital from another source. The idea is similar to our balancing problem from Chapter 7. When assets were greater than liabilities, we plugged liabilities with short-term debt. When liabilities were greater than assets, we plugged assets with excess cash. If current assets are greater than current liabilities, we will have a positive working capital figure. We need to compare this to the next period’s working capital in order to understand the working capital needs. If in the next period working capital increases, it means there is a need to fund it through other sources. This need therefore draws cash from our free cash flow.

Let’s take a look at a simple example involving the following current asset and liability accounts over two periods:

The other way to think about it is from a cash change perspective. In Chapter 8, we implemented the cash change method by examining the difference between current asset and current liability accounts each period. In the previous example, we see that current assets have increased between 2009 and 2010. An increase in assets costs cash. Think about current assets comprising solely inventory. In order to go from 200 in inventories to 500 in inventories we need to pay for 300 in raw materials, work in process, or finished goods. That’s a -300 effect on cash. The opposite is true for liabilities. As they increase, we are essentially taking in cash. Think about current liabilities comprising solely short-term debt. If it went from 100 to 200, it would mean we added 100 of funding. That’s a 100 effect on cash. If we sum up the cash change, we get -200.

We now have two amounts, 200 and -200, for use as the working capital component of the FCFF formula. This is exactly where the confusion lies. Either one is correct, as long as we apply it correctly. The positive 200 can be thought of as our working capital needs and should be subtracted from FCFF. Alternatively, the -200 can be thought of as the working capital cash change and should be added. Either method we choose will get us to the same FCFF answer.

While FCFF is a good indicator of cash flow to the firm, it is not representative of cash flow to an equity investor. The reason for this is that debt has priority over equity, and cash flow to debt reduces the available cash flow to equity. If we are looking at free cash flow from an equity perspective, we should instead use the following formula to derive the free cash flow to equity (FCFE):

Notice in this formula the post-tax interest expense is taken away from cash available. We use post-tax figures for the interest because from an equity holder’s point of view the interest is a tax shield to the company and reduces the tax liability. In addition, any principal repayments made to debt holders should be removed from the cash available to equity holders. However, if new debt is being issued, this could be available to the equity holder depending on the covenants attached to the issue. Finally, while not technically debt, preferred stock pays dividends that have a priority over common stockholders. Keep in mind that preferred dividends are often cumulative issues, and if their payment is missed one period it will have to be made up in future periods, prior to paying common shareholders. Figure 9.3 shows the difference between FCFF and FCFE.

The terminal value can be calculated in a number of ways. Figure 9.5 shows an overview of the ways to calculate terminal value. The simplest ways are the ones often tossed around conference calls when people estimate the value of a firm by multiplying its last year’s cash flow by an industry or market multiple. “That firm is trading at eight times EBITDA and this one is valued at ten times” is a statement akin to what you might hear. While rudimentary, this method can be applied to a terminal-year cash flow to estimate terminal value.

A more detailed method for assessing terminal value is examining the assets of the firm to see what they are worth after the forecast period. Some debt bankers might do a worst-case analysis and assume that if the company that they lent money to could not pay back or refinance debts at maturity, then as bondholders they would push for liquidation. Assessing the value of the assets versus the debt exposure is their exit strategy. Therefore, another view of terminal value in this situation is a liquidation of assets. In this case, the assets would have to be valued as if they were being sold off after the forecast period, taking into account any appreciation, depreciation, or inflation.

If a market value that far out is difficult to assess, then estimations of return value on the assets can be made. Estimating the periodic worth of the assets over the average life of the assets and discounting that stream of values to the time period at the end of the forecast period can help establish such a value.

Finally, many corporate founders and owners would shudder at the thought of breaking up their company or running it into the ground after a forecast period. Perhaps they have legitimate reasons to believe their company will continue operating and even grow beyond the forecast period. For this reason, valuation analysts began to use a stable-growth model. The stable-growth model assumes that a company will continue to operate and possibly grow in perpetuity. The idea is that the firm as a going concern has value. Just as the forecast period value is based on free cash flow, the stable-growth model is based on cash flow expected in perpetuity.

Formally, the stable-growth model examines a long-term cash flow expectation and takes that cash flow into perpetuity with or without a growth rate. We can formalize the stable-growth model with the following formula:

Free Cash Flow (t + 1)/(Discount Rate - Long-Term Growth Rate)

In this formula, the Free Cash Flow (t + 1) is a free cash flow (FCF) one period after the forecast period that can be created in two ways: by growing the final forecast period’s free cash flow by a long-term growth rate or by recalculating all of the components of free cash flow so they reflect the long term, in the period after the last forecast period. The first method is very easy. Simply take the last forecast free cash flow and grow it by the assumed long-term growth rate. The difference between short-term and long-term growth is one reason we have a forecast period versus a terminal value in the first place. Often, though, near-term assumptions are expected to change in the distant future. A major disadvantage of simply growing the last forecast period’s free cash flow is that that free cash flow might not be representative of the expected long-term cash flows of the firm. See Figure 9.6 for more detail.

The alternative method, which addresses the flaws of the first method, is to recalculate all of the components of free cash flow to make sure they are reflective of long-term assumptions. In our example model, think about the long-term attributes of each of the items that we identified for FCFF:

Once we determine the correct numerator in the stable-growth formula, there are two very important rates required to calculate the rest of the formula. The first rate is the discount rate. If we are looking at a firm that is comprised of debt and equity, this rate is the weighted average cost of capital (WACC). If we are looking at an equity-only firm, then this rate is the long-term cost of equity. Keep in mind that these are long-term rates, which can be different from the forecast period rates. We will cover discount rates later in this chapter, where we will discuss the components of WACC and what needs to be taken into consideration for a long-term rate.

The final rate and assumption that is needed is the expected long-term growth rate. Whatever the rate by which we grew our EBIT or prior period’s free cash flow, that is the rate that we should use for this part of the formula. You will quickly notice that the long-term growth rate of the firm cannot exceed the cost of capital; otherwise, a nonsensical answer will be returned.

CAPM suggests that investors should get paid an investment rate that is above the risk-free rate, accounts for market returns, and incorporates compensation for nondiversifiable risk. The first two are returns based on a default-free investment and the market as a whole, respectively. We will discuss them later in the chapter. To capture nondiversifiable risk we need to understand how the firm under consideration performs versus the market. Specifically, beta has been established as the metric to capture this risk and is formally defined as:

Beta is a metric of the firm’s expected returns given the market’s returns. Typically, the market is an index relevant to the firm. For many U.S. stocks, the S&P 500 is used as the benchmark.

Market risk is measured by calculating the actual returns of stocks compared to the actual returns of default-free securities (typically government securities). Be sure that the risk-free rate used to calculate the market risk premium is the same risk-free rate that is used for the risk-free rate part of the cost-of-equity calculation. Once the returns of the market and the risk-free rate are known, the difference between these two is the market risk premium. Both risks are shown in Figure 9.12.

We can piece together all of this information to get the formal cost-of-equity equation:

The only part we have not talked about is the risk-free rate. Typically, a long- dated Treasury rate, such as the 10-year Treasury, is used. In projections, this figure can be adjusted for inflation. We use the risk-free rate as the basis and then add the product of the firm’s beta and the market risk premium.

Aside from inflation there are other considerations when forecasting these items. For beta, we should be worried about the capital structure of the firm. When a firm’s capital structure changes, beta also changes. History has shown that as a firm’s leverage increases, so does the volatility of a firm’s returns. This means that the beta we use in one period may not be the correct beta to use in other periods. We may also assume that if a firm is in business in perpetuity, as in the stable-growth terminal value, beta stabilizes. Frequently, assumptions between 1.0 and 1.2 are used for a stable beta.

Since debt interest is tax deductible, the tax-shielded portion reduces the overall cost of the debt, which is why we multiply the pre-tax debt interest rate by (1 - Tax Rate). Note that in extreme cases the tax shield may be affected by other items, such as net loss for the year. If this is the case, the effective tax rate could be lowered and the benefit from an interest tax shield diminished.

Determining the pre-tax debt interest rate is more challenging. For a publicly rated company this rate is usually tied to the creditworthiness of the firm. Rating agencies such as Moody’s, Standard & Poor’s, and Fitch provide ratings of companies based on credit analysis. This credit analysis often involves assessing the company’s expected cash flow vis-à-vis its capital structure. Submetrics can include interest and debt service coverage ratios, quick ratios, liquidity ratios, and so on. Industry and market analyses and the company’s ability to respond to them under various stress scenarios are also factored into the ratings decision.

Once a company is rated, its debt tends to price close to other similarly rated entities. For instance, using Standard & Poor’s scale we could say that two A-rated firms would pay similar spreads over LIBOR. As a financial modeler, one can use the existing debt market prices to help price our example company’s debt. A challenge we may encounter is that our financial model is a projection over time, particularly the forecast period. Over time, a company’s ratings can change either up or down. To account for this, advanced work can be done to estimate rating changes. This is done by creating transition matrices, which are sets of probabilities of possible ratings upgrades or downgrades from a preexisting state. These transition matrices allow an analyst to simulate credit risk fluctuations of a firm. As the expected rating of the firm changes, so does the pre-tax debt interest rate.

For private companies this analysis can be difficult, but not impossible. The default risk of a private company can be estimated by examining the historical assets versus the liabilities of the firm. We can create probabilities of the asset/liability ratio changing based on history and simulate that ratio going forward. If that ratio drops below one, or in some cases below a certain threshold below one, we can assume that the company is defaulted. If we simulated this many, many times we could get a default probability for the firm and try to link that to a historical rating of companies in the same or related industry. We can then use the market spreads for the determined rating.

An error that permeates many discounted cash flow models with changing discount rates is overusing each discount rate. Let’s just use a simple two-period example. Assume the discount rate in period 1 is 5.0% and the cash flow 100, while the discount rate is period 2 is 6.0% and the cash flow 200. In theory, to get a value we should discount these rates to the present value and sum up the discounted amounts. However, some analysts discount the period 2 cash flow (200) at 6.0% for two periods and the period 1 cash flow (100) at 5.0% for one period. This is incorrect since the period 2 cash flow should be discounted only for one period at 6.0% and then at 5.0% for the next cash flow. Figure 9.14 shows the difference in results between the correct and incorrect methods.

With this data set, the values to which we want to apply a weighted average are the cost rates, weighted by the market values. You will not find a prebuilt weighted average function in Excel, but the closest we can get without creating our own user-defined function is using SUMPRODUCT and SUM in combination.

SUMPRODUCT is a mathematical function that takes the following entry parameters:

Multiple, equal-size arrays can be referenced as array 1, array 2, and so on. The function multiplies each respective value in each array, meaning that in a two-array example the first value in array 1 would be multiplied by the first value in array 2, the second value in array 1 would be multiplied by the second value in array 2, and so on. All of the products are then summed up to produce the final result.

Most understand the SUM function, so all that is left is how we use these two functions in combination. A simplified formula that can help us remember how to calculate the weighted average is to take the SUMPRODUCT of the values and weights and divide by the sum of the weights. Going back to our example earlier, with the cost of debt, cost of equity, market value of debt, and market value of equity, we can calculate the WACC by using the SUMPRODUCT function on the rate array and the market value array. In the same formula, we use the SUM function on the market value array. Figure 9.17 shows the complete calculation.

The discount rate is the first entry that is absolute necessary. This rate should correspond to the periodicity of the discount periods (e.g., if the discount periods are annual, then the rate should be per annum). Before we explain the next few parameters, we should understand that the PV function can be used in two ways: to derive the present value of a cash flow at a point in time or to derive the present value of a series of cash flows. Given the flexibility of this function to do either calculation, the second entry parameter is either the number of periods in the future the single cash flow is generated or the number of periods in the future series of cash flows. The third entry parameter is only in the case of using the PV function with a series of cash flows. This entry parameter is the cash flow that is assumed to be generated each period for the number of periods assumed in the second entry parameter. If the PV function is being used to calculate a present value based only on a single future value, the payment should be left blank and a comma inserted to move on to the fourth entry parameter. The fourth entry parameter is if the PV function is being used with a single future value. This entry parameter is the future value that is being discounted. Finally, regardless of whether the PV function is being used with a series of cash flows or a single future value, the last entry parameter sets whether the cash flow is assumed to come at the end of the period or at the beginning of the period. Most likely this is omitted, which sets the function to end-of-period calculation.

Figure 9.18 shows an example of how the PV function is used in different ways. The first way shown is a single future value of 100, discounted over three periods at 5.0%. The second way is a payment of 100 for three periods, discounted at 5.0%.

Many financial modelers take advantage of the NPV function’s ability to accept multiple cash flows. The entry parameters for NPV are:

An easy example is shown in Figure 9.19, where a bond’s cash flows are being discounted at 6.0%. Instead of calculating each period’s present value and summing them up, the NPV function provides this for us. In such an example, the NPV function is being used to calculate the gross present value since no cost assumption was entered. It’s when we begin to use the NPV function to determine that net present value that we run into errors. To help this, we should identify the two most common errors created when using NPV, the second of which involves periodicity:

The XNPV function is very similar to NPV in that it references multiple cash flows and calculates a present value with a single discount rate. The added functionality is that we can assign dates to each cash flow by referencing a corresponding set of dates. While this may seem to be a minor difference, there are actually a couple of considerations that we need to make regarding this function:

Now imagine going back in time one period to period 1. To calculate the present value as of that period, we would take the present value we calculated in period 2 and discount it one period at the period 2 discount rate to get the present value as of period 1. We have to remember to add the cash flow from period 1 to derive the period 1 present value. If we were to repeat this process one more time we would have today’s present value. Figure 9.20 shows this process and the formula that consolidates the calculations.

We can quickly calculate this formula in Excel using prebuilt functions. The first function to learn is COVAR, which stands for covariance. The entry parameters for COVAR are:

For our beta example, the first range of data is the company’s returns and the second range of data is the market index returns. Note that the order of range entry does not matter. Calculating the covariance is not like a regression, where we are concerned with dependency. Covariance is just quantifying how two data sets move together.

Two other functions can help us with the denominator in the beta equation: VAR and VARP. Both VAR and VARP calculate the variance of a data set. The entry parameters are any set of data in Excel. The key difference between the two functions is that VAR calculates a sample variance, while VARP calculates a population variance. Variance of a sample is calculated by the following formula:

In the case of calculating beta, we are assuming the market index represents a population and should therefore use the following Excel-based formula: