Short paper - Valuing an enterprise is one of the first steps to building an informed financial model. ( using this article to help you to answer)
- articulate what enterprise value (EV) is and why it is necessary to consider EV when constructing a financial model
- show how both WACC and FCFs influence EV by using the proper equation and examples
- interpret how using EV would influence the direction and methodology of a decision maker, ie what does EV really tell us, and what sort of decision can be made when you know that value????
The value of an enterprise is generally understood as the equity value (E) plus the value of the interest-bearing debt (i.e., the debt capital) (D). If, for example, equity is $10 million and the enterprise has $3 million in debt capital, the enterprise value is $13 million. The weighted cost of capital (WACC) method yields this total enterprise value, in this case $13 million, as a result. When applying the WACC method, one must first determine the expected free cash flows (FCFS). FCFs are cash flows that could be paid by the enterprise to the providers of capital after all the desired investments and divestments have been made. The WACC is the weighted average of the required return of the providers of equity and debt. For example, if the shareholders of a 50% leveraged firm (i.e., 50% debt and 50% equity) require a return of 14%, and the holders of debt require a 6% return, the WACC of this firm is 10%. In practice, when valuing enterprises, all the expected FCFs have to be estimated to turn them into present values. If the enterprise owns nonoperational assets, the market value of these assets should be added to the WACC value. The market value of equity, then, is the total enterprise value (including the nonoperational assets) minus current interest-bearing debt. Under the weighted average cost of capital (WACC) method, the value of a company is determined by discounting expected income streams with the company's cost of capital (or WACC). This article explains the WACC method using simple quantitative examples and a case study based on a real-life supermarket chain. The Basics (Without Corporate Taxes) The value of an enterprise is generally understood as the equity value (E) plus the value of the interest-bearing debt (i.e., the debt capital) (D). If, for example, equity is $10 million and the enterprise has $3 million in debt capital, the enterprise value is $13 million. The WACC method yields this total enterprise value, in this case $13 million, as a result. To determine the equity value of this enterprise value, one must subtract the value of the debt capital from the total enterprise value In this article, the term "value" does not represent the book value as found on a balance sheet, because that number is (often) based on historical costs; the value that is found using the WACC method usually deviates from that value. In general, if one can earn more with the assets of an enterprise than the assets cost, the calculated value will be higher than the book value. This calculated value is also called the market value. 1 How does the WACC method work? When applying the WACC method, one must first determine the expected free cash flows (FCFS). FCFs are cash flows that could be paid by the enterprise to the providers of capital after all the desired investments and divestments have been made. The providers of equity and debt are the providers of capital. Subsequently, these FCFs are turned into present values using the enterprise WACC. The WACC is the weighted average of the required return of the providers of equity and debt. For example, if the shareholders of a 50% leveraged firm (i.e., 50% debt and 50% equity) require a return of 14%, and the holders of debt require a 6% return, the WACC of this firm is 10%. Example 1. Enterprise "Salt" is expected to generate just three FCFs. Thereafter, Salt ceases to exist. The expected FCF at the end of year 1 is $110; at the end of years 2 and 3, the FCFs are $121 and $140 respectively. See Exhibit 1. The beginning of the first year is shown to be at time 0 (t=0) and the end of the first year is shown to be at time 1 (t=1). The beginning of year 2 is shown to be at time t=1, and the end of year 2 at t=2, etc. - The result ($305.18) is also called the present value of the expected FCFs. Now suppose Salt is financed 50% with interest- bearing debt; the market value of equity will then be 50% of $305.18, or $152.59. In practice, when valuing enterprises, all the expected FCFs have to be estimated to turn them into present values. For example, for valuation of an airline company, FCFs would not be estimated solely for the first three years. Instead, the horizon would be extended, since it would be presumed that the company will also generate FCFs after the first three years. To look into the future is difficult, but it is nevertheless indispensable for a WACC valuation. If the FCFs after three years are not taken into account, that would implicitly assume that the enterprise ceases to exist after three years. What often happens in practice, however, is that after a so-called explicit period, analysts hold the FCFs constant into infinity or let them grow at a constant (low) rate. The value of the FCFs after the explicit period is called the "continuing value" or the "horizon value"3 Example 2. Suppose that Salt continues to exist after the third year, and that the EXHTC at the end of years 1-4 and is rent Value annual FCFs from t=4 (the end of the fourth year) and onwards are $145. What is the value of Salt at t=0, given that FCFs are expected into the indefinite future? Exhibit 2 presents the expected FCFs for t=l until t=5 (the timeline continues infinitely to the right) and the FCFs present value. CEWNOCI+WACCUF +WACC-30616 Instead of discounting $145 to the present (t=0) for every year until infinity, one can use a more practical formula, also known as the "Gordon growth formula"4 See Exhibit 3 for the application of the Gordon growth formula to Salt. FCF 171 The WWOC of Satseguato, then the value of the entertae at the beginning of par 16. the value is also IFCF FCF FCF EXHIBIT 2 Expected to let the end of ears 1-5 and FCF Press Value Tine 4 5 FCF 110 140 145 145 IS WAOC 10%, the of the Begening your le As Exhibit 3 shows, the value of the enterprise can be split into the value of the FCFs from the explicit period ($305.18) and the "continuing value" ($1,089.41). EXHIBIT 1 Expected FCFs (at the end of years 1-3) Note that the continuing value is a high percentage of the total enterprise value. and FCF Present ValueEXHIBIT 2 Expected FCFS (at In Exhibit 3 it is 78% ($1,089.41/$1,394.59) of the enterprise value. the end of years 1-5) and FCF Present Value If Salt expects the FCF at t=5 to be 2% higher than at t=4, and that this growth will continue in a similar fashion into the indefinite future, the value of Salt at t=0 will then clearly be higher because of the higher FCF from t=5 onwards. See Exhibit 4. This means that Salt with growth is worth about 20% more than Salt without growth, and the continuing value as a percentage of the total enterprise value is now 82% ($1,361.76/$1,666.94) instead of 78%. How worthwhile is the result of this calculation? Forecasting is a difficult task, especially into the distant future. If the calculated value is determined to be 78% or even 82% from FCFs that are probably realized only after the explicit period, how reliable is the outcome? If the FCFs are not well founded, then the result of the valuation under the WACC method will be of little value. The rule "garbage in, garbage out" applies to the use of the WACC For instance, if the correct WACC is 10% but was incorrectly estimated at 8%, then the outcome shown in Exhibit 4 would be $2,233.30 instead of $1,666.94. The lower the WACC, the higher the calculated value, and vice versa. Due to the (unfortunately) high sensitivity of the outcome, incorrect estimations of the FCFs or the WACC have Accounting for Corporate Taxes Having tackled the basics of the WACC method without the influence of corporate taxes, it is time to develop a deeper understanding of the calculation by taking that influence into account. When an enterprise is financed with both equity and debt, it has a tax advantage as compared to a similar enterprise that is financed solely with equity, because interest costs are tax-deductible. This lowers the taxable profit and, as a result, the corporate tax due. Thus, the cash flows that can be paid to the providers of capital will be higher. Because cash flows are higher and the risk of the projects (i.e., the company's activities) is not influenced by the capital structure, the value of the company will be higher as the proportion of debt in the capital structure increases. 5 Naturally, there are limits to this growth. For example, excessive use of debt can endanger the flexibility of the enterprise, and consequently, reduce the expected cash flows, which would have a negative effect on the enterprise value. For the purposes of the Salt example, it will be assumed that Salt strives for a healthy amount of debt financing (for this example, approximately 40%). EXHIBIT 3Gordon Growth FormulaEXHIBIT 4Expected FCFs at the end of years 1-5 (g from t=4 onwards is 2%) EXHIBIT WACC WII Carpenale Teration considered WACC - 10 15 20 Rosanes for the required turn on debt espallar al debito forte Full Theme 15-1 caies that could be the wintesi come to the 51 due times the mines the meant as percege. Il for Salt it holds hair - 15.5%.185.28% and EVE 01-05 the WACC - - - -0.281-05-04 05-10% With the WACC method, the tax benefit is found not in higher FCFs (which would seem obvious), but in the lower cost of raising capital. Exhibit 5 shows how the WACC is determined when corporate taxation is taken into account. EXHIBIT Velus Pepper wc-0-**-0.30-10% 06-06 Alta vedoute e detalhari FOF. 900 In summary, the FCF is the cash flow after tax without taking into account the tax shields of debt capital. The WACC is the cost of raising capital taking into account the tax shield. If the tax benefits of debt capital are considered in both the calculation of the FCF and the WACC, this would unjustly double-count the advantage in the valuation, and the calculated value would turn out to be too high The crawl, where sequently reduce the expected cash Alternative Value of Pepper att flows, which would have a negative effect on the enterprise value. For the purposes of the Salt example, it will be assumed that Salt strives for healthy amount of debt financing (for EXHIBIT 5WACC With Corporate Taxation ConsideredEXHIBIT Value of PepperEXHIBIT 7Alternative Value of Pepper at t=0 Example 3. Enterprise "Pepper" generates an expected annual (into infinity) profit before tax (earnings before interest and taxes or EBIT) of $1 10. Pepper is financed for 40% of its market value with debt. The rD is 5%, tc is 30%, and rg is 16%. The total value of Pepper can be calculated by discounting the FCFs with the WACC (see Exhibit 6). The FCFs expected at the end of each year are $110 x (1-0.3) = $77 In this example, the value of equity is $420 (60% of $700) and debt is $280 (40% of $700). Note that the true yearly tax owed is not $33 (i.e., 30% of $110), but 30% of $110 less the owed interest (i.e., 30% ($110-(5% x $280)) = 30% ($110-14) = $28.8) Suppose that instead of an FCF of $77, the EBIT was reduced by the actual taxes to be paid (and not the taxes that would be owed if the enterprise was financed 100% with equity). In other words, assume that the FCF was wrongly calculated. What would be the consequences? The enterprise value, given a higher CF and the same discount rate, would then have been higher than $700. Exhibit 7 shows the value of Pepper at t=0. The tax benefit has now unjustly been double-counted, once in the calculation of the CF and once in the calculation of the WACC. The CF of 81.2 is not the FCF. Rather, it is the profit after taxes for the shareholders, the equity cash flow (ECF), plus the interest for the debt holders, the debt cash flow (DCF). ECF plus DCF is sometimes also called capital cash flow (CCF).7 A last remark about the WACC before looking at a more realistic example: The weights used in Exhibit 6 are based on market values, not on book values. Providers of equity capital, like providers of debt capital, require a return over the market value of their capital - not over the book value of their capital. If the market value of the equity capital is $10 million and the required return is equal to 10%, then the shareholders will require that the capital (including dividends) is worth 10% more after a year. The book value of the underlying capital is irrelevant. With the WACC method one usually assumes a constant capital structure (i.e., a constant mix of debt and equity in market values, not book values). Case Study: Superstore Bb In this section, the focus is on determining the market equity value of an enterprise, Superstore, as of 1/1/2009 using the WACC method. The first step is to calculate the total enterprise value of Superstore. Second, the value of the interest-bearing debt as of 1/1/20098 is deducted to determine the equity value as of 1/1/2009. The historical and forecasted balance sheets and income statements of Superstore and cash flow statements are provided in Exhibit 8. With the help of these cash flow statements, the expected FCFs can be determined. Thereafter, the FCFS will be discounted by the Superstore WACC. Assume that Superstore has a target capital structure in which 50% of its market value consists of equity, the providers of equity capital require a return of 14% (r^sub E^ = 14%), the providers of debt capital require a return of 6% (r^ = 6%), and the corporate tax rate is 25%. Using these assumptions, Exhibit 9 shows that Superstore's WACC is 0.0925. Assume that Superstore has a target capital structure in which 50% of its market value consists of equity, the providers of equity capital require a return of 14% (r^sub E` = 14%), the providers of debt capital require a return of 6% (r^ = 6%), and the corporate tax rate is 25%. Using these assumptions, Exhibit 9 shows that Superstore's WACC is 0.0925. The explicit period of this enterprise is from 2009 until 2012. From 2013 on, it is assumed all the ratios between the different items in the balance sheet and income statement will remain the same. Further assume that from 2013 onward, the expected annual growth rate is 2% until infinity. Exhibit 10 provides the ratios used for Superstore's income statements, balance sheets, and cash flow statements The FCF is equal to the sum of: 1. The operational cash flow. 2. The investment/divestment in working capital. 3. The investment/divestment in tangible fixed assets. 4. The corporate tax that would be owed if the enterprise was financed solely with equity. Step 1: Operational Cash Flow. The operational cash flow is the net cash flow before taxes. It is obtained from the company's activities without taking into account investments or divestments in working capital and tangible fixed assets. The operational cash flow is equal to the company profit corrected for costs that are not a cash outflow. The first correction to Superstore's cash flow is the addition of depreciation. Depreciation reduces company profits, but it is not a cash outflow. Therefore, yearly depreciation is added to the company profit. Evidently, Superstore invests each year in tangible fixed assets with a negative impact on FCF. These investments are taken into account in a separate line in the calculation of the FCF.10 The second correction concerns the change in provisions. 11 If, for example, the provisions at the end of 2008 amount to $867 and at the end of 2009 to $910, then there was an addition to the line item in 2009 of $43. These are costs (for example, maintenance) that are booked in 2009, but that have not yet led to cash flows. If the provisions increase, this change is added to the company profit, thereby increasing operational cash flow. If the provisions decrease, the difference is deducted from the company profit. Accounts have then been paid at the expense of the provisions. EXHIBIT 8Superstores income statement, balance sheets (book values), and cash flow statements Step 2: Investments in Working Capital. An increase in inventory is treated as an investment. Thus, if the inventory increases from $1,744 at the end of 2008 to $1,849 at the end of 2009, then $105 has been invested in inventory. If the accounts receivable increase from one year to the next, this means that part of the revenue was not received. Since part of the turnover did not lead to cash flows, this part has to be left out of the FCF. The increase in accounts receivable in 2009 will decrease the FCF. Thus, the increase is a correction to the reported revenue that has not yet been fully paid by the customers. For the balance sheet item accounts payable, the opposite is true. If accounts payable increase during a year, the enterprise has not yet paid some of the received invoices. An increase in the accounts payable can be seen as a cash inflow and increases the FCF. It is actually a correction to the investment in inventory that has not yet been paid. HT! at !!.. An increase in the necessary amount of cash decreases the FCF. This money cannot be paid to the providers of capital, because it is needed in the enterprise. EXHIBIT 8Superstores income statement, balance sheets (book values), and cash flow statementsEXHIBIT 9Superstores WACC Step 3: Investments In Tangible Fixed Assets. An increase in the tangible fixed assets will clearly lead to a decrease in the FCFs. The investments in the tangible fixed assets are equal to the change of that line item plus the depreciation in the given year. At the end of year 2008, the book value of the tangible fixed assets was $6,009; at the end of year 2009, the book value was $6,370. The difference between these amounts plus the depreciation in 2009 is the investment in tangible fixed assets for 2009 Step 4: Taxes as if Company Was Financed Solely With Equity. With the WACC method, the tax benefits of using debt are not expressed in a higher FCF but in a lower cost of capital. The tax that should be subtracted in computing FCF is equal to the corporate tax rate times the company's EBIT. As such, tax will be calculated as if the enterprise did not have any interest-bearing debt. For 2009, this is 25% x $973 = $243. The tax that is subtracted is not the same as the actual tax paid, as shown in the cash flow statement. For Superstore, this leads to the FCFs as provided in Exhibit 11. The FCF strongly increases in 2013 because the investments in tangible fixed assets decrease in EXHIBIT 10Ratios for Superstores income that year. During the period 2009-2012 there is an important yearly investment in statements, balance sheets, and cash flow growth, of which Superstore reaps the fruits from 2013 onwards. In 2013 the FCF statements increases 81%. From 2014 onwards, the FCF increases yearly by 2%. It is recommended to make a forecast for a minimum of two years after the explicit period, to avoid making mistakes with respect to the FCF used in the continuing value. The determination of Superstore's value is shown in Exhibit 12. If the enterprise is in possession of an excessive amount of cash (a "nonoperational asset), then one must add this amount to the calculated value. This amount is equal to zero for Superstore on 1/1/2009. The equity value ($3,943) is equal to the enterprise value ($6,816) minus the value of the interest-bearing debt as of 12/31/08 ($2,873). The creditors and the provisions are not deducted because these line items are taken into account in the cash flow statement and are part of the FCF. Hence, one deducts only the interest-bearing debt to determine the equity value. In the calculations, the present author assumed a WACC of 9.25% and that 50% of the enterprise value would be financed with equity. On 12/31/08, the actual portion of enterprise value that is equity was higher than 50%. 12 This means that to truly be allowed to use a WACC of 9.25%, Superstore has to slightly raise its leverage in the near future. If Superstore is not aiming to adjust this proportion, then the WACC of 9.25% is too low and the company is overvalued. More about the WACC The required return on equity is determined by the risk of the projects in which the enterprise is engaged (i.e., company risk), in combination with the leverage. The higher the leverage, the higher the financial risk for equity holders, which can be expressed with the help of the formula found in Exhibit 13. EXHIBIT 11 Calculation of the FCFs during the explicit period and the first 2 years thereafter.EXHIBIT 12Value of SuperstoreEXHIBIT 13Financial Risk far Equity Holders If a different capital structure is desired, the rg in Exhibit 5 must be adapted, since the cost of raising capital is positively dependent on the leverage. In Exhibit 14, it appears that the WACC decreases if the enterprise is financed with more debt. Exhibits 15 and 16 apply the formula in Exhibit 14 to Superstore with 0% and 50% debt financing, respectively. The decrease in WACC can be explained by the tax benefits that increase when debt financing increases. Moreover, when using the formula in Exhibit 14 to determine WACC instead of the formula employed in Exhibit 5, r^sub Edoes not have to be adapted every time. The formula already takes the influence of an increase in leverage on the required return of equity into account.13 The reader should know, however, what r^sub U^ is. Superstore s r^sub U^ was calculated with the help of the second formula in Exhibit 13. To determine that amount, Superstore needed an 'sub Ethat was valid for a capital structure with 50% debt financing. If the r^sub E^ of the enterprise to be valued is unknown, how is t^sub U^ determined? In other words, how does one then determine the required return on equity for bearing only business risk? R^sub U is often determined by looking at competing firms 14 and correcting the required return on equity for the "leverage of these firms. An average value of the found r^sub U^s of these enterprises could be a good estimate of the r^sub U^ needed for determining the subject firm's rasub E or the WACC. The return required by capital providers depends on company risk and financial risk. The proportion of debt to equity determines the financial risk - the higher the proportion, the higher the financial risk for the providers of equity. If an enterprise changes its target capital structure, this will influence the required return on equity and the WACC. The higher the leverage, the higher the rasub E^ and the lower the WACC (WACC decreases due to the increase in tax benefits of debt financing). Conclusion To value an enterprise, it is wise to start by analyzing past financial statements. Thereafter, a valuator should construct balance sheets and profit and loss accounts for as many years as possible. While looking into the future is difficult, it is indispensable for a WACC valuation. Valuators must check to see that projections are realistic and be aware of "hockey stick projections" that are often times) made by management. If the FCFs are well founded, they should be discounted with the WACC, which reflects the risk of the firm's projects. The outcome of the calculation gives the enterprise value, excluding the nonoperational assets. If the enterprise owns nonoperational assets, the market value of these assets should be added to the WACC value. The market value of equity, then, is the total enterprise value (including the nonoperational assets) minus current interest-bearing debt. EXHIBIT 14 WACC Farula EXHIBIT 14 WACC Formale WACT: WACCE: EXHIRIT 10 WACC W Leverpes lavorape is on the WOON WO-DE-L-010-05-000-0.25 -0. SCO Footnote 1 The term market value in this context is possibly confusing since the calculated market value of an enterprise can deviate from the buying or selling price. If, for example, a director who is a majority shareholder wants to sell his or EXHIBIT 10 her shares for a price that corresponds with the value that the director had WACC Worrage base If were 50% dubt, the WWOC calculated for the shares, but he or she fails in convincing buyers of the cash WACC ---10-01-06-006-623 -0.6 flow potential of the enterprise, then no buyer will be willing to pay a price near EXHIBIT 14WACC FormulaEXHIBIT 15WACC If the market value that he determined. Leverage is 0%EXHIBIT 16WACC If Leverage Is 50% 2 Assume X invests $100 and the expected return on this investment is 10% per period, then the $100 is expected to be worth $110 at the end of the first period (t=1). Conversely, it can be said that an expected value of $110 at the end of the first period is now (t=0) worth $110/1.1 = $100. In other words, the present value of the expected $110 at t=1 is $100 at t=0. 3 See also Brealey. Myers, and Allen. Principles of Corporate Finance. 9th Ed. (McGraw-Hill, 2008). 4 See Gordon and Shapiro, "Capital Equipment Analysis: The Required Rate of Profit" Vol. 3 Management Science No. 1. pages 102-110 (October 1956). 5 Some entrepreneurs posit that debt financing is unwise because the bank profits more. Assume that a business owner finances his or her company by not only investing personal equity, but also by giving loans to the company. As such, the owner is both an equity and debt provider to his or her company. In that case, the cash flow after corporate taxation will be higher than when the owner finances the company solely with equity, since in the latter scenario he or she will not make use of the tax-deductibility of interest costs. This discussion, however, ignores differences in income tax rates. If interest revenue is taxed more heavily than equity revenue, then the total tax benefit can turn out to be lower or even negative. 6 For the theoretical derivation of tax shields, see Schauten, "Valuation, Capital Structure Decisions, and the Cost of Capital" Dissertation, Erasmus University Rotterdam (2008). 7 If the CCF is discounted with the WACC before tax, we would find the correct value because the tax benefit of debt capital is omitted from the WACC calculation. The tax benefits are thus either expressed in the cost of capital (WACC) or in the expected cash flow, but not both. Moreover, applying the CCF in combination with the WACC before tax is annoying, because the CCF can be calculated only if one knows the size of the debt at the beginning of the years in the forecast (during the explicit period and the years thereafter). If one assumes that the amount of debt is a stable percentage of the enterprise value at the beginning of each year, then this is not an easy exercise because the enterprise value is unknown and is exactly what one is trying to calculate. Footnote 8 This corresponds to the interest-bearing debts as of 12/31/2008. 9 And so 50% of debt. 10 Companies that invest in growth will have higher investments than depreciation. 11 Provisions are equivalent to contingent liabilities or contingencies. 12 The equity proportion is now $3,943/$6,816. Footnote 13 As can be seen, r^sub E' does not even appear in the formula 14 "Competing firms" means firms that are active in the same industry, perform the same kind of activities, and preferably have the same profitability, size, and strategy. AuthorAffiliation MARC B. J. SCHAUTEN, Ph.D. is an assistant professor of finance at Erasmus University in Rotterdam, The Netherlands. Copyright Thomson Professional and Regulatory Services, Inc. Sep/Oct 2010 The value of an enterprise is generally understood as the equity value (E) plus the value of the interest-bearing debt (i.e., the debt capital) (D). If, for example, equity is $10 million and the enterprise has $3 million in debt capital, the enterprise value is $13 million. The weighted cost of capital (WACC) method yields this total enterprise value, in this case $13 million, as a result. When applying the WACC method, one must first determine the expected free cash flows (FCFS). FCFs are cash flows that could be paid by the enterprise to the providers of capital after all the desired investments and divestments have been made. The WACC is the weighted average of the required return of the providers of equity and debt. For example, if the shareholders of a 50% leveraged firm (i.e., 50% debt and 50% equity) require a return of 14%, and the holders of debt require a 6% return, the WACC of this firm is 10%. In practice, when valuing enterprises, all the expected FCFs have to be estimated to turn them into present values. If the enterprise owns nonoperational assets, the market value of these assets should be added to the WACC value. The market value of equity, then, is the total enterprise value (including the nonoperational assets) minus current interest-bearing debt. Under the weighted average cost of capital (WACC) method, the value of a company is determined by discounting expected income streams with the company's cost of capital (or WACC). This article explains the WACC method using simple quantitative examples and a case study based on a real-life supermarket chain. The Basics (Without Corporate Taxes) The value of an enterprise is generally understood as the equity value (E) plus the value of the interest-bearing debt (i.e., the debt capital) (D). If, for example, equity is $10 million and the enterprise has $3 million in debt capital, the enterprise value is $13 million. The WACC method yields this total enterprise value, in this case $13 million, as a result. To determine the equity value of this enterprise value, one must subtract the value of the debt capital from the total enterprise value In this article, the term "value" does not represent the book value as found on a balance sheet, because that number is (often) based on historical costs; the value that is found using the WACC method usually deviates from that value. In general, if one can earn more with the assets of an enterprise than the assets cost, the calculated value will be higher than the book value. This calculated value is also called the market value. 1 How does the WACC method work? When applying the WACC method, one must first determine the expected free cash flows (FCFS). FCFs are cash flows that could be paid by the enterprise to the providers of capital after all the desired investments and divestments have been made. The providers of equity and debt are the providers of capital. Subsequently, these FCFs are turned into present values using the enterprise WACC. The WACC is the weighted average of the required return of the providers of equity and debt. For example, if the shareholders of a 50% leveraged firm (i.e., 50% debt and 50% equity) require a return of 14%, and the holders of debt require a 6% return, the WACC of this firm is 10%. Example 1. Enterprise "Salt" is expected to generate just three FCFs. Thereafter, Salt ceases to exist. The expected FCF at the end of year 1 is $110; at the end of years 2 and 3, the FCFs are $121 and $140 respectively. See Exhibit 1. The beginning of the first year is shown to be at time 0 (t=0) and the end of the first year is shown to be at time 1 (t=1). The beginning of year 2 is shown to be at time t=1, and the end of year 2 at t=2, etc. - The result ($305.18) is also called the present value of the expected FCFs. Now suppose Salt is financed 50% with interest- bearing debt; the market value of equity will then be 50% of $305.18, or $152.59. In practice, when valuing enterprises, all the expected FCFs have to be estimated to turn them into present values. For example, for valuation of an airline company, FCFs would not be estimated solely for the first three years. Instead, the horizon would be extended, since it would be presumed that the company will also generate FCFs after the first three years. To look into the future is difficult, but it is nevertheless indispensable for a WACC valuation. If the FCFs after three years are not taken into account, that would implicitly assume that the enterprise ceases to exist after three years. What often happens in practice, however, is that after a so-called explicit period, analysts hold the FCFs constant into infinity or let them grow at a constant (low) rate. The value of the FCFs after the explicit period is called the "continuing value" or the "horizon value"3 Example 2. Suppose that Salt continues to exist after the third year, and that the EXHTC at the end of years 1-4 and is rent Value annual FCFs from t=4 (the end of the fourth year) and onwards are $145. What is the value of Salt at t=0, given that FCFs are expected into the indefinite future? Exhibit 2 presents the expected FCFs for t=l until t=5 (the timeline continues infinitely to the right) and the FCFs present value. CEWNOCI+WACCUF +WACC-30616 Instead of discounting $145 to the present (t=0) for every year until infinity, one can use a more practical formula, also known as the "Gordon growth formula"4 See Exhibit 3 for the application of the Gordon growth formula to Salt. FCF 171 The WWOC of Satseguato, then the value of the entertae at the beginning of par 16. the value is also IFCF FCF FCF EXHIBIT 2 Expected to let the end of ears 1-5 and FCF Press Value Tine 4 5 FCF 110 140 145 145 IS WAOC 10%, the of the Begening your le As Exhibit 3 shows, the value of the enterprise can be split into the value of the FCFs from the explicit period ($305.18) and the "continuing value" ($1,089.41). EXHIBIT 1 Expected FCFs (at the end of years 1-3) Note that the continuing value is a high percentage of the total enterprise value. and FCF Present ValueEXHIBIT 2 Expected FCFS (at In Exhibit 3 it is 78% ($1,089.41/$1,394.59) of the enterprise value. the end of years 1-5) and FCF Present Value If Salt expects the FCF at t=5 to be 2% higher than at t=4, and that this growth will continue in a similar fashion into the indefinite future, the value of Salt at t=0 will then clearly be higher because of the higher FCF from t=5 onwards. See Exhibit 4. This means that Salt with growth is worth about 20% more than Salt without growth, and the continuing value as a percentage of the total enterprise value is now 82% ($1,361.76/$1,666.94) instead of 78%. How worthwhile is the result of this calculation? Forecasting is a difficult task, especially into the distant future. If the calculated value is determined to be 78% or even 82% from FCFs that are probably realized only after the explicit period, how reliable is the outcome? If the FCFs are not well founded, then the result of the valuation under the WACC method will be of little value. The rule "garbage in, garbage out" applies to the use of the WACC For instance, if the correct WACC is 10% but was incorrectly estimated at 8%, then the outcome shown in Exhibit 4 would be $2,233.30 instead of $1,666.94. The lower the WACC, the higher the calculated value, and vice versa. Due to the (unfortunately) high sensitivity of the outcome, incorrect estimations of the FCFs or the WACC have Accounting for Corporate Taxes Having tackled the basics of the WACC method without the influence of corporate taxes, it is time to develop a deeper understanding of the calculation by taking that influence into account. When an enterprise is financed with both equity and debt, it has a tax advantage as compared to a similar enterprise that is financed solely with equity, because interest costs are tax-deductible. This lowers the taxable profit and, as a result, the corporate tax due. Thus, the cash flows that can be paid to the providers of capital will be higher. Because cash flows are higher and the risk of the projects (i.e., the company's activities) is not influenced by the capital structure, the value of the company will be higher as the proportion of debt in the capital structure increases. 5 Naturally, there are limits to this growth. For example, excessive use of debt can endanger the flexibility of the enterprise, and consequently, reduce the expected cash flows, which would have a negative effect on the enterprise value. For the purposes of the Salt example, it will be assumed that Salt strives for a healthy amount of debt financing (for this example, approximately 40%). EXHIBIT 3Gordon Growth FormulaEXHIBIT 4Expected FCFs at the end of years 1-5 (g from t=4 onwards is 2%) EXHIBIT WACC WII Carpenale Teration considered WACC - 10 15 20 Rosanes for the required turn on debt espallar al debito forte Full Theme 15-1 caies that could be the wintesi come to the 51 due times the mines the meant as percege. Il for Salt it holds hair - 15.5%.185.28% and EVE 01-05 the WACC - - - -0.281-05-04 05-10% With the WACC method, the tax benefit is found not in higher FCFs (which would seem obvious), but in the lower cost of raising capital. Exhibit 5 shows how the WACC is determined when corporate taxation is taken into account. EXHIBIT Velus Pepper wc-0-**-0.30-10% 06-06 Alta vedoute e detalhari FOF. 900 In summary, the FCF is the cash flow after tax without taking into account the tax shields of debt capital. The WACC is the cost of raising capital taking into account the tax shield. If the tax benefits of debt capital are considered in both the calculation of the FCF and the WACC, this would unjustly double-count the advantage in the valuation, and the calculated value would turn out to be too high The crawl, where sequently reduce the expected cash Alternative Value of Pepper att flows, which would have a negative effect on the enterprise value. For the purposes of the Salt example, it will be assumed that Salt strives for healthy amount of debt financing (for EXHIBIT 5WACC With Corporate Taxation ConsideredEXHIBIT Value of PepperEXHIBIT 7Alternative Value of Pepper at t=0 Example 3. Enterprise "Pepper" generates an expected annual (into infinity) profit before tax (earnings before interest and taxes or EBIT) of $1 10. Pepper is financed for 40% of its market value with debt. The rD is 5%, tc is 30%, and rg is 16%. The total value of Pepper can be calculated by discounting the FCFs with the WACC (see Exhibit 6). The FCFs expected at the end of each year are $110 x (1-0.3) = $77 In this example, the value of equity is $420 (60% of $700) and debt is $280 (40% of $700). Note that the true yearly tax owed is not $33 (i.e., 30% of $110), but 30% of $110 less the owed interest (i.e., 30% ($110-(5% x $280)) = 30% ($110-14) = $28.8) Suppose that instead of an FCF of $77, the EBIT was reduced by the actual taxes to be paid (and not the taxes that would be owed if the enterprise was financed 100% with equity). In other words, assume that the FCF was wrongly calculated. What would be the consequences? The enterprise value, given a higher CF and the same discount rate, would then have been higher than $700. Exhibit 7 shows the value of Pepper at t=0. The tax benefit has now unjustly been double-counted, once in the calculation of the CF and once in the calculation of the WACC. The CF of 81.2 is not the FCF. Rather, it is the profit after taxes for the shareholders, the equity cash flow (ECF), plus the interest for the debt holders, the debt cash flow (DCF). ECF plus DCF is sometimes also called capital cash flow (CCF).7 A last remark about the WACC before looking at a more realistic example: The weights used in Exhibit 6 are based on market values, not on book values. Providers of equity capital, like providers of debt capital, require a return over the market value of their capital - not over the book value of their capital. If the market value of the equity capital is $10 million and the required return is equal to 10%, then the shareholders will require that the capital (including dividends) is worth 10% more after a year. The book value of the underlying capital is irrelevant. With the WACC method one usually assumes a constant capital structure (i.e., a constant mix of debt and equity in market values, not book values). Case Study: Superstore Bb In this section, the focus is on determining the market equity value of an enterprise, Superstore, as of 1/1/2009 using the WACC method. The first step is to calculate the total enterprise value of Superstore. Second, the value of the interest-bearing debt as of 1/1/20098 is deducted to determine the equity value as of 1/1/2009. The historical and forecasted balance sheets and income statements of Superstore and cash flow statements are provided in Exhibit 8. With the help of these cash flow statements, the expected FCFs can be determined. Thereafter, the FCFS will be discounted by the Superstore WACC. Assume that Superstore has a target capital structure in which 50% of its market value consists of equity, the providers of equity capital require a return of 14% (r^sub E^ = 14%), the providers of debt capital require a return of 6% (r^ = 6%), and the corporate tax rate is 25%. Using these assumptions, Exhibit 9 shows that Superstore's WACC is 0.0925. Assume that Superstore has a target capital structure in which 50% of its market value consists of equity, the providers of equity capital require a return of 14% (r^sub E` = 14%), the providers of debt capital require a return of 6% (r^ = 6%), and the corporate tax rate is 25%. Using these assumptions, Exhibit 9 shows that Superstore's WACC is 0.0925. The explicit period of this enterprise is from 2009 until 2012. From 2013 on, it is assumed all the ratios between the different items in the balance sheet and income statement will remain the same. Further assume that from 2013 onward, the expected annual growth rate is 2% until infinity. Exhibit 10 provides the ratios used for Superstore's income statements, balance sheets, and cash flow statements The FCF is equal to the sum of: 1. The operational cash flow. 2. The investment/divestment in working capital. 3. The investment/divestment in tangible fixed assets. 4. The corporate tax that would be owed if the enterprise was financed solely with equity. Step 1: Operational Cash Flow. The operational cash flow is the net cash flow before taxes. It is obtained from the company's activities without taking into account investments or divestments in working capital and tangible fixed assets. The operational cash flow is equal to the company profit corrected for costs that are not a cash outflow. The first correction to Superstore's cash flow is the addition of depreciation. Depreciation reduces company profits, but it is not a cash outflow. Therefore, yearly depreciation is added to the company profit. Evidently, Superstore invests each year in tangible fixed assets with a negative impact on FCF. These investments are taken into account in a separate line in the calculation of the FCF.10 The second correction concerns the change in provisions. 11 If, for example, the provisions at the end of 2008 amount to $867 and at the end of 2009 to $910, then there was an addition to the line item in 2009 of $43. These are costs (for example, maintenance) that are booked in 2009, but that have not yet led to cash flows. If the provisions increase, this change is added to the company profit, thereby increasing operational cash flow. If the provisions decrease, the difference is deducted from the company profit. Accounts have then been paid at the expense of the provisions. EXHIBIT 8Superstores income statement, balance sheets (book values), and cash flow statements Step 2: Investments in Working Capital. An increase in inventory is treated as an investment. Thus, if the inventory increases from $1,744 at the end of 2008 to $1,849 at the end of 2009, then $105 has been invested in inventory. If the accounts receivable increase from one year to the next, this means that part of the revenue was not received. Since part of the turnover did not lead to cash flows, this part has to be left out of the FCF. The increase in accounts receivable in 2009 will decrease the FCF. Thus, the increase is a correction to the reported revenue that has not yet been fully paid by the customers. For the balance sheet item accounts payable, the opposite is true. If accounts payable increase during a year, the enterprise has not yet paid some of the received invoices. An increase in the accounts payable can be seen as a cash inflow and increases the FCF. It is actually a correction to the investment in inventory that has not yet been paid. HT! at !!.. An increase in the necessary amount of cash decreases the FCF. This money cannot be paid to the providers of capital, because it is needed in the enterprise. EXHIBIT 8Superstores income statement, balance sheets (book values), and cash flow statementsEXHIBIT 9Superstores WACC Step 3: Investments In Tangible Fixed Assets. An increase in the tangible fixed assets will clearly lead to a decrease in the FCFs. The investments in the tangible fixed assets are equal to the change of that line item plus the depreciation in the given year. At the end of year 2008, the book value of the tangible fixed assets was $6,009; at the end of year 2009, the book value was $6,370. The difference between these amounts plus the depreciation in 2009 is the investment in tangible fixed assets for 2009 Step 4: Taxes as if Company Was Financed Solely With Equity. With the WACC method, the tax benefits of using debt are not expressed in a higher FCF but in a lower cost of capital. The tax that should be subtracted in computing FCF is equal to the corporate tax rate times the company's EBIT. As such, tax will be calculated as if the enterprise did not have any interest-bearing debt. For 2009, this is 25% x $973 = $243. The tax that is subtracted is not the same as the actual tax paid, as shown in the cash flow statement. For Superstore, this leads to the FCFs as provided in Exhibit 11. The FCF strongly increases in 2013 because the investments in tangible fixed assets decrease in EXHIBIT 10Ratios for Superstores income that year. During the period 2009-2012 there is an important yearly investment in statements, balance sheets, and cash flow growth, of which Superstore reaps the fruits from 2013 onwards. In 2013 the FCF statements increases 81%. From 2014 onwards, the FCF increases yearly by 2%. It is recommended to make a forecast for a minimum of two years after the explicit period, to avoid making mistakes with respect to the FCF used in the continuing value. The determination of Superstore's value is shown in Exhibit 12. If the enterprise is in possession of an excessive amount of cash (a "nonoperational asset), then one must add this amount to the calculated value. This amount is equal to zero for Superstore on 1/1/2009. The equity value ($3,943) is equal to the enterprise value ($6,816) minus the value of the interest-bearing debt as of 12/31/08 ($2,873). The creditors and the provisions are not deducted because these line items are taken into account in the cash flow statement and are part of the FCF. Hence, one deducts only the interest-bearing debt to determine the equity value. In the calculations, the present author assumed a WACC of 9.25% and that 50% of the enterprise value would be financed with equity. On 12/31/08, the actual portion of enterprise value that is equity was higher than 50%. 12 This means that to truly be allowed to use a WACC of 9.25%, Superstore has to slightly raise its leverage in the near future. If Superstore is not aiming to adjust this proportion, then the WACC of 9.25% is too low and the company is overvalued. More about the WACC The required return on equity is determined by the risk of the projects in which the enterprise is engaged (i.e., company risk), in combination with the leverage. The higher the leverage, the higher the financial risk for equity holders, which can be expressed with the help of the formula found in Exhibit 13. EXHIBIT 11 Calculation of the FCFs during the explicit period and the first 2 years thereafter.EXHIBIT 12Value of SuperstoreEXHIBIT 13Financial Risk far Equity Holders If a different capital structure is desired, the rg in Exhibit 5 must be adapted, since the cost of raising capital is positively dependent on the leverage. In Exhibit 14, it appears that the WACC decreases if the enterprise is financed with more debt. Exhibits 15 and 16 apply the formula in Exhibit 14 to Superstore with 0% and 50% debt financing, respectively. The decrease in WACC can be explained by the tax benefits that increase when debt financing increases. Moreover, when using the formula in Exhibit 14 to determine WACC instead of the formula employed in Exhibit 5, r^sub Edoes not have to be adapted every time. The formula already takes the influence of an increase in leverage on the required return of equity into account.13 The reader should know, however, what r^sub U^ is. Superstore s r^sub U^ was calculated with the help of the second formula in Exhibit 13. To determine that amount, Superstore needed an 'sub Ethat was valid for a capital structure with 50% debt financing. If the r^sub E^ of the enterprise to be valued is unknown, how is t^sub U^ determined? In other words, how does one then determine the required return on equity for bearing only business risk? R^sub U is often determined by looking at competing firms 14 and correcting the required return on equity for the "leverage of these firms. An average value of the found r^sub U^s of these enterprises could be a good estimate of the r^sub U^ needed for determining the subject firm's rasub E or the WACC. The return required by capital providers depends on company risk and financial risk. The proportion of debt to equity determines the financial risk - the higher the proportion, the higher the financial risk for the providers of equity. If an enterprise changes its target capital structure, this will influence the required return on equity and the WACC. The higher the leverage, the higher the rasub E^ and the lower the WACC (WACC decreases due to the increase in tax benefits of debt financing). Conclusion To value an enterprise, it is wise to start by analyzing past financial statements. Thereafter, a valuator should construct balance sheets and profit and loss accounts for as many years as possible. While looking into the future is difficult, it is indispensable for a WACC valuation. Valuators must check to see that projections are realistic and be aware of "hockey stick projections" that are often times) made by management. If the FCFs are well founded, they should be discounted with the WACC, which reflects the risk of the firm's projects. The outcome of the calculation gives the enterprise value, excluding the nonoperational assets. If the enterprise owns nonoperational assets, the market value of these assets should be added to the WACC value. The market value of equity, then, is the total enterprise value (including the nonoperational assets) minus current interest-bearing debt. EXHIBIT 14 WACC Farula EXHIBIT 14 WACC Formale WACT: WACCE: EXHIRIT 10 WACC W Leverpes lavorape is on the WOON WO-DE-L-010-05-000-0.25 -0. SCO Footnote 1 The term market value in this context is possibly confusing since the calculated market value of an enterprise can deviate from the buying or selling price. If, for example, a director who is a majority shareholder wants to sell his or EXHIBIT 10 her shares for a price that corresponds with the value that the director had WACC Worrage base If were 50% dubt, the WWOC calculated for the shares, but he or she fails in convincing buyers of the cash WACC ---10-01-06-006-623 -0.6 flow potential of the enterprise, then no buyer will be willing to pay a price near EXHIBIT 14WACC FormulaEXHIBIT 15WACC If the market value that he determined. Leverage is 0%EXHIBIT 16WACC If Leverage Is 50% 2 Assume X invests $100 and the expected return on this investment is 10% per period, then the $100 is expected to be worth $110 at the end of the first period (t=1). Conversely, it can be said that an expected value of $110 at the end of the first period is now (t=0) worth $110/1.1 = $100. In other words, the present value of the expected $110 at t=1 is $100 at t=0. 3 See also Brealey. Myers, and Allen. Principles of Corporate Finance. 9th Ed. (McGraw-Hill, 2008). 4 See Gordon and Shapiro, "Capital Equipment Analysis: The Required Rate of Profit" Vol. 3 Management Science No. 1. pages 102-110 (October 1956). 5 Some entrepreneurs posit that debt financing is unwise because the bank profits more. Assume that a business owner finances his or her company by not only investing personal equity, but also by giving loans to the company. As such, the owner is both an equity and debt provider to his or her company. In that case, the cash flow after corporate taxation will be higher than when the owner finances the company solely with equity, since in the latter scenario he or she will not make use of the tax-deductibility of interest costs. This discussion, however, ignores differences in income tax rates. If interest revenue is taxed more heavily than equity revenue, then the total tax benefit can turn out to be lower or even negative. 6 For the theoretical derivation of tax shields, see Schauten, "Valuation, Capital Structure Decisions, and the Cost of Capital" Dissertation, Erasmus University Rotterdam (2008). 7 If the CCF is discounted with the WACC before tax, we would find the correct value because the tax benefit of debt capital is omitted from the WACC calculation. The tax benefits are thus either expressed in the cost of capital (WACC) or in the expected cash flow, but not both. Moreover, applying the CCF in combination with the WACC before tax is annoying, because the CCF can be calculated only if one knows the size of the debt at the beginning of the years in the forecast (during the explicit period and the years thereafter). If one assumes that the amount of debt is a stable percentage of the enterprise value at the beginning of each year, then this is not an easy exercise because the enterprise value is unknown and is exactly what one is trying to calculate. Footnote 8 This corresponds to the interest-bearing debts as of 12/31/2008. 9 And so 50% of debt. 10 Companies that invest in growth will have higher investments than depreciation. 11 Provisions are equivalent to contingent liabilities or contingencies. 12 The equity proportion is now $3,943/$6,816. Footnote 13 As can be seen, r^sub E' does not even appear in the formula 14 "Competing firms" means firms that are active in the same industry, perform the same kind of activities, and preferably have the same profitability, size, and strategy. AuthorAffiliation MARC B. J. SCHAUTEN, Ph.D. is an assistant professor of finance at Erasmus University in Rotterdam, The Netherlands. Copyright Thomson Professional and Regulatory Services, Inc. Sep/Oct 2010
