Web Extension: Comparison of Alternative Valuation Models

19878_26W_p001-009.qxd 3/14/06 3:08 PM Page 1 C H A P T E R 26 Web Extension: Comparison of Alternative Valuation Models We described the APV model in Chapter 26 because it is easier to implement when the target s capital structure is changing than either the corporate value model or the free cash flow to equity model. In this extension we discuss the benefits and shortcomings of the two alternative valuation models and show how the debt and interest projections were made. You should refer back to Chapter 26 when reading this extension, and remember that all three valuation models give the same answers when implemented correctly using the same assumptions. However, it can be difficult to do this when the capital structure is changing. The toolkit to this extension, IFM9 Ch 26 Tool Kit.xls, has detailed Excel models that show all of the calculations. Corporate Valuation Model IMAGE: GETTY IMAGES, INC., PHOTODISC COLLECTION Analysts have used many versions of the corporate valuation model to value mergers. A traditional implementation involves the following steps, most of which are the same steps we used in this chapter but with some important differences in the details: 1. 2. 3. 4. Forecast financial statements and free cash flows for a specified period of time. Estimate the long-term growth rate and target capital structure. Estimate the WACC at the horizon using the long-term capital structure. Calculate the horizon value using the constant growth model with the WACC calculated above, the forecasted long-term growth rate, and the last projected FCF. 5. Discount the horizon value and the specified free cash flows back to the present using the estimated WACC. Note that the traditional approach to estimating the WACC at the horizon involves using the Hamada equation (Equation 15-8 in the text) to unlever the marketdetermined beta and then to relever it at the new target capital structure. This new 26E-1

19878_26W_p001-009.qxd 3/14/06 3:08 PM Page 2 beta is used to calculate a levered required return to equity. The WACC is then calculated using this Hamada-determined cost of equity and the new capital structure. This approach may give incorrect results for several reasons. First, if the capital structure is changing over time, the WACC will be changing over time, and it is difficult to specify the correct discount rate. The changing capital structure also affects the interest tax shield, and this too can lead to errors. Another, and more serious, problem is using the Hamada equation to unlever and then relever the equity return. The Hamada equation assumes that both the debt and the interest tax shield are risk free. This means that as the equity return is relevered using more and more debt, all of the risk is concentrated on the equity. Because the interest rate on corporate debt is always greater than the risk-free rate, clearly the debt is not risk free. Furthermore, our discussion in Chapter 16 showed that the appropriate discount rate for the tax shield should be the unlevered cost of equity, not the cost of debt. Therefore, using Hamada to relever equity returns in calculating the horizon WACC will give an incorrect WACC and thus an incorrect valuation. The equation we use in this chapter to unlever and relever equity returns, Equation 16-15, assumes that the interest tax shield is risky and thus should be discounted at the unlevered cost of equity. To correctly implement the corporate valuation model when the capital structure is changing you must take the following steps: 1. Project financial statements for a period of time, and calculate free cash flows. 2. Project a long-term growth rate and a long-term target capital structure. 3. Estimate the WACC at the horizon using the long-term expected capital structure, using Equation 16-15 to relever the equity return. 4. Calculate the horizon value using a constant growth model with the WACC calculated above, the growth rate assumed, and the last projected FCF. 5. Calculate a new value of operations and WACC each year before the horizon using the actual debt ratio for that year in Equation 16-15 for the WACC calculation. 6. Discount the horizon value and the intermediate free cash flows back to the present using the individual WACCs estimated above. Although this will, in principle, work, the APV is simpler to implement and should be used when the capital structure is changing. Note also that simply using the WACC calculated in Step 3 to discount the free cash flows in the years before the horizon will give an incorrect answer: Because the capital structure is changing each year, the appropriate WACC is also changing each year. Discounting free cash flows at an incorrect WACC gives the wrong answer. Free Cash Flow to Equity (FCFE) Model The FCFE model has some intuitive appeal since the value of equity is directly estimated from its cash flows rather than having to find the value of operations first. However, its traditional implementation when the capital structure is changing has some problems, just like the corporate valuation model. The first difficulty is defining free cash flow to equity. The idea of FCFE is to identify all of the cash flows available to equity holders. In our framework FCFE is calculated as Free cash flow Interest expense Interest tax shield Increase in debt Free cash flow to equity 26E-2 Chapter 26 Web Extension: Comparison of Alternative Valuation Models

19878_26W_p001-009.qxd 3/14/06 3:08 PM Page 3 The first three terms are clear; the equity holders have a claim on free cash flow less after-tax interest expense. The last term, increase in debt, is also a cash flow to equity since, by definition, free cash flow already includes any required reinvestment. Additional debt over and above free cash flow is available for share repurchases or dividends and so is available to shareholders. This term, however, adds a wrinkle to the FCFE model that isn t part of the other two models. The FCFE model requires knowing both interest expense and debt level since changes in debt level affect FCFE. A traditional implementation of the FCFE model would involve the following steps: 1. Project financial statements for a period of time, and calculate FCFE. 2. Project the long-term growth rate and the long-term capital structure. 3. Estimate the required rate of return to equity at the horizon using the longterm expected capital structure. 4. Calculate the horizon value using a constant growth model with the return to equity calculated above, the growth rate assumed, and the last projected FCFE. 5. Discount the horizon value and the intermediate FCFEs back to the present using the equity return estimated above. As with the traditional implementation of the corporate valuation model, the traditional implementation of the FCFE model involves unlevering a marketdetermined beta and then relevering it using Hamada. This levered beta is then used to calculate a levered return to equity, which is used as the discount rate. These steps are subject to the same criticisms as the traditional implementation of the corporate valuation model: (1) Using a single discount rate when the capital structure is changing results in incorrectly valuing the cash flows, and (2) using Hamada for unlevering and relevering assumes risk-free debt and uses the risk-free rate to discount the tax shield, which we argue in Chapter 16 is incorrect. However, this technique suffers from an even more serious problem. The joint assumption at the horizon that the firm is at its target capital structure and that FCFE is growing at a constant rate can only be true if the firm is already at its target capital structure in the next-to-last projected year. This can be seen in the following example. Suppose a firm has the following financial projections and is expected to grow at a constant steady-state rate of 6 percent after 2008. Its tax rate is 40 percent, its cost of debt is 8 percent, its horizon target percent of debt is 20 percent, and its cost of equity at that debt ratio is 13 percent. This steady-state growth rate means free cash flow and debt will both grow at 6 percent. 2006 2007 2008 2009 2010 FCF $ 3.00 $ 2.00 $ 2.12 $ 2.25 Debt $15.00 20.00 15.00 15.90 16.85 Interest 1.20 1.60 1.20 1.27 Interest tax shield 0.48 0.64 0.48 0.51 Change in debt 5.00 5.00 0.90 0.95 FCFE 7.28 3.96 2.30 2.44 Growth in FCF 33% 6% 6% Growth in debt 25% 6% 6% Growth in FCFE 154% nmf 6% Chapter 26 Web Extension: Comparison of Alternative Valuation Models 26E-3

19878_26W_p001-009.qxd 3/14/06 3:08 PM Page 4 As assumed, the growth rate of FCF and debt stabilize at 6 percent in 2009. This means, among other things, that a constant growth horizon value can be calculated using FCF 2008. However, notice that growth in FCFE does not stabilize until the following year, 2010. A constant growth horizon value cannot be calculated using FCFE 2008, and, in this case, since FCFE 2008 is negative, the calculation would be nonsensical. Instead, a horizon value must be calculated the year after free cash flows stabilize. The horizon value in 2009 is HV Equity2009 2.30 (1.06) $34.83 0.13 0.06 A second, less tractable, problem with the horizon value is that we don t actually know what the level of debt should be in 2009. Based on our assumed debt ratio of 20 percent, a horizon value of $34.83 gives a debt level of $8.71 in 2009, not the $15.90 we assumed. But if we, instead, assume a debt level of $8.71 in 2009, FCFE 2009 will be different (because the change in debt over 2009 will no longer be 0.90) and so HV Equity2009 will no longer be $34.83. Thus, the joint assumptions that debt, and hence FCFE, will grow at a constant rate of 6 percent after 2008, that the 2008 debt level is $15.00, and that the horizon debt ratio will be 20 percent are inconsistent with each other. This particular problem is avoided in both the corporate valuation model and the APV model because the firm can recapitalize in 2009 to reach its target debt ratio without affecting its free cash flows and, hence, horizon value. Because of these difficulties, the FCFE model is actually quite difficult to implement correctly into a spreadsheet when the capital structure is changing. To do so you must take the following steps: 1. Project financial statements for a period of time, and calculate free cash flow to equity. 2. Project a long-term growth rate and a long-term target capital structure. 3. Estimate the levered cost of equity at the horizon using the long-term expected capital structure, using Equation 16-15 to relever the equity return. 4. Calculate the horizon value using a constant growth model in the year after steady state is reached with the cost of equity calculated above, the growth rate assumed, and the last projected FCFE. 5. Calculate a new value of equity and cost of equity each year before the horizon using the actual debt ratio for that year in Equation 16-15 for the cost of equity calculation. 6. Pick a debt level in the horizon year so that the actual debt ratio is equal to the projected debt ratio. 7. Discount the horizon value and the intermediate free cash flows back to the present using the individual costs of equity estimated above. Again, although these steps are, in principle, implementable, the extra complexity is unnecessary. The APV is much easier and should be used when the capital structure is changing. Projecting Consistent Debt and Interest Expenses if Capital Structure Is Constant Recall that the APV model and the FCFE model both require a projection of interest expense. If the projected interest expense is not consistent with the assumed 26E-4 Chapter 26 Web Extension: Comparison of Alternative Valuation Models

19878_26W_p001-009.qxd 3/14/06 3:08 PM Page 5 constant capital structure, then the APV and FCFE models will produce incorrect answers. This section will show how the debt levels and interest expenses in Table 26-3 in the text were constructed in a manner consistent with the assumed constant capital structure. Keep in mind, though, that if the capital structure is assumed to be constant, then it is always easier to use the corporate valuation model rather than either the APV model or the FCFE model. Line 9 in Table 26-3 in the text shows Tutwiler s projected free cash flows, and Lines 13 and 19 show the projected interest expense and debt. Here are the steps required to project the debt levels in Line 19: 1. Calculate the WACC that corresponds to the constant capital structure. 2. Calculate the horizon value of operations using the corporate valuation model horizon value formula. 3. Calculate the value of operations in each year of the projections as the present value of the next year s value of operations and the next year s free cash flows. 4. Calculate the projected debt level by multiplying the value of operations by the percent of debt in the assumed constant capital structure. The projected interest expense in any year is the projected interest rate multiplied by the projected amount of debt at the beginning of the year, as calculated above in Step 4. The results of Steps 1 through 4 are shown in Table 26E-1. Step 1. WACC Calculation This is the same calculation we performed in Chapter 26. Tutwiler will maintain its current capital structure consisting of 30.17 percent debt and 69.83 percent equity. Tutwiler s cost of equity was calculated to be 13 percent, and its cost of debt is 9 percent. Tutwiler s tax rate is 40 percent so its WACC is WACC w d (1 T)r d w S r S 0.3017(1 0.40)(9%) 0.6983(13%) 10.707% Table 26E-1 Value of Operations, Debt, and Interest Calculations (Millions of Dollars) 1/1/07 12/31/07 12/31/08 12/31/09 12/31/10 12/31/11 FCF $ 3.2 $ 3.2 $ 5.6 $ 6.4 $ 6.8 Horizon value 153.1 Value of operations $110.1 118.7 128.2 136.3 144.5 153.1 Value of debt a 33.2 35.8 38.7 41.1 43.6 46.2 Interest expense b 3.0 3.2 3.5 3.7 3.9 a Tutwiler has $27 million in debt before the acquisition. Once the acquisition is consummated, we are assuming Caldwell will increase the debt to $33.2 million to maintain the 30.17 percent debt level. This additional debt is needed because we are assuming the capital structure will remain constant after the acquisition. The additional debt will be on the books by the first day of 2007. b The interest expense in 2007 will be based on the debt level at the start of 2007, which is $33.2 million. Chapter 26 Web Extension: Comparison of Alternative Valuation Models 26E-5

19878_26W_p001-009.qxd 3/14/06 3:08 PM Page 6 Step 2. Horizon Value of Operations Tutwiler s free cash flow in 2011, FCF 2011, was projected to be $6.8 million with an expected growth rate of 6 percent. In the text, we calculated the horizon value, HV 2011, to be HV 2011 FCF 2011 (1 g) WACC g $6.8 (1.06) $153.1 million 0.10707 0.06 Step 3. Calculate the Value of Operations Each Year The value of operations at the end of 2011 is simply the horizon value of operations, $153.1 million. The value of operations at the end of 2010 is the present value of all of the cash flows to be received after 2010, discounted back to 2010. This is equal to the present value of the value of operations in 2011 plus the 2011 free cash flow, discounted back one year: Similarly, V Ops2010 V Ops2011 FCF 2011 1 WACC $6.8 $153.1 1 0.10707 $144.5 million V Ops2009 V Ops2010 FCF 2010 1 WACC Step 4. Calculate the Amount of Debt Each Year We assumed that the capital structure will remain constant each year, with debt set at 30.17 percent of the value of operations. Thus in 2011 debt will be $153.1(0.3017) $46.2 million, and in 2010 debt will be $144.5(0.3017) $43.6 million. Interest expense is equal to the debt level at the start of the year, which is the debt level at the end of the previous year, multiplied by the interest rate on debt. The interest rate on debt is 9 percent, so in 2011 interest expense is $43.6(0.09) $3.9 million. The interest expenses for 2007 through 2010 are calculated similarly and are shown in Table 26E-1. The debt level in 2006 and the interest expense in 2007 deserve comment. In 2006, prior to the merger, Tutwiler has $27 million in debt, and this comprises 30.17 percent of its capital structure based on its premerger value. However, if the merger goes through, then Tutwiler s value will increase because of synergies with Caldwell, and, to maintain the assumed 30.17 percent of debt, Tutwiler will immediately issue an additional $6.2 million in debt, for a total of $27.0 $6.2 $33.2 million in debt outstanding. This additional $6.2 million in debt will be in Tutwiler s capital structure by the start of 2007 and will therefore contribute to its interest expense in 2007. Thus, Tutwiler s projected 2007 interest expense is $33.2(0.09) $3.0 million. Debt levels and their corresponding interest expense appear in Table 26E-1. Projecting the Interest Expense at the Horizon When Using the APV Approach $6.4 $144.5 1 0.10707 $136.3 million In some situations, the capital structure is assumed to change during the forecast period prior to becoming constant at the horizon. Neither the corporate valuation model nor the FCFE model is appropriate because the discount rates vary during the forecast period. The APV is the appropriate approach, but it is necessary to 26E-6 Chapter 26 Web Extension: Comparison of Alternative Valuation Models

19878_26W_p001-009.qxd 3/14/06 3:08 PM Page 7 project the interest expense at the horizon in a manner that is consistent with the assumed post-horizon constant capital structure. In this section we show how the interest expense at the horizon is calculated for the case in which Tutwiler s capital structure changes during the forecast period. To ensure correct calculations of the horizon value of the unlevered firm (using Equation 26-2) and the horizon value of the tax shield (using Equation 26-3), the company must be at its long-term constant capital structure in the last year of projections, in this case 2011. This means the debt level at the end of 2010 must be consistent with the assumed long-term capital structure so that the interest expense in 2011 is also consistent with the long-term capital structure. The steps to project a consistent debt level for 2010 are the same as in the previous section: 1. Calculate the WACC that corresponds to the projected long-term capital structure. 2. Calculate the horizon value of operations using the corporate valuation model horizon value formula. 3. Calculate the value of operations in the last two years. 4. Calculate the projected debt level by multiplying the value of operations by the percent of debt in the assumed constant capital structure. In this example, Tutwiler will have a varying amount of debt until the end of 2010, at which point its debt level will be consistent with a long-term capital structure consisting of 50 percent debt. The results of these calculations appear in Table 26E-2. Step 1. Calculate the WACC at the New Target Capital Structure In Chapter 26 we calculated the unlevered cost of equity based on the premerger capital structure and premerger costs of debt and equity: r su w s r sl w d r d 0.6983(13%) 0.3017(9%) 11.793% Under the proposed 50 percent debt capital structure, the interest rate on the debt will increase to 9.5 percent. The cost of equity, r sl, will also increase due to the increased leverage. This new cost of equity can be calculated using Equation 16-15 and the new debt and equity levels and the new cost of debt: r sl r su (r su r d )(D/S) 11.793% (11.793% 9.5%)(0.50/0.50) 14.086% Table 26E-2 Value of Operations, Debt, and Interest Calculations (Millions of Dollars) 2007 2008 2009 2010 2011 FCF $3.2 $3.2 $5.6 $ 6.4 $ 6.8 Horizon value 185.1 Value of operations 174.6 185.1 Value of debt 87.3 Interest expense 8.3 Chapter 26 Web Extension: Comparison of Alternative Valuation Models 26E-7

19878_26W_p001-009.qxd 3/14/06 3:08 PM Page 8 The new WACC can then be calculated from this new r sl and r d : WACC w d (1 T)r d w s r sl 0.50(1 0.40)(9.5%) 0.50(14.086%) 9.893% This is the WACC that should persist at the horizon and thereafter. Step 2. Calculate the Horizon Value of Operations operations at the new WACC is The horizon value of HV 2011 FCF 2011 (1 g) WACC g $6.8 (1.06) $185.1 0.09893 0.06 Step 3. Calculate the Value of Operations in the Next to Last Year The value of operations at the end of 2011 is simply the horizon value, $185.1 million. The value of operations at the end of 2010 is the present value of the value of operations in 2011 and the free cash flow in 2011: V Ops2010 V Ops2011 FCF 2011 1 WACC $6.8 $185.1 $174.6 million 1 0.09893 Step 4. Calculate the Debt Level in the Next to the Last Year The debt level in 2010 is now easy to calculate. It is the target percent of debt multiplied by the value of operations in 2010: Debt 2010 0.50($174.6) $87.3 million and the interest in 2011 is simply the debt at the end of 2010 multiplied by the interest rate: Interest 2011 $87.3(9.5%) $8.3 million This is the interest used to calculate the horizon value of the interest tax shield in the text. Note that this procedure suggests a shortcut when calculating the APV value if you don t happen to need to know separately the value of the unlevered firm and the value of its tax shields. Table 26E-3 shows the shortcut calculations. In the shortcut, first use the corporate valuation model s horizon value calculation to calculate the horizon value based on the WACC that will persist in the long term and the last year s projected free cash flows. Second, calculate the interest tax shields that will result from the assumed debt levels prior to the horizon. These assumed debt levels prior to the horizon need not be consistent with any particular long-term debt policy; however, in Table 26E-3 we have used the tax shields that we projected earlier. Third, add the interest tax shields, the horizon 26E-8 Chapter 26 Web Extension: Comparison of Alternative Valuation Models

19878_26W_p001-009.qxd 3/14/06 3:08 PM Page 9 Table 26E-3 Shortcut APV Calculation 2007 2008 2009 2010 2011 FCF $3.2 $3.2 $5.6 $6.4 $ 6.8 Horizon value 185.1 Interest tax shield 2.0 2.4 2.8 3.0 3.3 FCF, tax shield, and HV $5.2 $5.6 $8.4 $9.4 $195.2 value, and the free cash flows together for each year. Fourth, discount these cash flows at the unlevered cost of equity. V Ops $5.2 $5.6 $8.4 $9.4 $195.2 $133.0 1.11793 2 3 4 5 1.11793 1.11793 1.11793 1.11793 This gives the value of the firm s operations, without separating out the unlevered value and the value of the tax shield. Notice that this is the same value of operations we calculated in Chapter 26; however, the calculations are simpler because a final interest expense consistent with the long-term capital structure need not be calculated, nor must separate unlevered values and tax shield values be calculated. This simplified calculation is also called the compressed adjusted present value model. 1 1 See S. N. Kaplan and R. S. Rubak, The Valuation of Cash Flow Forecasts: An Empirical Analysis, Journal of Finance, September 1995, pp. 1059 1093, for a discussion of the compressed adjusted present value model. Chapter 26 Web Extension: Comparison of Alternative Valuation Models 26E-9