WEB EXTENSION26A Projecting Consistent Debt and Interest Expenses Projecting financial statements for a merger analysis requires explicit assumptions regarding the capital structure in the post-merger years. This Extension shows how to project debt and interest expenses that are consistent with the capital structure assumptions. Refer to the worksheet Web 26A in the file IFM10 Ch26 Tool Kit.xls for all calculations. PROJECTING CONSISTENT DEBT AND INTEREST EXPENSES WHEN CAPITAL STRUCTURE IS CONSTANT See the worksheet Web 26A in IFM10 Ch26 Tool Kit.xls on the textbook s Web site for calculations. 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 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. Here are the steps required to project debt levels that are consistent with the assumed constant capital structure: 1. Use the techniques of Chapter 9 to project the operating items on the financial statements needed to calculate free cash flows. Notice that these projections don t depend on the capital structure because they are for operating items and not financial items. 2. Calculate the WACC that corresponds to the constant capital structure. 3. Calculate the horizon value of operations using the corporate valuation model horizon value formula.
26A-2 Web Extension 26A Projecting Consistent Debt and Interest Expenses TABLE 26A-1 Constant Capital Structure: The Value of Operations, Debt, and Interest Expense (Millions of Dollars) 1/1/10 12/31/10 12/31/11 12/31/12 12/31/13 12/31/14 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 Debt w d (V ops ). b The interest expense is based on the amount of debt at the beginning of the year: Interest expense in Year t r d (Debt t 1 ). 4. 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. 5. 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. Step 1. Project Operating Items The worksheet Web 26A in the file IFM10 Ch26 Tool Kit.xls shows the projected financial statement items related to Tutwiler Controls s operations and its projected free cash flows. The free cash flows are shown here in the first row of Table 26A-1. The following sections explain the other rows of Table 26A-1. Step 2. WACC Calculation This is the same calculation we performed in Chapter 26. Tutwiler will maintain its current capital structure consisting of 30.17% debt and 69.83% equity. Tutwiler s cost of equity was calculated to be 13%, and its cost of debt is 9%. Tutwiler s tax rate is 40% 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% Step 3. Horizon Value of Operations Tutwiler s free cash flow in 2014, FCF 2014, was projected to be $6.8 million with an expected growth rate of 6%. In Chapter 26, we calculated the horizon value, HV 2014, to be HV 2014 FCF 2014(1 + g) WACC - g This horizon value is shown in the second row of Table 26A-1. $6.8(1.06) 0.10707-0.06 $153.1 million Step 4. Calculate the Value of Operations Each Year Tutwiler s value of operations at the end of 2014 is simply the horizon value of operations, $153.1 million. The value of operations at the end of 2013 is the present
Projecting Consistent Debt and Interest Expenses When Capital Structure Is Not Constant 26A-3 value of all of the cash flows to be received after 2013, discounted back to 2013. This is equal to the present value of the value of operations in 2014 plus the 2014 free cash flow, both discounted back 1 year: Similarly, V op 2013 V op 2014 + FCF 2014 1 + WACC V op 2012 V op 2013 + FCF 2013 1 + WACC The value of operations for each year is shown in the third row of Table 26A-1. Step 5. Calculate the Amount of Debt Each Year We assumed that Tutwiler s capital structure will remain constant each year, with debt set at 30.17% of the value of operations. Thus in 2014 debt will be $153.1(0.3017) $46.2 million, and in 2013 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%, so in 2014 interest expense is $43.6(0.09) $3.9 million. The interest expenses for 2010 through 2013 are calculated similarly and are shown in Table 26A-1. The debt level in 2009 and the interest expense in 2010 deserve comment. In 2009, prior to the merger, Tutwiler has $27 million in debt, and this comprises 30.17% 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% 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 2010 and will therefore contribute to its interest expense in 2010. Thus, Tutwiler s projected 2010 interest expense is $33.2(0.09) $3.0 million. Debt levels and their corresponding interest expenses are shown in the fourth and fifth rows of Table 26A-1. PROJECTING CONSISTENT DEBT AND INTEREST EXPENSES WHEN CAPITAL STRUCTURE IS NOT CONSTANT $6.8 + $153.1 1 + 0.10707 $6.4 + $144.5 1 + 0.10707 $144.5 million $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 in these situations because the discount rates vary during the forecast period. Rather, the APV is the appropriate approach, but it is necessary to 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 before becoming constant at the end of the horizon. To ensure correct calculations of the horizon value of the unlevered firm and the horizon value of the tax shield, the company must be at its long-term constant capital structure in the last year of projections, in this case 2014. This means the debt level at the end of 2013 must be consistent with the assumed long-term capital structure so that the interest expense in
26A-4 Web Extension 26A Projecting Consistent Debt and Interest Expenses TABLE 26A-2 Nonconstant Capital Structure during Forecast Period: The Value of Operations, Debt, and Interest Expense at the End of the Forecast Period (Millions of Dollars) 2010 2011 2012 2013 2014 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 2014 is also consistent with the long-term capital structure. The steps to project a consistent debt level for 2013 are similar to those described in the previous section: 1. Use the techniques of Chapter 9 to project the operating items on the financial statements needed to calculate free cash flows. Notice that these projections don t depend on the capital structure because they are for operating items and not financial items. 2. Calculate the levered cost of equity and WACC that will prevail in the posthorizon period when the capital structure has become constant. 3. Calculate the horizon value of operations using the corporate valuation model horizon value formula. 4. Calculate the value of operations in the last 2 years of the forecast period. 5. 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 2013, at which point its debt level must be consistent with a long-term capital structure consisting of 50% debt. The results of these calculations appear in Table 26A-2. Step 1. Project Operating Items The worksheet Web 26A in the file IFM10 Ch26 Tool Kit.xls shows the projected financial statement items related to Tutwiler s operations and its projected free cash flows. The free cash flows are shown here in the first row of Table 26A-2. The following sections explain the other rows of Table 26A-2. Step 2. Calculate the Unlevered Cost of Equity and WACC at Post-Horizon Target Capital Structure In Chapter 26 we calculated Tutwiler s 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% debt capital structure for the post-horizon period, the interest rate on the debt will increase to 9.5%. The cost of equity, r sl, will also increase due to the increased leverage. This post-horizon cost of equity can be calculated with Equation 26-4, using the post-horizon capital structure 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%
Projecting Consistent Debt and Interest Expenses When Capital Structure Is Not Constant 26A-5 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 3. Calculate the Horizon Value of Operations The horizon value of operations at the new WACC is HV 2014 FCF 2014(1 + g) WACC - g $6.8(1.06) 0.09893-0.06 $185.1 This value is shown in the second row of Table 26A-2. Step 4. Calculate the Value of Operations in the Last Year and the Prior Year The value of operations at the end of 2014 is simply the horizon value, $185.1 million. The value of operations at the end of 2013 is the present value of the value of operations in 2014 and the free cash flow in 2014: V op 2013 V op 2014 + FCF 2014 1 + WACC $6.8 + $185.1 $174.6 million. 1 + 0.09893 The values of operations for 2013 and 2014 are shown in the third row of Table 26A-2. Step 5. Calculate the Debt Level in the Year Prior to the End of the Horizon The debt level in 2013 is now easy to calculate. It is the post-horizon target percent of debt multiplied by the value of operations in 2013: Debt 2013 0.50($174.6) $87.3 million The interest in 2014 is simply the debt at the end of 2013 multiplied by the interest rate: Interest 2014 $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. The debt levels and interest tax shields during the prior years need not conform to a constant capital structure. As long as the interest expense in the last projected year is expected to grow at a constant rate, which our calculations guarantee, the APV approach may be applied.
26A-6 Web Extension 26A Projecting Consistent Debt and Interest Expenses TABLE 26A-3 Shortcut APV Calculation 2010 2011 2012 2013 2014 FCF $3.2 $3.2 $5.6 $6.4 $ 6.8 Horizon value 185.1 Interest tax saving 2.0 2.4 2.8 3.0 3.3 FCF, tax saving, and HV $5.2 $5.6 $8.4 $9.4 $195.2 There is a shortcut when calculating the APV if you don t need to know the separate values of the unlevered firm and the value of its tax shields. 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. Third, add the interest tax shields, the horizon value, and the free cash flows together for each year. Fourth, discount these cash flows at the unlevered cost of equity. For example, Table 26A-3 shows the free cash flows from Table 26A-2 and the horizon value that we calculated for the case in which Tutwiler s capital structure was nonconstant during the forecast period but stabilized with 50% debt in the posthorizon period. The interest tax savings in the horizon year are from Table 26A-2, while the other tax savings are from the example in Section 26.11. These values are summed on the last row of Table 26A-3. The value of operations is their present value when discounted at the unlevered cost of equity: V Ops $5.2 1.11793 + $5.6 1.11793 2 + $8.4 1.11793 3 + $9.4 1.11793 4 + $195.2 1.11793 5 $133.0 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 for the case in which the capital structure changed during the forecast period; 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.