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A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 B C D E F G H I J Your Name: Problem Set 6: Compiled from Problem (22-7) on Textbook page 905 Merger Analysis Wansley Portal Inc., a large Internet service provider, is evaluating the possible acquisition of Alabama Connections Company (ACC), a regional Internet service provider. Wansley's analysts project the following post merger data for ACC (in thousands of dollars): Net sales Selling and administrative expense Interest 2016 $500 60 30 2017 $600 70 40 2018 $700 80 45 2019 $760 90 60 2020 $806 96 74 If the acquisition is made, it will occur on January 1, 2016. All cash flows shown in the income statements are assumed to occur at the end of the year. ACC currently has a capital structure of 30 percent debt, which costs 9 percent, but Wansley would increase that to 40 percent debt, costing 10 percent if the acquisition were made. ACC, if independent, would pay taxes at 30 percent, but its income would be taxed at 35 percent if it werre consolidated. ACC's current market-determined beta is 1.40. The cost of goods sold is expected to be 65 percent of sales, but it could vary somewhat. Gross investment in operating assets is expected to be equal to depreciation--replacing worn out equipment, so net investment in operating assets will be zero. The risk-free rate is 7 percent, and the market risk premium is 6.5 percent. Wansley currently has $400,000 in debt outstanding. Tax rate of ACC before the merger Tax rate after merger Cost of goods sold as a % of sales Debt ratio (percent financed with debt) before the merger Cost of debt before merger Debt ratio (percent financed with debt) after the merger Cost of debt after merger Beta of ACC Risk-free rate Market risk premium Terminal growth rate of free cash flow Pre-merger debt (in thousands) 30% 35% 65% 30% 9% 40% 10% 1.40 7% 6.5% 6.0% 400 $ a. What is the unlevered cost of equity? The unlevered cost of equity should be used to discount the FCFs, tax shields and horizon value. Step 1: Find the levered cost of equity at old capital structure. rL = Step 2: Find the unlevered cost of equity. rU= b. What is the horizon value of the tax shields and the unlevered operations? What is the value of ACC's operations and the value of ACC's equity to Wansley's shareholders? Before we can proceed with this problem, we must generate pro forma income statements for ACC's operations after the proposed merger so we can calculate free cash flow and interest tax shields. 2016 2017 2018 2019 2020 Sales Cost of Goods Sold (including depreciation) Gross Profit Selling and admin. Costs EBIT Interest EBT Taxes Net Income EBIT NOPAT Investment in net operating capital FCF * In this scenario, we state that investment in net operating capital is zero. This arises from the fact that the only needed investments are those needed to replace worn out capital, and that they equal depreciation. We must determine the tax shields. From this point, we can derive horizon value from the basic DCF framework. The tax shield is the interest multiplied by the post-merger tax rate. 2016 0.0 Interest Tax shield HVTS 2020 HVTS 2020 HVTS 2020 HVTS 2020 = = = = TS2020 * * / 2017 0.0 (1+g) 2018 0.0 / / 2019 0.0 (rsU 2020 0.0 - To calculate the value of the tax shields add the horizon value of the tax shields to the 2020 tax shield g) 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 A B C D E F G H to get the total tax shield cash flow in 2020. In the other years the total TS cash flow is just the annual TS Then find the NPV of this stream of tax shields at the unlevered cost of equity. 2016 2017 2018 2019 I 2020 Total TS Cash Flows NPV of TS Cash Flows This is the value of all of the tax shields. To calculate the unlevered value of operations you need the unlevered horizon value and the the annual free cash flows. To calculate the unlevered horizon value, we just need the free cash flow for 2020 HVUL 2020 HVUL 2020 HVUL 2020 HVUL 2020 = = = = FCF2020 * * / (1+g) (rsU / / - g) To calculate the unlevered value of operations, add the unlevered horizon value to the free cash flow in 2020 to get the total unlevered cash flow in 2020. In the other years the unlevered cash flow is just the annual free cash flow. The unlevered value of operations is the NPV of the unlevered cash flows at the unlevered cost of equity. Year Total unlevered CFs NPV of unlevered CFs 2016 2017 2018 2019 2020 This is the unlevered value of operations The value of operations is the value of the interest tax shields plus the unlevered value of operations VTS Vunlevered + Vops = + Vops = To find the value of ACC to Wansley's shareholders take the value of operations, add in any non-operating assets (there are none for ACC) and subtract off the debt. Vops Debt Equity = = = J Module 6 Practice Problems with Solutions The following three problems are related. Practice Problem 1- Valuation Problem (22-1) Textbook page 903 Vandell's free cash flow (FCF0) is $2 million per year and is expected to grow at a constant rate of 5% a year. Its beta is 1.4. What is the value of Vandell's operations? If Vandell has $10.82 million in debt, what is the current value of Vandell's stock? (Hint: If you forgot about the corporate valuation model, see Textbook Chapter 7.) Practice Problem 2 - Merger Valuation Problem (22-2) Textbook page 903 Hastings estimates that if it acquires Vandell, interest payments will be $1.5 million per year for 3 years, after which the current target capital structure of 30% debt will be maintained. Interest in the fourth year will be $1.472 million, after which interest and tax shield will grow at 5%. Synergies will cause the free cash flows to be $2.5 million, $3.4 million, and $3.57 million in Years 1 through 4, respectively, after which the free cash flows will grow at a 5% rate. What is the unlevered value of Vandell, and what is the value of its tax shields? What is the per share value of Vandell to Hastings Corporation? Assume that Vandell now has $10.82 million in debt. Practice Problem 3 - Merger Bid Problem (22-3) Textbook page 903 On the basis of your answers to the previous two problems, indicate the range of possible prices that Hastings could bid for each share of Vandell common stock in an acquisition. Solutions 1. FCF1 = 2.00(1.05) = $2.1 million; g = 5%; b = 1.4; rRF = 5%; RPM = 6%; wd = 30%; T = 40%; rd = 8% Vops = ? P0 = ? rsL = rRF + RPM(b) = 5% + 6%(1.4) = 13.4%. WACC = wdrd(1-T) + wsrs = 0.30(8%)(0.60) + 0.70(13.4%) = 10.82% Vops = FCF0 (1 + g ) $2.1 = = $36.08 million WACC g 0.1082 0.05 VS = Vops - debt = 36.08 - 10.82 = $25.26 million Price = 25.26 million / 1 million shares = $25.26 per share 2. FCF1 = $2.5 million, FCF2 = $2.9 million, FCF3 = $3.4 million, and FCF4 = 3.57 million; Interest in the 4th year = $1.472 million. g = 5%; b = 1.4; rRF = 5%; RPM = 6%; wd = 30%; T = 40%; rd = 8% Vops = ? P0 = ? Page 1 of 3 Module 6 Practice Problems with Solutions rsU = wdrd + wsrsL = 0.30(8%) + 0.70(13.4%) = 11.78% (Note: rsL was calculated in Practice Problem 1 to be 13.4%) WACC was calculated in Practice Problem 1 to be 10.82%. Since the horizon capital structure is the same as in Practice Problem 1, the WACC is the same, although we don't need WACC to apply the APV. Tax shields are TS1 = TS2 = TS3 = Interest T = $1,500,000 (0.40) = $600,000, and TS4 = $1,472,000 (0.40) = $588,800. Tax shield horizon value = TS4(1+g)/(rsU-g) = 0.5888 (1.05)/(0.1178-0.05) = 9.12 Value of tax shields = 0.600 0.600 0.600 0.5888 + 9.12 + + + 2 3 1.1178 (1.1178) (1.1178) (1.1178) 4 = $7.67 million. Unlevered horizon value = FCF4(1+g)/(rsU-g) = 3.57(1.05)/(0.1178-0.05) = 55.29 Unlevered Vops = 2.5 2.9 3.4 3.57 + 55.29 = $44.69 + + + 2 3 1.1178 (1.1178) (1.1178) (1.1178) 4 Value of operations = unlevered Vops + value of tax shields = 44.69 + 7.67 = 52.36 million Equity value to Harrison = Vops - Debt = 52.36 million - 10.82 million = 41.54 million or $41.54 per share since there are 1 million shares outstanding. Note: Since the capital structure isn't changing and the company has reached its target capital structure by the horizon, we could have just used the corporate valuation model to calculate the value of operations. In the corporate valuation model, we discount the FCFs at the WACC to get the value of operations: Corporate Valuation Model Horizon Value = FCF4(1+g)/(WACC-g) = 3.57(1.05)/(0.1082 - 0.05) = 3.7485/(0.0582) = $64.41 million Value of operations = 2.5 2.9 3.4 3.57 + 64.41 + + + 1.1082 (1.1082) 2 (1.1082) 3 (1.1082) 4 = $52.19 million Page 2 of 3 Module 6 Practice Problems with Solutions which is the same as the value of operations calculated above, except for rounding differences (the answer above was $52.36 million). 3. On the basis of the answers in Practice Problems 1 and 2, the bid for each share should range between $25.26 and $41.54. Page 3 of 3