第五次作业答案 a) In an M&M frictionless environment, where there are no taxes and contracts are costless to make and enforce, the wealth of the shareholders is the same no matter what capital structure the firm adopts In such an environment, neither the stock price nor shareholders wealth would be affected. In the real world divido's management might be able to create shareholder value by issuing debt and repurchasing shares in two ways By reducing corporate taxes By reducing the free cash flow available to management and exposing itself to greater arket discipl b) The formula for EPS without debt is EBIT EPSallequity1.000,000 If we assume the interest rate is 6%(conclusions will not change if you assume different interest rates), then the interest payments will be $1. 2 million per year(20 x0.06=1.2) regardless the realised value of EBIT. The number of shares outstanding after exchanging debt for equity will be 800,000. EPS with debt is therefore EBIT-1.2 EPSdebt800, 000 The probability distribution of Divido's EBIT and EPS is as follows With $20 million Debt State of EBIT Net Earnings EPS (million)(I million shares (million) (800,000 shares) Bad 4 $2.8 $3.5 Fair S12 S12 $l08 13.5 Good 20 $l8.8 23.5 N Standard 6.53 s8.16 Although the shares of stock become riskier with debt financing, the expected earnings per share go up. In a frictionless financial environment, the net effect is to leave the price
第五次作业答案 1. a) In an M&M frictionless environment, where there are no taxes and contracts are costless to make and enforce, the wealth of the shareholders is the same no matter what capital structure the firm adopts. In such an environment, neither the stock price nor shareholders' wealth would be affected. In the real world Divido's management might be able to create shareholder value by issuing debt and repurchasing shares in two ways: − By reducing corporate taxes − By reducing the free cash flow available to management and exposing itself to greater market discipline. b) The formula for EPS without debt is 1,000,000 all equity EBIT EPS = If we assume the interest rate is 6% (conclusions will not change if you assume different interest rates), then the interest payments will be $1.2 million per year ( 200.06 =1.2 ) regardless the realised value of EBIT. The number of shares outstanding after exchanging debt for equity will be 800,000. EPS with debt is therefore 800,000 1.2 debt − = EBIT EPS The probability distribution of Divido's EBIT and EPS is as follows: State of Economy EBIT (million) All Equity Financing With $20 million Debt EPS (1 million shares) Net Earnings (million) EPS (800, 000 shares) Bad $4 $4 $2.8 $3.5 Fair $12 $12 $10.8 $13.5 Good $20 $20 $18.8 $23.5 Mean $12 $13.5 Standard Deviation $6.53 $8.16 Although the shares of stock become riskier with debt financing, the expected earnings per share go up. In a frictionless financial environment, the net effect is to leave the price of stock unchanged. 2
a) The unlevered free cash flow for the Tango Shoes Division would be(in millions Sales $l0 Variable Costs $5.5 Depreciation: $1 Taxes(@40%)$14 After-tax Profit: $2.1 Depreciation: $1 Investment: S1 Free Cash Flow: $2. 1 million If unlevered, Tango is worth S13. 125 million 0.16 b) If Tango issued $5 million debt, its total value would be VL=+z2B=13.25+0.4×5=15.125 Tango equity: $10. 125 million c)The weighted average cost of capital (WACC) is given by (bodie and Merton, p436) WACC 15.12 And WACC -YE D+6+(1-t/DD+E 10.12 5.125 15.125 +(1-04)×0.10 15125=17.78% Alternatively, you can use equation 16. 1 of Bodie and Merton, p435) d)The expected net income is: 2.1-0.6x(0.10x5)=$1. 8million The value of equity $.125 million 17.78% 13.125 a) Current price per share =$2625 0.5 b) Amount to borrow: 40% of$13. 125 million=$5.25 million PⅤ of tax shield:04×5.25=$2.1 million Value of levered firm: 13. 125+2.1=$.225 million value of equity: 15.225-5.25=$9.975 million The number of shares repurchase 0.2 million
a) The unlevered free cash flow for the Tango Shoes Division would be (in millions): Sales: $10 Variable Costs $5.5 Depreciation: $1 Profit before Tax: $3.5 Taxes (@40%) $1.4 After-tax Profit: $2.1 Depreciation: $1 Investment: $1 Free Cash Flow: $2.1 million If unlevered, Tango is worth: $13.125 0.16 2.1 = million b) If Tango issued $5 million debt, its total value would be: VL =VU + cB =13.125 + 0.45 =15.125 Tango equity: $10.125 million c) The weighted average cost of capital (WACC) is given by (Bodie and Merton, p436) 15.125 2.1 = WACC 15.125 2.1 WACC = And ( ) D E D r D E E WACC rE c D + + − + = 1 ( ) 15.125 5 1 0.4 0.10 15.125 10.125 15.125 2.1 = rE + + − rE =17.78% (Alternatively, you can use equation 16.1 of Bodie and Merton, p435) d) The expected net income is: 2.1− 0.6(0.105) = $1.8 million The value of equity: $10.125 17.78% 1.8 = million 3. a) Current price per share: $26.25 0.5 13.125 = b) Amount to borrow: 40% of $13.125 million = $5.25 million PV of tax shield: 0.45.25 = $2.1 million Value of levered firm: 13.125 + 2.1 = $12.225 million Value of equity: 15.225 − 5.25 = $9.975 million The number of shares repurchased: 0.2 26.25 5.25 = million
c) Foxtron's management must trade off the tax saving due to additional debt financin he costs of financial distress that rise with the degree of debt financing The valuation process involves four steps Step 1: Calculating the present value of unlevered cash flows for 1989-9 The unlevered cash flows for 1989-93 are shown in the last line of Table 1 TABLE 1. RJR Operating Cash Flows(in Millions 1990 1992 1993 Operating income $2.620S3.410$3645$3,950$4.310 891 1.142 1222 1.326 1448 After-tax operating income 1,7292,268 2.423 2.624 2.862 Add back depreciation 449 Less capital expenditures 512 (203) (275) 3.545 1.805 Unlevered cash flow (UCF) 说明:这里给的是根据原始文献中的数据的计算结果。在原始文献中的“ Change in working capital”一项与作业中给出的值的符号是相反的。这是编辑此道题时出现的错误之一,在此 表示歉意 These flows are discounted by the required asset return, ro, which is 14 percent. The value as of the end of 1988 of the unlevered cash flows expected from 1989 through 1993 54044.3112.1732.3362.536 Step 2: Calculating the present value of m e.=$12.224billion 1.14 +142+145+1.14+ ered cash flows beyond 1993(.e. unlevered terminal value With the indications given in Table 4.3, it's easy to calculate the value, as of the end of 1993, which 2.536(1.03) $23. 746billic 0.14-0.03 This translates to a 1988 value of 23.746 $12.333billion Therefore, the total unlevered value of the firm is ($12. 224+$12. 333=)$24.557 billion To calculate the total buyout value, we must add the interest tax shields expected to be realized by debt financing Step 3: Calculating the present value of interest tax shields for 1989-93 It's easy to calculate interest tax shields for 1989-93 according to Table 4.2 TABLE 2. Tax Shields for 1989-93(in Millions)
c) Foxtron's management must trade off the tax saving due to additional debt financing against the costs of financial distress that rise with the degree of debt financing. 4． The valuation process involves four steps: Step 1: Calculating the present value of unlevered cash flows for 1989-93. The unlevered cash flows for 1989-93 are shown in the last line of Table 1. TABLE 1. RJR Operating Cash Flows (in $millions) 1989 1990 1991 1992 1993 Operating income $2,620 $3,410 $3,645 $3,950 $4,310 Tax on operating income 891 1,142 1,222 1,326 1,448 After-tax operating income 1,729 2,268 2,423 2,624 2,862 Add back depreciation 449 475 475 475 475 Less capital expenditures 522 512 525 538 551 Less change in working capital (203) (275) 200 225 250 Add proceeds from asset sales 3,545 1,805 Unlevered cash flow (UCF) $5,404 $4,311 $2,173 $2,336 $2,536 说明：这里给的是根据原始文献中的数据的计算结果。在原始文献中的“Change in working capital”一项与作业中给出的值的符号是相反的。这是编辑此道题时出现的错误之一，在此 表示歉意。 These flows are discounted by the required asset return,r0,which is 14 percent. The value as of the end of 1988 of the unlevered cash flows expected from 1989 through 1993 is $12.224billion 1.14 2.536 1.14 2.336 1.14 2.173 1.14 4.311 1.14 5.404 2 3 4 5 + + + + = Step 2: Calculating the present value of the unlevered cash flows beyond 1993(i.e. unlevered terminal value) . With the indications given in Table 4.3, it’s easy to calculate the value, as of the end of 1993, which is: $23.746billion 0.14 0.03 2.536(1.03) = − This translates to a 1988 value of $12.333billion 1.14 23.746 5 = Therefore, the total unlevered value of the firm is ($12.224+$12.333=) $24.557 billion. To calculate the total buyout value, we must add the interest tax shields expected to be realized by debt financing. Step 3: Calculating the present value of interest tax shields for 1989-93. It’s easy to calculate interest tax shields for 1989-93 according to Table 4.2: TABLE 2. Tax Shields for 1989-93 (in $millions)
1989 1990 1991 1992 1993 Interest expenses $3,3843,004$3,111S3,294$3,483 Interest tax shields(Tc=34%) 1.151 1021 581, 1,184 The discounted value of these tax shields is 1.151102110581.1201.184 S3.877billion 1.1351.13521.13531.13541.135 Step 4: Calculating the present value of interest tax shields beyond 1993 Finally, we must calculate the value of tax shields associated with debt used to finance the operations of the company after 1993. Since it's assumed that debt will be maintained at 25 percent of the value of the firm after 1993, it is appropriate to use the WACC method to calculate a terminal value for the firm at the target capital structure. This in turn can be de all-equity value and a value from tax shields F (1-34%)×13.5%+×14%=12.8% Second use it to calculate the levered terminal value as of the end of 1993 2.536(1.03) 526. 654billion Since the levered value of the company is the sum of the unlevered value plus the value of interest tax shields, it is the case the Value of tax shields(end 1993)= Vi(end 1993)-Vu(end 1993) S26.654 billion -$23. 746 billi S2.908 bill Then, we again discount by rowing rat nt to get 2.908 S1.544billion The total value of interest tax shields therefore equals($3.877+$1. 544=$5. 421 billion Adding all of these components together, the total value of RjR under the buyout proposal is 24.557+5.241=$29978 billion. Deducting the $5 billion market value of assumed debt yields a value for equity of $24.978 billion, or $109.07 per share The above process are concluded in Table TABLE 3 RJR LBO Valuation(in Millions except share data) 1989 1990199119921993 Unlevered cash flow(UCF) 5,404$4,311$2,173$2,36$2,536 Terminal value: (3% growth after 1993) Unlevered terminal value (UTV) 23,746 Terminal value at target debt Tax shield in terminal value 2,908 Interest tax shields 1.15110211.0581.1201.184
The discounted value of these tax shields is : $3.877billion 1.135 1.184 1.135 1.120 1.135 1.058 1.135 1.021 1.135 1.151 2 3 4 5 + + + + = Step 4: Calculating the present value of interest tax shields beyond 1993. Finally, we must calculate the value of tax shields associated with debt used to finance the operations of the company after 1993. Since it’s assumed that debt will be maintained at 25 percent of the value of the firm after 1993, it is appropriate to use the WACC method to calculate a terminal value for the firm at the target capital structure. This in turn can be decomposed into an all-equity value and a value from tax shields. First, we can calculate its WACC, which is: 14% 12.8% 4 3 (1 34%) 13.5% 4 1 − + = . Second, use it to calculate the levered terminal value as of the end of 1993: $26,654billion 0.128 0.03 2.536(1.03) = − Since the levered value of the company is the sum of the unlevered value plus the value of interest tax shields, it is the case that Value of tax shields (end 1993) = VL(end 1993) – VU(end 1993) = $26.654 billion - $23.746 billion = $2.908 billion Then, we again discount by the borrowing rate of 13.5 percent to get $1.544billion 1.135 2.908 5 = The total value of interest tax shields therefore equals ($3.877+$1.544)=$5.421 billion. Adding all of these components together, the total value of RJR under the buyout proposal is 24.557+5.241=$29.978 billion. Deducting the $5 billion market value of assumed debt yields a value for equity of $24.978 billion, or $109.07 per share. The above process are concluded in Table 3: TABLE 3 RJR LBO Valuation (in $millions except share data) 1989 1990 1991 1992 1993 Unlevered cash flow (UCF) $5,404 $4,311 $2,173 $2,336 $2,536 Terminal value:(3% growth after 1993) Unlevered terminal value (UTV) 23,746 Terminal value at target debt 26,654 Tax shield in terminal value 2,908 Interest tax shields 1,151 1,021 1,058 1,120 1,184 1989 1990 1991 1992 1993 Interest expenses $3,384 $3,004 $3,111 $3,294 $3,483 Interest tax shields(TC=34%) 1,151 1,021 1,058 1,120 1,184
PV of UCF 1989-93 at 14% PV of uTv at 14% 12333 Total unlevered value $24,557 PV of tax shields 1989-93 at 13. 5% PV of tax shields in Tv at 13.5% 1.544 Total value of tax shield 5.42 Total value 29,978 Less value of assumed debt 5.000 Number of shares 229 million Value per share $109.07 Concluding Comments on LBO Valuation Methods The WACC method is by far the most widely applied approach to capital budgeting. One could analyze an lBo and generate the results of the second section of this appendix using this technique, but it would be a much more difficult process. We have tried to show that the APV approach is the preferred way to analyze a transaction in which the capital structure is not stable over time Consider the WACC approach to valuing the kkr bid for RR. One could discount the operating cash flows of RR by a set of weighted average costs of capital and arrive at the same $30 billion total value for the company. To do this, one would need to calculate the appropriate rate for each year since the WACC rises as the buyout proceeds. This occurs because the value of the tax subsidy declines as debt principal is repaid In other words, there is no single return that represents the cost of capital when the firms capital structure is changing There is also a theoretical problem with the WACC approach to valuing a buyout. To calcul ate the changing WACC, one must know the market value of a firms debt and equity. But if the debt and equity values are already known, the total market value of the company is also known. That is, one must know the value of the company to calculate the WACC. One must therefore resort to using book-value measures for debt and equity, or make assumptions about the evolution of their market values of their market values, in order to implement the WACC meth
PV of UCF 1989-93 at 14% 12,224 PV of UTV at 14% 12,333 Total unlevered value $24,557 PV of tax shields 1989-93 at 13.5% 3,877 PV of tax shields in TV at 13.5% 1,544 Total value of tax shields 5,421 Total value 29,978 Less value of assumed debt 5,000 Value of equity $24,978 Number of shares 229 million Value per share $109.07 Concluding Comments on LBO Valuation Methods The WACC method is by far the most widely applied approach to capital budgeting. One could analyze an LBO and generate the results of the second section of this appendix using this technique, but it would be a much more difficult process. We have tried to show that the APV approach is the preferred way to analyze a transaction in which the capital structure is not stable over time. Consider the WACC approach to valuing the KKR bid for RJR. One could discount the operating cash flows of RJR by a set of weighted average costs of capital and arrive at the same $30 billion total value for the company. To do this, one would need to calculate the appropriate rate for each year since the WACC rises as the buyout proceeds. This occurs because the value of the tax subsidy declines as debt principal is repaid. In other words, there is no single return that represents the cost of capital when the firm’s capital structure is changing. There is also a theoretical problem with the WACC approach to valuing a buyout. To calculate the changing WACC, one must know the market value of a firm’s debt and equity. But if the debt and equity values are already known, the total market value of the company is also known. That is, one must know the value of the company to calculate the WACC. One must therefore resort to using book-value measures for debt and equity, or make assumptions about the evolution of their market values of their market values, in order to implement the WACC method
