第五次作业答案 1. 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. The formula for EPS without debt is  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 () 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  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. 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:  million If Tango issued $5 million debt, its total value would be:  Tango equity: $10.125 million The weighted average cost of capital (WACC) is given by (Bodie and Merton, p436)  (  And   (  (Alternatively, you can use equation 16.1 of Bodie and Merton, p435) The expected net income is:  million The value of equity:  million 3. Current price per share:  Amount to borrow: 40% of $13.125 million = $5.25 million PV of tax shield:  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:  million 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  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:  This translates to a 1988 value of  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 $3,384 $3,004 $3,111 $3,294 $3,483  Interest tax shields(TC=34%) 1,151 1,021 1,058 1,120 1,184   The discounted value of these tax shields is :  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: . Second, use it to calculate the levered terminal value as of the end of 1993:  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  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  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.