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University of Texas at Dallas School of Management Finance 6301 Professor Day Corporate Finance Fall 1999 Lecture 9: Capital Structure The purpose of this note is to examine how the value of the firm is affected (holding investment policy and dividend policy constant) by the way in which the firm finances its investments. For example, can the value of the firm be increased by financing new investments with debt rather than equity? In order to examine the effect of the firm's financing decisions (the firm's capital structure) on the value of the firm, assume that 1. the firm's investment decision is given, 2. the firm's dividend policy is given, 3. there are no transaction costs involved in either the purchase or sale of securities, 4. investors can borrow and lend at the same rate that corporations can borrow and lend. Value of Tax Shields from the Corporate Deduction for Interest Expense The capital investment projects undertaken by the firm are usually financed with some combination of debt and equity. In order to understand the effect of this choice on the value of the firm, consider the case where the firm is currently financed entirely (100 percent) by equity. We will also assume that the firm's production capacity is already in place (i.e., the investment decision by the firm is a given) so that any changes in the firm's financing mix (such as replacing equity with debt financing) will have no impact on the cash flows from operations. To see how the value of the firm changes if equity financing is replaced with debt financing, suppose that the firm issues a perpetual bond that pays one dollar of interest each year. Assuming that the interest payments for the bond are riskfree and that the opportunity cost for riskfree cash flows (before personal tax) is r, the amount that is raised by issuing this bond is . The proceeds from the debt issue will be used to repurchase an equal dollar amount of the firm's outstanding equity shares. Although firms do not issue perpetual debt in practice, the consequences of using debt as a more or less permanent component of a firm's financing mix are virtually identical. The implications of the “recapitalization” (change in financing mix) described above is to divert one dollar of beforetax operating income (profit before financing charges and taxes) from stockholders to bondholders. If no debt had been issued, the firm would have to pay corporate taxes on the dollar in question at a rate of t_{c} . The remainder would be paid to the shareholders, either in the form of a dividend or through reinvestment in the firm resulting in appreciation in the stock price. Since the dividend to the shareholders would have been taxed at a rate of t_{E} , the aftertax value of one dollar of operating income directed toward the stockholders in the firm is ( 1  t_{E }) ( 1  t_{c }) $1 . The net benefit created by corporate borrowing can be determined by comparing the aftertax cash flows to the stockholders with the aftertax cash flows which bondholders receive if the firm issues enough perpetual debt so that one dollar is diverted to the payment of interest expense. Since corporations are allowed to deduct interest expense prior to computing their corporate tax liability, the interest income to the bondholders is equal to one dollar. Since interest income is taxed at a rate of t_{o} , the aftertax cash flow received by the bondholders is ( 1  t_{o} ) $1 . The value (if any) of diverting one dollar of beforetax operating cash flow from the shareholders to the bondholders can be determined by comparing (subtracting) the aftertax cash flows that would have been received by the stockholders to (from) the aftertax payment received by the new bondholders, [ ( 1  t_{o} )  ( 1  t_{E} ) ( 1  t_{c} ) ] $1 . If these aftertax cash flows are capitalized in perpetuity (i.e., valued as a perpetuity) using the aftertax return required by the bondholders, ( 1  t_{o} ) r_{D} , then the value which is created by diverting one dollar of beforetax operating income from the stockholders to the bondholders is $1 . Rearranging the expression above shows that the value created in a recapitalization that causes the firm to pay an additional one dollar per year of interest expense (in perpetuity) is [ 1  ] . For a firm having outstanding debt in the amount of D with yearly interest expense of rD , the total value created by replacing D dollars of equity (starting from a point of relying solely on equity financing) with D dollars of debt is obtained by simply multiplying the firm's yearly interest expense (rD) by the value per dollar of yearly interest expense given above. Therefore, the incremental value created by financing with debt rather than equity is given by D [ 1  ] . The incremental value of the tax shields generated by debt financing is used as an adjustment to the value of an unlevered firm (i.e., one that is 100 percent equity financed). That is the value of the recapitalized or levered firm (i.e., the value after debt has been added to the firm's financial structure) is equal to the value of the unlevered firm (V) plus the value of the tax shields from debt financing V= V+ D [1  ] . To illustrate the application of the formula, consider the following special cases. Example 1: Suppose that the corporate tax rate (t_{c }) is 50 percent, the tax rate on interest income (t_{o }) is 40 percent and the tax rate on equity income (t_{E}) is equal to zero. Then the value of the tax shields from one dollar of debt (not one dollar of interest expense) is $1 [1  ] = $1 [1  ] = $1 [ 1  ] = $ .17 . Therefore, the value of each dollar of debt added to the firm's financial structure (up to some level consistent with sustained profitability for the firm) is $.17 per dollar of debt (not interest expense). Example 2: Assume that the corporate tax rate (t_{c }) is 50 percent and that the tax rate on interest income (t_{o }) is 40 percent as in Example 1. However, assume that the tax rate on equity income (t_{E}) reflects the fact that 20 percent of the income to stockholders is in the form of dividend income taxed at 40 percent while 80 percent is in the form of capital gains having (according to many economists) an effective tax rate of zero. Therefore, the tax rate on equity income is approximately 8 percent (.20x.40 + .80x0). In this case, the value of the tax shields from one dollar of debt is $1 [1  ] = $1 [1  ] = $1 [ 1  ] = $ .23 . Note that the higher the tax rate on equity income, the greater is the value of the tax shields from replacing equity with debt financing. Example 3: A particularly important example is the case where the tax rate on interest income (t_{o }) is equal to the tax rate on equity income (t_{E}) . In this case the value of the tax shields from one dollar of debt (not one dollar of interest expense) is $1 [1  ] = $1 [1  (1  t_{c}) ] = $1 t_{c} . This example shows that when equity income and interest income are taxed at identical rates the value of the tax shields from financial leverage is determined entirely by the corporate tax rate, just as if the marketplace ignored the effects of personal income taxes. In other words, when t_{E} is equal to (t_{o }) , the value each dollar of debt is equal to t_{c} so that the value of the levered firm is given by V_{L} = V_{U} + t_{c} D . Note that the adjustment that has been used to the value of the unlevered firm (with no debt financing) to reflect the value of the tax shields from debt implicitly assumes that the firm holds the level of debt to a (“moderate”) level that allows the firm to sustain consistent (taxable) profitability. So long as the firm is consistently profitable, the full value of the tax shields may be realized (without resorting to tax loss carryforwards). What is moderate will depend critically on the nature of the industry in question. For example, firm's engaged in highly speculative research and development activities have little assurance of utilizing the tax deductions for the interest expense on debt (in addition to providing poor collateral). Therefore, firm's engaged in heavy research and development activities will tend to rely primarily on equity financing. On the other hand, firms in mature industries (e.g., tobacco or food products) that have relatively stable cash flows can often support relatively high levels of debt, as evidenced by the leveraged buyout of RJ Reynolds. The Impact of Financial Structure in a World with No Taxes To illustrate the important impact of taxes on the value of financing decisions, it is useful to examine the impact of a recapitalization (issue debt and buy back equity) on the value of the firm under the (artificial) assumption that all of the tax rates considered previously are equal to zero. Given this assumption, the example shows that even though a change in financial structure has no impact on the total value of the firm, the resulting change in the risk profile of the remaining equity shares (including an increase in the expected dividend) precipitates an increase in the cost of equity capital. MacBeth Spot Removers Example: Number of Shares = 1000 Price Per Share = $10 Firm Value = $10,000 State 1 State 2 State 3 Net Operating Income $500 $1000 $2000 Probability 1/4 1/8 5/8 Earnings Per Share $ .50 $1.00 $2.00 Return on Equity (ROE) 5% 10% 20% Given the three possible values for the Return on Equity, the expected (required) rate of return on MacBeth's stock is r_{E} = .05 + .10 + .20 , = .15 (15 percent). Assume that all earnings will be paid out as a dividend (in perpetuity). Then the expected dividend for the firm will be E() = $.50 + $1.00 + $2.00 , = $1.50 . Given that the required rate of return on equity (the cost of equity capital) is 15 percent, it is easy to verify that the price of one share in the firm should be (as we have already assumed) P_{0} = = = $10 , where r_{E} is the required rate of return on equity. Suppose now that the firm decides to a. sell $5000 of debt b. retire 500 shares of stock with the proceeds from the debt issue. Then the new capital structure will be Number of Shares = 500 Price Per Share = $10 Value of Shares = $5000 Value of Debt = $5000 To see why this must be the case, consider the possible realizations of earnings per share and return on equity for the recapitalized or levered firm. State 1 State 2 State 3 Operating Income $500 $1000 $2000 Interest Expense $500 $500 $500 Net Income 0 $500 $1500 Earnings Per Share (EPS) 0 $1.00 $3.00 Return on Equity (ROE) 0 10% 30% It can be shown that the recapitalization of the firm has increased the expected dividend for the remaining shareholders of MacBeth to $2.00 per share. (You should be able to compute the expected dividend for the recapitalized firm in the same way that we computed the expected dividend for the unlevered version of MacBeth). However, since the required rate of return increases to 20 percent (you can show that the expected Return on Equity is 20 percent), the stock price remains unchanged at $10 per share. Therefore, the recapitalization has no effect on the total value of the firm. The increase in the expected rate of return demanded by shareholders can be motivated by examining the respective payoff patterns for the unlevered (the original debtfree firm) and levered (recapitalized to include debt financing) firm. Consider our projections for ROE and EPS for each of the possible outcomes for net operating income. Although the recapitalization has increased the expected dividend per share, the increase in financial leverage has also increased the range (variability) for both dividends per share (from $.50$2.00 to 0$3.00) and Return on Equity (from 5%20% to 0%30%). In other words, financial leverage increases the risk associated with the expected returns promised to shareholders. Since we have assumed that there are no tax benefits associated with debt financing (these will be discussed later), the value of the firm's equity shares will not change (this “can be shown”). To see why the recapitalization has no impact on the total value of the firm, consider the position of an investor who initially owned two shares of stock. Prior to the recapitalization, the investor's income from these two shares would have had the following distribution across states of the world State 1 State 2 State 3 Earnings Per Share $ .50 $1.00 $2.00 Income from 2 Shares of Stock $1.00 $2.00 $4.00 Given our assumption that the firm is recapitalized by issuing debt to buy back one half of the firm's outstanding stock, an investor with two shares prior to the recapitalization would now have one share of stock and $10 (from the sales of one of the shares of stock), which could be invested at 10 percent interest by purchasing $10 of the bonds of the recapitalized firm. The total income to the investor from one share of stock (with a market price of $10) and one bond (also worth $10) paying interest at a rate of 10 percent would be State 1 State 2 State 3 Income from 1 Levered Share 0 $1.00 $3.00 Income from $10 in Bonds $1.00 1.00 1.00 Total Investment Income $1.00 $2.00 $4.00 The Table above shows that the total investment income for an investor with $20 invested in a portfolio consisting of one share of stock in the recapitalized firm and $10 in bonds is identical to the pattern of returns obtained from owning 2 shares in the all equity (unlevered) firm. Therefore, the investor can undo the impact of the recapitalization by simply using the proceeds from selling stock back to the firm to purchase the newly issued bond. Similarly, so long as an investor can borrow at the same interest rate (roughly) as corporations, shareholders can replicate (match) the pattern of payoffs from the levered firm by financing onehalf of an investment in 2 shares of stock in an all equity firm by borrowing $10 at an interest rate of 10 percent. The distribution of payoffs from this portfolio is shown below State 1 State 2 State 3 Income from 2 Shares of Stock $1.00 $2.00 $4.00 Interest on Personal Debt of $10 $1.00 1.00 1.00 Total Investment Income $0.00 $1.00 $3.00 Which is identical to the dividends from an investment of $10 in the shares of the recapitalized firm. In other words, the firm cannot create value for investors by recapitalizing an all equity firm since the shareholders are able to do this for themselves if they wish. The implications of the analysis above, for which Merton Miller and Franco Modigliani received the Nobel Prize in Economics, is that the financing mix used by the firm (the capital structure) does not matter as long as investors are able to costlessly duplicate (or reverse) the financial implications of any financing decision which the firm might make. These implications can be summarized as 1. The total market value of the debt and equity of a levered firm (using debt financing in addition to equity financing) must be equal to the market value of an unlevered (all equity) firm having the same degree of operating risk. In other words, V_{U} = V_{L}_{ }. 2. Since V_{L}_{ }is equal to V_{U}, the two firms must have the same blended cost of funds or weighted average cost of capital, which requires that the cost of equity capital for the levered firm be greater than the cost of equity capital for the unlevered firm (since the cost of debt will always be less than the cost of risky equity capital). Weighted Average Cost of Capital The weighted average cost of capital (WACC) is the firm's hurdle rate or opportunity cost of capital. The WACC is used in capital budgeting to compute the net present value for projects which have the same risk and debt capacity as the firm as a whole. In general, the weighted average cost of capital may be thought of as the required return on the portfolio of securities that has been issued to finance the firm's operations. In general, the firm's WACC may be computed using the formula WACC = r_{D} + r_{E} where D is the value of the firm's debt, S is the value of the firm's equity, V_{L} is the total value of the firm, r_{D} is the beforetax cost of debt, r_{E} is the cost of equity and t_{c} is the corporate tax rate. In the previous example, we assumed that the corporate tax rate (t_{c}) was equal to zero. After the firm was recapitalized to include debt financing, the outstanding value of the firm's debt was $5,000, the value of the equity was $5,000 and the total value of the firm was $10,000. Since the beforetax cost of debt is 10 percent and the required rate of return on the equity in the recapitalized firm is 20 percent, the weighted average cost of capital is WACC = r_{D} + r_{E} = .10 + .20 = .15 (15 percent) . Note that prior to the recapitalization (using debt financing), the firm relied solely on equity financing with a cost of 15 percent. In other words, there is only one security in the financing portfolio of the all equity firm. Therefore, the weighted average cost of capital for an all equity firm must be equal to the cost of equity (which is also the required return on the firm's assets for an all equity firm), which in this case was 15 percent. The computations above show that when there is no tax deduction for corporate interest expense, a firm cannot change it's weighted average cost of capital by altering the financing mix used to finance its operations. Valuation There are three general approaches to valuation, 1. Adjusted Present Value 2. Adjusted Discount Rate 3. Equity Capitalization For the relatively straightforward examples illustrated here, the three approaches give identical values for the firm and its component securities. However, in some instances, one or more of the valuation approaches suggested above may be difficult to implement. Therefore, it is usually convenient to have more than one valuation technique at your disposal. Adjusted Present Value The adjusted present value approach to valuation is a twostep approach requiring that we 1. value the firm as if the project were to be financed entirely by equity, 2. then add on the present value of any special benefits associated with the financing of the project. Examples of special financing benefits whose value should be accounted for include 1. the value of the tax shields from debt financing, 2. the value of subsidized financing which may be tied to undertaking the project (e.g., industrial development bonds or below market loans from foreign governments), 3. the flotation costs of issuing securities. To simplify the discussion of the Adjusted Present Value (APV) approach to valuation, consider the case where a firm generates perpetual beforetax operating cash flows denoted by EBIT. As noted above, the first step in the APV approach is to value the firm (or project) as if the financing were all equity. Note that if the financing for a project is 100 percent equity then the cost of equity capital ris equal to the required return on assets, r. In other words, if there were no debt financing, then after paying corporate taxes at a rate of t_{c} , 100 percent of EBIT can be used to pay dividends to the shareholders. Therefore, the value of the all equity/unlevered firm (V_{u} ) is equal to aftertax EBIT capitalized in perpetuity at the required return on assets V_{u} = . The second step of the APV approach requires that we determine the value of any financing effects associated with a firm or project separately and then add the value of these benefits to the unlevered value of the project. For example, if the firm issues D dollars of debt then the value of the “recapitalized” firm will be V_{L} = V_{U} + t_{c} D . To illustrate the application of the Adjusted Present Value approach, consider a firm which has perpetual EBIT of $1,000,000 per year. Assume that the corporate tax (t) rate is 46 percent and that the required return on assets (r) is 20 percent. If the firm issues $3,000,000 of perpetual debt at an interest rate of 15 percent, then the pre and postrecapitalization cash flows to the stockholders and bondholders will be PreRecapitalization PostRecapitalization (All Equity) ($3,000,000 of Debt) EBIT $1,000,000 $1,000,000 Less: Interest 0 450,000 Net Income $1,000,000 $550,000 Less: Tax @ .46 460,000 253,000 Equity Income $540,000 $297,000 Interest (to Bondholders) 0 450,000 Total AfterTax Payout $540,000 $747,000 Note that when the firm is financed entirely by equity, the firm pays no interest and the total aftertax payout from the firm is equal to ( 1  t_{c} ) EBIT = ( 1  .46) $1,000,000 , = $540,000 . If the firm issues $3,000,000 in debt at 15 percent, then the cash flow to the stockholders is ( 1  t_{c} ) [EBIT  r_{D} D ] = ( 1  .46 ) [ $1,000,000  .15 x $3,000,000 ] , = $297,000 . The interest to the bondholders is equal to r_{D} D or $450,000. Therefore, the sum of the aftertax cash flow to the stockholders and bondholders is ( 1  t_{c} ) [EBIT  r_{D} D ] + r_{D} D = ( 1  t_{c} ) EBIT + t_{c} r_{D} D . = ( 1  .46 ) $1,000,000 + .46 x .15 x $3,000,000 , = $540,000 + $207,000 . The example shows that adding debt to the financial structure of the firm increases the total aftertax cash flow paid out by $207,000, the tax savings attributable to the corporate deduction for interest expense. If this amount is capitalized in perpetuity using the cost of debt (note that we are ignoring personal taxes here), the additional cash flow increases the value of the firm by $1,380,000 ($207,000/.15). Applying the formula for the value of the unlevered firm shows that V_{u} = , = , = $2,700,000 . So that the total value of the levered firm is V_{L} = V_{u} + t_{c} D = $2,700,000 + .46 x $3,000,000 , = $4,080,000 . The example above raises an important fundamental question concerning the application of the formula for the value of the levered firm. The assumption that the firm can issue $3,000,000 of debt to repurchase equity is questionable given that the initial value of the all equity firm is only $2,700,000. If the primary security for the loan is the collateral (i.e., the value of the underlying assets), then it is unlikely that the required debt financing can be obtained. Note however that the operating cash flow for the firm is more than twice as large as the required interest payments on the debt. While this level of interest coverage would likely place the rating on the firm's debt in the BB to B+ range, the initial willingness of fixed income investors to purchase the debt of the firm is in doubt given the fact firms in the BBB ratings category have great difficulty issuing debt in tight credit markets. Nevertheless, if the cash flow of the firm is stable (e.g., as the cash flows generated by RJ Reynolds in 1988, then bondholders may be willing to purchase the debt of the firm based on the adequacy of the cash flows generated by the firm's assets. Adjusted Discount Rate The most important alternative to the Adjusted Present Value method of valuation is the Adjusted Discount Rate approach. Under the Adjusted Discount Rate approach, the present value of the “aftertax operating cash flows” (i.e., the aftertax profits if the project were financed entirely with equity) is determined using an “adjusted discount rate” which takes into account any benefits from the utilization of debt in the financing of the project. That is, the value of the firm or project may also be determined by capitalizing the “aftertax operating cash flows” for the unlevered firm using a discount rate that is adjusted to reflect the tax shields associated with debt financing. This approach can be represented using the following formula for the value of the levered firm V_{L} = , where WACC (sometimes referred to as the weighted average cost of capital) represents the adjusted discount rate. The adjusted discount rate is most easily defined by noting that the adjusted present value approach and the adjusted discount rate approach should suggest the same value for a firm with perpetual operating cash flow of EBIT and debt financing in the amount of D. In other words, an adjusted discount rate or weighted average cost of capital is defined by the identity, + t_{c} D = . Note that when the corporate tax rate is equal to zero, = , which implies that the value of the tax shields from debt are equal to zero, which in turn implies that the weighted average cost of capital (the adjusted discount rate) is equal to the required rate of return on assets. In other words, when the tax shields from debt have no value, the cost of financing the firm does not depend on the amount of debt in the firm's financial structure. It is fairly easy to show that the weighted average cost of capital defined above is simply the average cost of the portfolio of securities used to finance the firm's operations. For example, if the firm uses only debt and equity to finance its operations, then the WACC is a weighted average of the aftertax cost of debt (to account for the corporate deduction for interest expense) and the cost of equity. The formula for the weighted average cost of capital is WACC = r_{D} + r_{E} where the weights of debt and equity in the capital structure are respectively D/V_{L} and S/V_{L} . To use the formula above to value the firm, we need to know both the cost of equity and the aftertax cost of debt. In the previous example, the cost of debt was 15 percent. Although we know that the required return on assets is 20 percent, which is the cost of equity for a firm with no debt in its financial structure, we don't know the cost of equity for the levered (or recapitalized) firm. We have already shown that financial leverage increases the risk of the cash flows to the shareholders. Further, we know that the increase in risk increases the rate of return required by the shareholders. It turns out that the cost of equity capital is related to the required return on assets (r_{A} ) and the amount of debt in the firm's financial structure by the following formula r_{E} = r_{A} + . To show how this formula works, consider the previous example. We saw that after the firm issued $3,000,000 of debt (D), the total value of the firm was $4,080,000, which implies that the value of the firm's equity is $1,080,000. Given a required return on assets of 20 percent, a beforetax cost of debt of 15 percent, and a corporate tax rate of 46 percent, the cost of equity capital is r_{E} = .20 + , = .275 (27.5 percent) . Given the cost of equity capital, we can now determine the weighted average cost of capital, WACC = r_{D} + r_{E} = .15 + .275 , = .13235 (approximately 13.25 percent) . Once we know the weighted average cost of capital we can determine the value of the firm by discounting the aftertax operating cash flow of the firm using the weighted average cost of capital or adjusted discount rate, V_{L} = , = , = $4,080,000 . The calculations above show that under ideal conditions, the Adjusted Discount Rate approach to valuation and the Adjusted Present Value approach give the same value for the firm. Wonderful you say. So what? Since we needed the value of the firm and the value of the equity (obtained using the APV approach) to determine the weights of debt and equity required to determine the WACC, isn't the logic above circular and therefore useless? The answer to the question above is clearly no, the Adjusted Discount Rate approach (WACC) to valuation is very useful. In fact, we have been using an Adjusted Discount Rate approach to valuation all semester. Recall that our estimates of the cash flows from capital investment projects have never included a charge for any financing costs associated with the project. In other words, the approach that we have followed has always been to estimate the aftertax cash flow from operations, without considering the costs associated with the financing of the project. Implicitly, the costs of financing the project were always taken care of by making the appropriate adjustment to the discount rate used to compute the present value of the project. With regard to the question of how we determine the relative weights of debt and equity in the capital structure, the Adjusted Discount Rate approach is typically used to value projects that will be financed with the same mix of securities as the firm's existing assets. Firms usually have a reasonable estimate of the relative importance of debt and equity in both the mix of securities used to finance existing operations and the mix of securities that will be required to finance projects currently in the planning stage. Since the corporation usually has a reasonable estimate of the weights of the various components of the financing mix, computing the weighted average cost of capital is not usually a problem in practice. Therefore, the choice between the Adjusted Discount Rate approach and the Adjusted Present Value approach hinges on whether the financing benefits associated with a project take the form of the tax savings from issuing debt that will provide longterm financing for the project (use APV) or whether the financing benefits include shortterm financing benefits such as subsidized financing or loan guarantees. Equity Capitalization Approach The equity capitalization approach to valuation calls for valuing the equity of the firm separately using the cost of equity capital. In other words, we value the stock by computing the present value of the aftertax cash flows (after paying interest to the bondholders) available for distribution to the shareholders using the cost of equity capital. The total value of the firm is then determined by adding the value of the firm's outstanding debt to the value of the equity. The equity capitalization approach is most often used to value 1. Real Estate Investments These projects are usually heavily leveraged. The fact that the debt financing is often specific to the project makes the weighted average cost of capital difficult to determine in some cases. 2. Joint Ventures Since the debt associated with a joint venture is usually a liability of the venture itself rather than of the individual partners, each partner is concerned primarily with the value of their respective equity shares, rather than with the value of the venture as a whole. 3. Foreign Investments Debt financing is often obtained in one or more foreign countries in order to hedge political and exchange rate risk. Other financing aspects as loan guarantees and subsidized interest rates make the computation of an adjusted discount rate or weighted average cost of capital difficult in such cases. To illustrate the equity capitalization approach, we continue the preceding example. Since we have already determined that the cost of equity capital for the recapitalized firm is .275 (27.5 percent), all that remains is to determine the aftertax cash flows available for distribution to the shareholders, ( 1  t_{c} ) [EBIT  r_{D} D ] = ( 1  .46 ) [ $1,000,000  .15 x $3,000,000 ] , = $297,000 . If we discount the aftertax cash flows to the shareholders at the cost of equity capital, the value for the firm's outstanding equity shares is S = , = , = $1,080,000 . Adding the value of the firm's outstanding debt, which is $3,000,000, we find that the value of the firm is $4,080,000 as before. 
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