OPTIMAL CAPITAL STRUCTURE & CAPITAL BUDGETING WITH TAXES Topics: Consider Modigliani & Miller s insights into optimal capital structure Without corporate taxes è Financing policy is irrelevant With corporate taxes è Leverage increases value by reducing tax liabilities Incorporate corporate taxes into capital budgeting Does Capital Structure Matter? Big Picture: Does each firm have an optimal capital structure, which maximizes its market values? When firms issue both debt and equity, we can decompose the market value of the firm into the market values of their debt and equity. MV of the firm = MV of debt + MV of equity Question: Why should stockholders, who only own equity, care about maximizing the MV of the firm? Answer: If we ignore default risk and treat the market value of debt as being fixed by the indenture (the contract constraining firm behavior), then any increase or decrease in firm value becomes an identical increase or decrease in the market value of equity. Let s consider an example Capital Structure and MV of Equity Firm has 100 shares of common stock selling at $10 and no debt. Should it change its capital structure by borrowing $500 and paying a $500 dividend to its shareholders? The just-issued debt will have a fixed MV of $500. Since shareholders are the residual claimants, the MV of the firm will increase if and only if the MV of equity increases (after adjusting for the dividend). If the MV of equity falls by $500 (such that the dividend payment exactly offsets the simultaneous $500 capital loss), the change in capital structure has no impact on the MV of the firm. 1
If the MV of equity falls by less than the $500 (perhaps because there are tax benefits to debt), the shareholders receives a $500 dividend and a capital loss of less than $500. Here, the MV of the firm and the MV of equity increase by the same amount. Example: Buy More s Capital Structure Question: Can a change in capital structure change the MV of the firm? What ratio of debt to equity maximizes the MV of the firm? Buy More Corporation s current capital structure is 100% equity financed. Notice how their EPS vary with economic conditions. Buy More Corporation is considering issuing $4000 in debt to retire $4000 in equity. The change in capital structure will reduce the number of shares outstanding from 400 to 200. 2
Modigliani and Miller s Proposition 1 Changing Buy More s capital structure changes the risks faced by its shareholders (see Topic 9), but does it change the MV of the firm? Proposition 1 of Modigliani and Miller s seminal paper (AER 1958) says no: The MV of the unlevered firm is the same as the MV of the levered firm. Consider two investment strategies: Strategy A: Use $2000 to buy 100 shares of Buy More s levered equity at $20/share Strategy B: Borrow $2000 from a brokerage house and spend $4000 on 200 shares of Buy More s unlevered equity at $20/share Both the cost and the payoff from the two strategies are the same M&M Proposition 1 so, an investor is not receiving anything from corporate leverage that she could not receive with some homemade leverage. If the levered firm s equity sold for more than the unlevered firm s equity, investors could receive the same payoffs by borrowing on their own account and buying equity in the unlevered firm. Under the following assumptions Summary of M&M Proposition 1 Individuals can borrow at the same rates as corporation (which may be the case when borrowing on margin) Neither individuals nor corporations pay taxes 3
There are no transaction or information costs Fixed real investment policy firms pre-commit to using NPV to evaluate all projects at all times in all state of the world no role for agency conflicts It follows that the market value of the firm is independent of the choice of capital structure, so there is no unique capital structure which maximizes the market value of the firm. Of course, this is a frictionless experiment that focuses on financing policy by holding investment policy fixed. Another Proof of M&M Proposition 1 The M&M Proof Consider two firms with identical investment opportunities. Fixed real investment policy says that they will have the same cash flows. Firm U is unlevered V U = E U Firm L is levered V L = E L + D L Consider the returns to buying 1% of Firm U versus 1% of Firm L Investments have identical returns, so they must have identical prices! Importance of M&M Proposition 1 Basic idea is that with no market frictions, investors can duplicate or modify the capital structures of firms on their own. Therefore, it can t be valuable for firms to repackage their assets for investors. But were they seriously arguing that capital structure doesn t matter? No. Many of the assumptions are questionable approximations to the real world. Moreover, if M&M Proposition 1 were true, we d see random D/E ratios across firms and industries and we do not. The insight is that if financing policy does affect the firm value it will do so for one or more of the following reasons: 4
Firms and shareholders pay taxes Firms and shareholders face transactions and/or information costs Firms do not follow fixed real investment policies M&M Proposition 2 For Buy More, the expected return on unlevered equity is 15% and the expected return on levered equity is 20%. Why does levered equity have higher expected returns? Because it carries more risk (as we saw in Topic 9). Levered equity pays higher EPS in good times and lower EPS in bad times. Ignoring taxes, M&M Proposition 1 implies that the required return on a firm s assets equals WACC, and does not change with changes in the firm s capital structure. For Buy More, WACC unlevered = (15%)(1.0) + (10%)(0.0) = 15% and WACC levered = (20%)(0.5) + (10%)(0.5) = 15% Since WACC does not vary with leverage, we can interpret r Assets to be the required return on equity in an all-equity financed firm and derive: Typically labeled M&M Proposition 2 (with no corporate taxes): If neither r Debt nor WACC varies with the debt-equity ratio (D/E), it follows that r Equity must increase sharply. 5
M&M s Tax Correction Paper Studied impact of taxes on the relation between capital structure and firm value. The firm now has three claims on its assets: shareholders, bondholders, and Uncle Sam! Any action which reduces the government s claim against the firm must increase the value of the firm to shareholders and bondholders. PV Tax Shield The first pie is the value of an all-equity firm that pays no corporate taxes. The second pie is the value of an all-equity firm that pays corporate taxes. The third pie is the value of a levered firm. Issuing debt allows the firm to reduce its taxable income and, thereby, its tax payments. The firm s value increases by PV of the tax shield. What is the PV of the tax shield? Assume debt is a perpetuity and that risk of the tax shield equals the risk of the debt (because you must pay debt to enjoy the tax shield). PV of Tax Shield = 6
Note: formula overstates PV of Tax Shield if debt is not permanent or there is additional risk that the firm cannot use the tax shield. So, in a world with corporate taxes, levered firms will have higher values than unlevered firms, everything else equal. Moreover, the difference in market values equals the PV of the tax shield. V L = V U + (PV Tax Shield) M&M s Proposition 1 with Taxes Ignoring depreciation, but letting the corporate tax rate equal τ c, after-tax cash flow from the unlevered firm are EBIT(1-τ c ) per year and the value of the unlevered firm equals: Because adding debt to the capital structure decreases tax payments, the value of the levered firm equals: When we model the tax benefit of debt (and ignore financial distress), we find that firm value is strictly increasing in leverage. Example: Divided Airlines Divided Airlines expects to generate $153.85 in EBIT in perpetuity. Since the corporate tax rate is 35%, it has after-tax earnings of $100. Currently, DA is an unlevered (100% equity) firm that pays all of its earnings out as dividends. DA is considering a capital restructuring that would replace $200 in Equity with $200 in Debt. The cost of debt is 10% and the cost of equity for (unlevered) airlines is 20%. V U = $100 / 0.2 = $500 100 shares @ $5 per share V L = V U + τ c Debt = $500 + (0.35)($200) = $570 Since the MV of debt is $200, the MV of equity falls to $370. Before long, however, we ll see that the MV per share actually increases. 7
M&M s Proposition 2 with Taxes According to M&M s Proposition 1, we can express the market-value balance sheet for any levered firm as follows: MV Assets V U = Value Unlevered Firm τ c Debt = Value Tax Shield MV Liabilities D = MV of Debt E = MV of Equity The fact that the expected cash flows from the LHS of the balance sheet must equal the expected cash flows from the RHS implies: Using some algebra and V U = E + (1-τ c )D implies: Example: Divided Airlines (cont.) Before the restructuring, the required return on DA s unlevered equity is 20%. What is the required return on Divided Airline s equity after the restructuring? To verify this is the correct required return on equity with leverage, let s use it to verify that the MV of equity equals $370. 8
WACC with Taxes With taxes, the weighted-average cost of capital expression becomes E WACC requity ( 1 c) r V L where market values are measured with leverage and V L = E + D. Debt D V L For the Buy More example, if r Debt = 10%, r Assets = 15% and τ c = 35%, then r Equity increases by less per unit of leverage (because the tax shield reduces effective debt obligation) and WACC declines from 15% with no leverage to 13.43% when D/E = 9. Example: Divided Airlines (cont.) Before the restructuring, DA s WACC = r Assets = 20%. What is DA s WACC after the proposed restructuring? WACC r Equity E V L (1 ) r c Debt 370 200 0.2351 0.650.10.1754 570 570 To verify this is the correct WACC with leverage, let s use it to verify that the MV of the firm equals $570. D V L V L ( EBIT )(1 c) WACC ($153.85)(0.65) $570 0.1754 9
Finally, let s focus on how the restructuring impacts DA s stock price. The unlevered version of Divided Airlines has assets that generate a constant annual EBIT of $153.85. Since the tax rate is 35% and the appropriate discount rate is 20%, the MV of this asset is $500. If there are originally 100 shares of equity, they will trade at $5/share. When DA announces the restructuring, the MV of assets increases from $500 to $570, reflecting the value of the tax shield, and the price per share increases to $5.70 (= $570 / 100). When DA raises the $200 in debt, they are able to buy back 35.09 shares (= $200 / $5.70). The MV of equity falls from $570 to $370 and the number of shares falls from 100 to 64.91. The MV per share? It still equals $5.70 (= $370 / 64.91). Cool, huh? Beta and Leverage When β Debt = 0 and there are no corporate taxes, the required return on levered equity is given by: Equity Assets Assets Debt Equity When the firm is unlevered (with or without corporate taxes): Since interest expenses reduce taxable income, with corporate taxes, the required return on levered equity is given by: 10
Connecting the Dots What have we seen so far? 1. CAPM 2. M&M What did we just add to the mix? 3. Beta and leverage For completeness, let s plug 3 into 1 and show that we can derive 2. 11
1 st Example on Beta and Leverage Bokken Batons is considering a scale-enhancing project. The market value of equity is $200 and the market value of debt is $100. The corporate tax rate is 34%. The beta on BB s equity is 2.0 and the beta on BB s debt is 0. The risk-free rate is 10% and the market risk premium is 8.5%. What discount rate should BB use to evaluate this project if it were 100% equity financed? What discount rate should Bokken Baggage use to evaluate the project given its current capital structure? Why is this discount rate lower? The tax subsidy of debt, of course! 2 nd Example on Beta and Leverage Epee Enterprises (EE), which caters to fencers, is considering a $1 million investment in the aircraft adhesives industry. Clearly, this project is not scaling-enhancing! Unlevered (after-tax) cash flows estimated to be $300,000 in years 1 through. The corporate tax rate is 34%. EE will finance the project with debt-equity ratio of 1:1 Three competitors in this industry (including Precision Castparts) have unlevered betas of 1.2, 1.3, and 1.4. Risk-free rate is 5.0% and the market risk premium is 9.0%. What is the NPV of this project? 12
Figure out WACC and use it to discount the UCF. 1. What is our best guess of the beta of assets (unlevered equity) for this project? 2. What does this estimate imply about the beta of EE s levered equity? 3. What is the required return of EE s levered equity? 4. What is EE s WACC? WACC r Equity (1 ) r 1 1 0.244 0.660.05 2 2 13.9% 5. Finally, what is the net present value of EE s project? E V L c Debt D V L Some Observations Conceptually, we want to discount each cash flow at a discount rate that reflects its level of systematic risk. Because the beta of equity varies with leverage, we can think of firms assigning some or all of their risk-free CFs to bondholders and any remaining risk-free CFs plus all of their risky CFs to stockholders. When calculating the present value of the tax shield, we are using the risk-free rate because we receive the tax savings whenever we make our interest payments. This makes good economic sense. However, modeling the systematic risk of each cash flow can get tricky and there are diminishing returns. In practice, many firms use WACC to discount their depreciation tax shields because this is conservative 13
Some Final Observations Of course, if we re going to acknowledge the different levels of risk across different cash flows, we should also acknowledge the different levels of risk through time. For example, when yield curves imply that risk-free rates will vary through time, we should use forward rates to estimate a difference discount rate for each time period. Getting firms to replace WACC with discount rates that reflect the unlevered cash flows of the assets they are buying or the levered cash flows of the equity they are buying is a big step forward. The fact that financial institutions were using the wrong discount rate to value mortgage-backed securities caused them to overvalue the securities. The fact that they were highly leveraged made it hard to re-value the securities without triggering financial distress 14