Capital Structure with Taxes EC Borja Larrain

Transcription

1 Capital Structure with Taxes EC 1745 Borja Larrain

2 Today: 1. M&M recap. 2. Tax advantage of interest expense. 3. APV and WACC. 4. Personal taxes. 5. Empirical evidence on taxes and capital structure. Readings: Chapters 17 & Welch Assignment 6 due next Monday 11/24

3 In this class: Introducing taxes breaks down the Modigliani-Miller irrelevance result. Now: firm value = project value + financing value. Corporate taxes give an advantage to debt against equity financing. How to adjust the NPV formula and WACC to reflect the tax-advantage of debt? What if investors, and not only corporations, face a differential tax treatment of interest and dividends?

4 1 M&M recap The M&M irrelevance theorem implies that the value of a firm is independent of its leverage. Under M&M, the value of the firm is simply: V = E( F ) 1+E(r a ) E( F ) are expected cash flows, and E(r a ) is the expected return on the real assets or projects of the firm. The value of a firmhastodowiththevalueofits projects, not with the way in which the financing of these projects was arranged.

5 Also, V = E( F ) 1+E(r a ) = E( F ) 1+WACC WACC stands for Weighted Average Cost of Capital: WACC = w d E(r d )+(1 w d )E(r s ) In an M&M world, the average expected return on the securities issued by the firm is equal to the expected return on the projects owned by the firm: WACC = E(r a ). If WACC 6= E(r a ) there is an arbitrage opportunity. It s like a portfolio with an expected return different from the average expected return of what is inside the portfolio. Remember that arbitrage is costless in an M&M world!

6 The WACC of a corporation does not depend on leverage, but E(r d ) and E(r s ) do depend on leverage. Why? Because leverage changes the cash flows going to debt and equity. However, it does not change the cash flows for the entire firm (in a frictionless M&M world) The expected return on equity as a function of the other parameters is: E(r s )=E(r a )+ w d [E(r a ) E(r d )] 1 w d Is M&M useless? The assumptions are hard to swallow and the empirical implications are not true! Looking back now, perhaps we should have put more emphasis on the other, upbeat side of the nothing matters coin: showing what doesn t matter can also show, by implication, what does. (Merton Miller, 1988).

7 Also, M&M exposed some fallacies. E.g., firms should borrow more, because debt is cheap and this lowers the WACC...false! The expected return on equity is increasing with leverage so the WACC stays the same! What if markets are not perfect? In this case: V 6= E( F ) 1+E(r a ) WACC 6= E(r a ) With imperfect capital markets, V = E( F ) ± financing value 1+E(r a ) WACC = E(r a ) ± financing wedge There are 4 types of frictions that break down M&M s logic: Taxes.

8 Transaction costs. Differences of opinion. Big players (buyers/sellers). We ll start with taxes because it is the easiest one. In future classes we will study other frictions and how these give advantages or disadvantages to debt and equity financing.

9 2 Tax advantage of interest expense The simplified income statement: Sales Costs of sales Other costs (e.g., depreciation) Operating profit Interest expense Income before taxes Taxes Net Income "Income before taxes" is the tax base of the company. This base is multiplied by some τ% to compute taxes. Note: IRS rules are very similar to accounting principles. Interest expense lowers the tax base of the company.

10 Dividends are paid from whatever is left after Uncle Sam has taken his share. With corporate taxes, the firm s cash flows are split into three pieces: debt, equity, and taxes. We cannot change the size of the pizza by changing the capital structure. But what the firm can do is to change the amount taken by Uncle Sam and give more to investors as a group (debtholders + shareholders). For now assume that investors are not taxed (you wish...) Example: think of a project that delivers operating income of $80 next year. Corporate tax is 30%. Compare the cash flows of a 100% equity firm and a firm with $80 in interest expense.

11 Unlevered Firm Levered Firm Operating income Interest 0 80 Income before tax 80 0 Tax 24 0 Investors get Uncle Sam gets 24 0 Cash flows to investors are higher in the case with debt. Of course, the private NPV of the firm is higher in this case. A quick way to get the cash-flow shelter provided by debt is to multiply interest expense by the tax rate: $80 30% = 24.

12 3 APV and WACC 3.1 Adjusted Present Value How can we adjust the NPV calculations to take into account the tax advantage of debt? As always, start with the relevant cash flows, i.e., after-tax, expected, total cash flows to investors: E (EBIT (1 + r d )D)(1 τ) {z } dividends {z } interest +(1+r d )D Or: E EBIT(1 τ) {z } div. unlevered firm {z } tax shelter + τ(1 + r d )D

13 The tax shelter is the extra cash flow distributed to investors in a firm with debt. The value of the unlevered firm is: E[EBIT(1 τ)] V U = 1+E[r a ] Here E[r a ] is the relevant after-tax opportunity cost of capital for the projects of the firm. The value of the "levered" firm: V L = E[EBIT(1 τ)] + E[τ(1 + r d)d] 1+E[r a ] 1+E[r a ] = V U + PV(tax shelter) Thesecondtermisthepresentvalueofthetaxshelter or the tax advantage of debt.

14 Here we are discounting the tax shelter using the same discount rate as the assets of the firm. Basically, we are assuming that the tax shelter is as risky as the firm. See he appendix to Chapter 17 for more on this issue. If the appropriate discount rate for the tax shelter is equal to E[r d ], then the present value of the tax shelter assuming a perpetuity is simply τd.but this is a special case. Notice that the value of the firm is increasing with leverage: firm value = project value + financing value Project value is the value of the firm with 100% equity, and the value of financing is increasing in the value of debt.

15 3.2 WACC A related way of adjusting the NPV calculation for the tax-advantage of debt is to correct the discount rate. This new discount rate is a generalized version of the WACC that includes the preferential tax treatment of debt. Intuition: highly levered firms discount the same cash flows at a lower rate so their value is higher. Therearetwowaystoexpressthetotalcashflow distributed to investors: E[EBIT(1 τ)+τ(1 + r d )D] = S(1 + E[r s ]) +D(1 + E[r d ])

16 The RHS side of the last equation comes from the fact that the market value is simply the expected cash flow properly discounted: S = E[(EBIT (1 + r d)d)(1 τ)] 1+E[r s ] D = E[(1 + r d)d] 1+E[r d ] Define WACC as the discount rate that gives you the value of the levered firm, but starting from the unlevered cash-flows: V L = E[EBIT(1 τ)] 1+WACC Using this definition: V L [1 + WACC]+E[τ(1 + r d )D] = S(1 + E[r s ]) +D(1 + E[r d ])

17 Doing some algebra: WACC = (1 τ) D V L E[r d ]+ S V L E[r s ] WACC = (1 τ)w d E[r d ]+(1 w d )E[r s ] ThisformulafortheWACCgivesalowercostof capital than the formula from last class. The (1 τ) factor is the difference. Also note that WACC is not equal to E[r a ]: WACC = E[r a ] τw d E[r d ] The WACC is decreasing in leverage! Homework: as in last class, express E[r s ] as a function of the expected return on assets and debt, leverage, and now also the tax rate. Compare the slope of this function with the slope from last class.

18 In this world with only corporate taxes the optimal capital structure would be to take as much debt as possible, i.e., w d =100%. This recommendation is obviously too extreme, but the intuition is still useful. For example, a project that can be collateralized may be more valuable because it can add a tax shield to the firm. What has been left outside this model? Personal taxes, costs of default, and so on. We ll start with personal taxes.

19 4 Personal taxes Unfortunately, not only corporations pay taxes, but also investors. Taxes are different across different types of income: capital gains, dividends, interest, etc. Personal taxes can affect dramatically the recommendations from the previous section. Assume, for example: Interest can be deducted from profits, but not dividends. Investors pay lower taxes on dividends than interest.

20 Now it is not so clear that debt is a dominant strategy. It will depend on the tax rates. We can derive similar formulas as before considering that investors pay τ p on interest (or personal) income, τ e on dividends, and that τ c is the corporate tax rate. Total cash flow to investors (no expectation for simplicity) (EBIT (1 + r d )D)(1 τ c )(1 τ e ) {z } dividends +(1 + r d )D(1 τ p ) {z } interest Assuming that the risk of the tax shelter is the same as the risk of debt, and after some algebra, you can derive the following relationship: V L = V U + " 1 (1 τ c)(1 τ e ) (1 τ p ) # D

21 If taxes on interest are sufficiently high, the tax advantage of debt can be very close to zero or even negative.

22 5 Empirical Evidence My personal view: taxes can be important for many things, and they do play a role in capital structure, but it seems that they are a second order consideration. Extreme example: technology firms with zero debt: are they leaving money on the table by not taking advantage of the tax benefits of debt? Most probably the tax-based story is incomplete. The tax advantage of debt depends a lot on the marginal investor we have in mind. Rich retail investors are heavily taxed, but pension funds are taxed lightly or tax exempt. If we ask CFOs about what factors influence their debt-financing decisions: taxes are in a paltry 6th place.

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24 Fig. 5. Survey evidence on some of the factors that a!ect the decision to issue debt. The survey is based on the responses of 392 CFOs.