# Ch. 18: Taxes + Bankruptcy cost

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1 Ch. 18: Taxes + Bankruptcy cost If MM1 holds, then Financial Management has little (if any) impact on value of the firm: If markets are perfect, transaction cost (TAC) and bankruptcy cost are zero, no taxation, then finance is easy! But what if the assumptions of MM1 do not hold? 1. If investors pay higher interest rates (imperfect credit markets), then the above examples do not work. 2. If corporate and individual tax rates differ => capital structure may serve as a tax shield. 3. If bankruptcy cost occurs, then capital structure may have incentive effects => agency theory. 261

2 With corporate taxation, the WACC after tax is given by D ra ( at) = rd (1 TC ) + A r E E A where TC is the marginal corporate tax rate. (f the tax rate increases in the tax base, then the marginal tax rate exceeds the average tax rate) 262

3 With corporate taxes, the equity Beta after tax is given by β E ( at ) = β A + ( β A β D )(1 T C ) D E if debt is fixed and permanent, and as long as only corporate tax is considered (see BM 7, ch. 19.6). With changing D, things are more complicated. Multiplication of a random variable with a constant factor (1-TC) implies that its variance has to be multiplied with (1-TC) 2, while its standard deviation as well as its covariance (with an unaffected random variable) are multiplied with (1-TC). 263

4 C.S. & Corporate Taxes: Example You own all the equity of Space Babies Diaper Co.. The company has no debt. The balance sheet shows an asset value (=equity) of \$ 2,000. The company s annual cash flow is \$1,000, before interest and taxes. The corporate tax rate is 40%. You have the option to exchange 1/2 of your equity for 10% bonds with a face value of \$1,000. Should you do this and why? 264

5 All Equity Leveraged (1/2 Debt) EBIT 1,000 1,000 Interest Pmt Pretax Income 1, % Net Cash Flow \$600 \$540 Total Cash Flow for investors: All Equity => 600 Leveraged => =640 Corporate Tax (on profit/dividends) is reduced, but there is also taxation on personal income (e.g., from interest) 265

6 Capital Structure Turning part of the equity (profit is taxable) into debt (interest rates are deductible) reduces the company s tax burden. In particular this makes sense for the investor s if the MARGINAL corporate tax rate exceeds their personal marginal tax rate on interest earnings. The Tax Shield amounts to D x rd x Tc = 1,000x0.1x0.4=40 in the running period => present value of all future tax shields? Tax shield is a (risky) cash flow, and it is to be discounted at the same rate as as the firm s debt (as this is the interest rate that generates it). 266

7 PV of Tax Shield = (assume perpetuity) D x rd x TC rd = D x TC Thus, the PV is independent of the interest rate Perpetuity = if the firm intends to borrow/use tax shield permanently Tc = corporate tax rate DrD = interest payment Firm Value = Value of an all equity financed firm + PV Tax Shield 267

8 268

9 Capital Structure & Taxes (Personal & Corporate) According to figure 18.1, lending to the firm is better than buying its stock if (1-TP) is greater than (1-TPE)(1-TC), or if the Relative Advantage of Debt over Equity (RADE) 1 - TP (1-TPE) (1-TC) is greater than 1. TP=Personal tax rate on interest earnings TPE=effective personal tax rate on dividends TC=corporate tax rate 269

10 Two special cases: 1. TPE=TP: The relative advantage 1/(1-TC) only depends on (is increasing in) the corporate tax rate. 2. RADE = 1, so debt policy is irrelevant for taxation. <=> 1-TP = 1-TPE-TC+TPETC <=> TP = TPE+(1-TPE)TC <=> TC=(TP-TPE)/(1-TPE), which can only happen if TPE is small and TC<TP. For other cases, the RADE formula seems to give a simple, but useful decision rule. 270

11 RADE empirically in the US (2001) 1.33 (1-.16) (1-.35) =1.23 > 1 Are, hence, all US companies only debt financed? To the contrary, equity is much more popular in the US than in Germany (but the German tax situation since 2008, with the Halbeinkünfteverfahren, is a bit difficult to analyze). => other factors play a role (e.g., bankruptcy risk) 271

12 Capital Structure One possible explanation of this puzzle may lie in the fact that bond yield rates depend on debt ratio (which influences the bankruptcy risk). With a very high bankruptcy risk, rd may even overtake re because debt may become more volatile than equity (the value of a loan depends on the bankruptcy quota). If bankruptcy plays only a minor role, then equity is always more volatile than debt. 272

13 Cost of Financial Distress Costs arising from bankruptcy or distorted business decisions before bankruptcy. Market Value of the firm = Value if all Equity Financed + PV Tax Shield - PV Costs of Financial Distress Next figure: If D=0 (E=A), then tax shield and bankruptcy risk are zero. If D>0 (E<A), then the value of the tax shield increases. But also the bankruptcy risk increases (and, hence, the expected cost of financial distress). This results in a concave curve describing the market value. 273

14 274

15 Financial Distress Games Risk shifting High stakes, high risk (even with negative ENPV) can easily be accepted by managers (or even by investors) under limited liability. Refusing new equity If a company is in distress, investors may be reluctant to buy new shares to finance projects with positive NPV if the returns would primarily go to the bondholders (in case of bankruptcy and even if a success prevents the firm from default). 275

16 Cash In and Run If shareholders are keen to get their money back as long as there is some Playing for Time While bondholders are impatient to settle their claims, shareholders would prefer a delay (accounting steam, using reserves). Bait and Switch Start conservatively, and then continue with aggressive bonds/projects => burdens additional risk on the initial bondholders. 276

17 What is the problem if such games are played among consenting adults? Playing them leads to distortions =>inefficient investment decisions caused by asymmetric information (agency cost). The more a firm borrows, the larger the temptation to play. If investors anticipate this, they will demand a higher rate, the higher the debt ratio. 277

18 Two theories on choice of the debt ratio Trade-off Theory - Capital structure is based on a trade-off between tax savings and distress costs of debt (firms choose capital structure so as to max. firm value for their investors after tax). Pecking Order Theory - Firms prefer to finance new projects by 1. internal sources (retained earnings) 2. debt 3. new equity in that order (Myers 1984, JoFin 39, 581) 278

19 Simple moral hazard problem: Choice of risky projects Lit.: Jensen/Meckling 1976 Entrepreneur/Manager M may choose between two projects: Project X yields either 0 ( bad state, with prob. 1-q) or 200 ( good state, with q) => expected return 200q. Project Y yields -50 (with 1-q) or 300 (with q) => expected return 300q-50(1-q)=350q-50. => Y is more risky than X for each value of q. Both projects require an investment of 20. Manager is promised a share 0<µ<1 of the project returns. Firm s assets=200; it can take up debt at an interest rate of 10%. => before investment: A=200=E if D=0 => after investment, before returns: A=180=E if D=0. 279

20 Which project is preferred by the principal (bank/owner)? ) => normative analysis Which one will, however, be chosen by the agent M? => positive analysis => we distinguish three cases: 1. Unlimited liability on the part of the agent M 2. Limited liability without and with leverage => the principal-agent-problem 3. Limited liability and the debt whip => the solution to the PA-problem 280

21 Normative analysis: What do the shareholders prefer? The expected returns are maximized by chosing Y if 200q<350q-50 <=>150q>50 <=> q>1/3 (which implies 350q-50>20) X if q<1/3 and 200q>20 <=>0.1<q<1/3 none of the projects if q<0.1 (shareholders may have to deduct interest and manager s compensation) Subsequently, we only look at the case 0.1<q<1/3 (e.g., q=1/4) => X is preferred by the SH (if compensation is not too high) => 50-20=30 281

22 Positive analysis 1: What does the manager choose? 1. if he is fully liable 2. if his liability is limited 3. under limited liability and with the debt whip? Positive analysis 1: full liability The manager receives/pays a share µ of all profits/losses If the manager chooses project her expected payoff is X 200µq Y 300µq-50µ(1-q) => Manager s and shareholders interest are perfectly aligned. 282

23 Positive analysis 2: Limited liability The manager receives a share µ of all profits, but has no personal wealth to cover a share of losses If the manager chooses project her expected payoff is X 200µq Y 300µq => Manager always prefers Y. What are the consequences for the shareholders if the manager chooses project Y? => depends on whether or not the firm is levered. 283

24 If the firm is unlevered (E=A=200 => D=0) then, due to the Manager s limited liability, project Y leads to the following positions in the balance sheet: with prob q: A=E= (1-µ)= (1-µ); D=0 with prob (1-q): A=E= =130; D=0 284

25 The levered firm (e.g., E=20, D=180 => interest rate=18) expects the following positions in its balance sheet with prob q: A= (1-µ)-18= µ, D=180 E=300(1-µ)-18 with (1-q): A=130-18=112, D=180, E=-68 => bankruptcy. Assume 300(1-µ)-18>0 <=>1- µ>3/50 µ<47/50 (e.g., µ=0.2) Then: the levered firm goes bankrupt with probability (1-q); and no bankruptcy occurs with probability q. 285

26 Positive analysis 3: Limited liability with a debt whip The manager receives a share µ of all profits, but has no personal wealth; she fears a reputational loss of R in case of a bankruptcy (which occurs with probability 1-q): If the manager chooses project her expected payoff is X 200µq Y 300µq-(1-q)R => She prefers X iff 300µq-(1-q)R<200µq <=> R >100µq/(1-q) => If R is high enough, then manager s and shareholders interest are perfectly aligned. => E.g., with q=0.25 and µ=0.2: R>20/3 (if R=8, then the expected payoff from X is 10; from Y it is 15-6=9) 286

27 Possible incentive effect of debt financing (the debt whip ): Debt creates bankruptcy risk (increases with debt ratio). If managers are bankruptcy averse (e.g., have reputational concerns) then the debt ratio may have an incentive effect. Managers put their reputation at stake (besides income). Alleviates limited liability problem (even with empty pockets, the manager now has something to lose). However, the bankruptcy risk would also hurt the owners. Main lesson here: Leveraging a firm may increase bankruptcy risk (financial instability, in the absence of strategic effects) can even decrease the bankruptcy risk if the debt whip incentivizes the managers to choose the less risky projects (strategic effect). 287

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