Out of the perfect capital market: Role of taxes Capital structure II Out of the perfect capital market: Role of taxes

Back to the assumptions of MM Taxes are ignored Bankruptcy was cheap, quick and painless. There are costs associated with financial distress. Ignoring potential interest conflicts between firm’s security holders. (transaction cost due to agency problem) => Introducing taxes

The pie again All-Equity firm Levered firm Debt Taxes Taxes Equity The sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm With tax, what is the optimal capital structure of firms?

Capital structure and corporate taxes EBIT EBIT -B× RB B× RB (EBIT - B× RB) × (1-TC ) (EBIT - B× RB) ×TC Operating cf: ebit We depart from MM since future cash-flows available for investors depend on the amount of taxes, i.e. on the amount of leverage.

MM Proposition I (With Taxes) The present value of this stream of cash flows is VL The cash flow to all stakeholders is made up of cash flow to stockholders plus cash flow to bondholders. The present value of the first term is VU The present value of RBBTC is PV(interest tax shield) => VL =VU + PV (Interest tax shield)

Present value of the tax shield Advantage to debt Interest = B× RB Per period tax shield from debt: TC × B× RB Ex: Suppose DFB plans to pay $100 million in interest each year for the next 10 years, and then to repay the principal of $2 billion in year 10. These payments are risk free, and DFB’s marginal tax rate will remain 35% throughout this period. If the risk-free interest rate is 5%, by how much does the interest tax shield increase the value of DFB? - The interest payment is exempt from the tax. The amount of exemption is just tc X rb X D. Tax shield can be valuable asset. At what discount rate should the tax shield perpetuity be discounted? Since the it is generated by the interest payment, a common assumption is that the risk of the tax shields is the same as that of the interest payments generating them.

Present value of the tax shield Solution: In this case, the interest tax shield is 35% * $100 million = $35 million each year for the next 10 years. Therefore, we can value it as a 10-year annuity. Because the tax savings are known and not risky, we can discount them at the 5% risk-free rate: The final repayment of principal in year 10 is not deductible, so it does not contribute to the tax shield. - The interest payment is exempt from the tax. The amount of exemption is just tc X rb X D. Tax shield can be valuable asset. At what discount rate should the tax shield perpetuity be discounted? Since the it is generated by the interest payment, a common assumption is that the risk of the tax shields is the same as that of the interest payments generating them.

Interest tax shield with permanent debt Per period tax shield from debt: TC × B× RB Assume that the debt payment is fixed and permanent. => the tax shield cash flow is perpetual. Assume that the cash flow from tax shield has the same risk as the interest on debt: The PV of tax shield: (TC × B× RB)/RB = TC × B It is independent of the interest rate. - The interest payment is exempt from the tax. The amount of exemption is just tc X rb X D. Tax shield can be valuable asset. At what discount rate should the tax shield perpetuity be discounted? Since the it is generated by the interest payment, a common assumption is that the risk of the tax shields is the same as that of the interest payments generating them.

Value of the unlevered firm VU = (EBIT×(1-TC ))/R0 VU = PV of an unlevered firm EBIT×(1-TC ))= Firm cash flow after corporate taxes TC = corporate tax rate R0 = The cost of capital for an all-equity firm = Required return on assets = Discount rate for aftertax cash flow

Value of the levered firm MM Proposition I (with Corporate Taxes) Firm value increases with leverage VL = (EBIT×(1-TC ))/R0 + (TC RB B )/ RB = VU + TC B VL VU Debt (B)

Example. Larger pie with leverage Firm U Firm L(borrow $1,000 at 8%) EBIT $1,000 $1,000 Interest 0 80 EBT 1000 920 Taxes at 35% 350 322 Net income $650 $598 Total cash flow 0+650=650 80+598=678 to both B &S Interest tax shield $0 $28 Interest tax shield = total cf of levered- CF of unlevered = interest X tax rate.

Example (cont.): Value of firms Assume that both firm U and L are in the same industry. Firm U has a cost of equity capital of 20%. What will be the value of both firms?

Value of firms VU = Net Income / R0 =EBIT (1-tC)/ R0 VL = VU+ tC B = 650/ 0.2 = 3250 VL = VU+ tC B = 3250 + 0.35*1,000 = 3600

Value of firms Market value balance sheet Market value balance sheet Unlevered firm Levered firm VU =EBIT (1-tC)/ R = 650/ 0.2 = 3250 Market value balance sheet Assets 3250 | Equity 3250 | Total 3250 | B+S 3250 VL = VU+ tC B = 3250 + 0.35*1,000 = 3600 Market value balance sheet Assets 3250 | Equity 2600 PV of tax shield | Debt 350 | 1000 Total 3600 | B+S 3600 The value of the levered equity is reduced but all tax shield goes to shareholders The value of equity= Physical assets – debt+ tax shield

Expected Return under taxes MM Proposition II (with Corporate Taxes) Some of the increase in equity risk and return is offset by the interest tax shield RS = R0 + (B/S)×(1-TC)×(R0 - RB) RB is the interest rate (cost of debt) RS is the return on equity (cost of equity) R0 is the return on unlevered equity (cost of capital) B is the value of debt S is the value of levered equity

MM Proposition II (With Taxes) Start with M&M Proposition I with taxes: Since The cash flows from each side of the balance sheet must equal: Divide both sides by S Which quickly reduces to

The Effect of Financial Leverage Cost of capital: R (%) No tax With tax RWACC without tax R0 Beta: BetaAsset= B/V X beta debt X (1-Tc) + S/V X beta equity. RB Debt-to-equity ratio (B/S)

Impact of personal taxes Investors pay taxes too. Equity income is taxed at both the corporate and the personal levels. The value of a firm= value of cash flows investors receive after all taxes have been paid. When deciding the optimal capital structure of a firm, one should take into account the after tax cash-flows accruing to investors. If personal tax rates differ according to the type of claim held, the optimal capital structure may change.

After tax cash-flows to investors TB, Tax rate on interest income TS: Tax rate on equity income Suppose now that creditors have a personal tax rate TB, and that equity holders have a personal tax rate TS.

Personal & Corp taxes Operating Income ($1.00) Or paid out as equity income Paid out as interest Corporate Tax None Tc Income after Corp Taxes 1 1 – Tc Personal Taxes . TB TS (1 -Tc) Income after All Taxes 1 – TB 1-TC - TS (1- TC) =(1- TC) (1-TS ) To bondholders To stockholders

Relative tax advantage of debt Prefers debt to equity if 1- TB > (1-TC)(1-TS) The relative tax advantage= (1- TB )/ (1-TC)(1-TS) If debt and equity income were at the same rate (TB = TS): Relative advtg= 1/(1-TC ) >1 Tax advtg depends only on TC What capital structure should the firm choose? Eg: In the US: The top tax bracket TC = TB=35%. TS=15%. What will be the optimal capital structure in the presence of dividend and interest taxes? The firm should choose the capital structure that gets the most cash into the hands of its investors. If 1- TB > (1-TC)(1-TS), then the firm should choose to use fully debt instead of equity. If TB = TS , 1/(1-TC ) >1 then should use debt. Intuitively, the net income given to stockholders is taxed twice. Note that the case without personal tax is a special case of TB = TS =0. Hence it turns out that we should always use debt. Some remark of the tax rate: Normally, the effective tax rate on the net income is lower. i.e. TS<15%. This is because the capital gain is taxed only on the gain from sales. If the firm repurchase stock instead of paying dividends, the income of stockholders will not be taxed. In china, the corporate tax rate is in general 33% (top tax bracket), individual will be taxed both for its interest income or for the capital payment. The tax rate is about 20%. However, the interest payment from the bond issued by the state is for free.

Implications to the capital structure The tax-based explanation for firms’ capital structure choice implies the following. When tax rates are « extremely » favorable to equity holders, we should observe more equity financing (e.g. venture capital) Otherwise firms should use more debt when their pretax cash-flows are high: leverage should increase with EBIT.

Low leverage puzzle

Why are companies not all debt? Back to the assumptions of MM Taxes are ignored Bankruptcy was cheap, quick and painless. Ignoring potential interest between firm’s security holders. (transaction cost due to agency problem) => Introducing bankruptcy cost

Homework In book of Ross, Westerfield and Jaffe, “Corporate Finance”, 9th edition. Chapter 16—Questions and problems: 6, 9, 20, 25, 26. Chapter 16—Minicase: Stephenson Real Estate Recapitalization. To be submitted no later than 11:30 Thursday 13 October. No electronic version is accepted.