Advanced Corporate Finance 3. Capital structure
Practical Information Change of groups! A => : Group 3 Friday 10-12 am F => N : Group 2 Monday 4-6 pm O => Z : Group 1 Friday 4-6 pm 2
Objectives of the session So far, NPV concept and possibility to move from accounting data to cash flows => But necessity to go further regarding the discount rate to use. This sessions objectives: 1. Understand the impact of the capital structure on the value of the firm in a world with and without taxes 2. Understand the impact of the capital structure on the cost of capital in a world with and without taxes 3. Set the theoretical model in perspective with real world observations 3
Practice of corporate finance: evidence from the field Graham & Harvey (2001) : survey of 392 CFOs about cost of capital, capital budgeting, capital structure. «..executives use the mainline techniques that business schools have taught for years, NPV and CAPM to value projects and to estimate the cost of equity. Interestingly, financial executives are much less likely to follows the academically prescribed factor and theories when determining capital structure» Are theories valid? Are CFOs ignorant? Are business schools better at teaching capital budgeting and the cost of capital than at teaching capital structure? 4
Cost of Capital with ebt Up to now, the analysis has proceeded based on the assumption that investment decisions are independent of financing decisions. oes the value of a company change the cost of capital change if leverage changes? If so, how to compute the impact of the financing decision on the company value? 5
xample CAPM holds Risk-free rate = 5%, Market risk premium = 6% Consider an all-equity firm: Market value V 100 Beta 1 Cost of capital 11% (=5% + 6% * 1) Now consider borrowing 20 to buy back shares. Why such a move? ebt is cheaper than equity Replacing equity with debt should reduce the average cost of financing What will be the final impact On the value of the company? (quity + ebt)? On the weighted average cost of capital (WACC)? 6
The intuition (no tax) In perfect market (no tax) 20% debt 80% equity = 40% debt 60% equity 7
Balance sheet in market values The principle of the sum of the parts V U = + In perfect market (no tax) r A = WACC; β A = β wacc Value of all-equity firm: Value of equity: r ; β V U Value of debt: r ; β r WACC r r V A V 8
Weighted Average Cost of Capital (WACC) An average of: The cost of equity r equity The cost of debt r debt Weighted by their relative market values (/V and /V) r wacc r equity V r debt V Note: V = + 9
Modigliani Miller I (1958) Assume perfect capital markets: not taxes, no transaction costs, no asymmetry of information. Proposition I: Proposition II: The market value of any firm is independent of its capital structure: V = + = Assets = V U The weighted average cost of capital is independent of its capital structure r wacc = r A In perfect market (no tax) r A is the cost of capital of an all-equity firm (unlevered) NB: Whatever the capital structure, the total assets of the firm remain constant here 10
In Practice Value of company: V = 100 In perfect market (no tax) Initial Final quity 100 80 ebt 0 20 Total 100 = 100 (MM I) WACC = r A 11% = 11% (MM II) Cost of debt - 5% (assuming risk-free debt) /V 0 0.20 Cost of equity 11% 12.50% (to obtain WACC = r A = 11%) /V 100% 80% 11
Why do we observe a constant r wacc? Consider someone owning a portfolio of all firm s securities (debt and equity) with X equity = /V (80% in example ) and X debt = /V (20%) xpected return on portfolio = r equity * X equity + r debt * X debt This is equal to the WACC (see definition): r portoflio = r wacc But she/he would, in fact, own the company. The expected return would be equal to the expected return of the unlevered (all equity) firm r portoflio = r A The weighted average cost of capital is thus equal to the cost of capital of an all equity firm r wacc = r A In perfect market (no tax) 12
How are MM I and MM II related? Assume (to simplify the presentation): Perpetuities In perfect market (no tax) For a levered company, earnings before interest and taxes will be split between interest payments and dividends payments BIT = Int + iv Market value of equity: present value of future dividends discounted at the cost of equity = iv / r Market value of debt: present value of future interest discounted at the cost of debt = Int / r 13
Relationship between the value of company and WACC From the definition of the WACC: r wacc * V = r equity * + r debt * As r equity * = iv and r debt * = Int r wacc * V = BIT In perfect market (no tax) V = BIT / r wacc Market value of levered firm BIT is independent of leverage If value of company does not vary with leverage (MM I), neither does the WACC (MM II) 14
MM II and the cost of equity (no tax) The equality WACC = r A can also be written: r r ( r r ) A A The expected return on equity is a growing function of the leverage ratio r 12.5% 11% r A r Additional cost of equity due to leverage WACC In perfect market (no tax) Observable Implicit 5% 0.25 r / 15
Why does r equity increases with leverage? Because leverage increases the risk of equity. To see this, back to the portfolio with both debt and equity. In perfect market (no tax) Beta of portfolio: portfolio = equity * X equity + debt * X debt But also: portfolio = Asset Consider A as a given by nature which does only depend on company activity (independently from the leverage ratio) So: Asset quity ebt or quity ( ) Asset Asset ebt 16
Back to our example Consider a risk-free debt In perfect market (no tax) A(1 ) A V 20 1 (1 ) 1.25 80 r r ( r r ) 5% 6% 1.25 12.50% F M F 17
Capital structure in perfect markets Wrap-up To finance operations, firm issue debt or equity In perfect market (no tax) Capital Structure : firm s mix of securities oes this mix selection affect firm value? Miller & Modigliani (MM) say NO (in perfect capital markets) Firm value is determined by its real assets value is independent of capital structure Capital structure irrelevant (for fixed investment decisions, no taxes, no costs of financial distress) Allows separation of investment and financing decisions 18
However we are not in a perfect world Let us add one complexity: suppose we are in perfect capital markets, except one imperfection: corporates have to pay taxes Interests are tax deductible => tax shield Tax savings Transfer of value from the State to the company Tax shield = Interest payment Corporate Tax Rate In perfect market with tax (and perpetual debt) = (r ) T C r : cost of new debt : market value of debt How valuable is the corporate tax shield? Compute the PV of the tax shield Assuming permanent borrowing: Value of levered firm = Value if all-equity-financed + PV(Tax Shield) V L = V U + T C PV( TaxShield ) T C r r T C 19
The intuition (with taxes) 20% debt 80% equity < 40% debt 60% equity 20
Balance sheet in market values Back to the principle of the sum of the parts V U + T c = + In perfect market with tax (and perpetual debt) r A ; β A Value of all-equity firm: Value of equity: r ; β V U r ; β Value of tax shield: PV(TS) Value of debt: r ; β r A V V U L + r Tc V L = r V L + r V L 21
A Numerical Illustration B In perfect market with tax (and perpetual debt) Balance Sheet Total Assets 1,000 1,000 Book quity 1,000 500 ebt (8%) 0 500 Income Statement BIT 240 240 Interest 0 40 Taxable Income 240 200 Taxes (40%) 96 80 Net Income 144 120 ividend 144 120 Interest 0 40 Total 144 160 Assume r A = 10% (1) Value of all-equity-firm: V U = 144 / 0.10 = 1,440 (2) PV(Tax Shield): Tax Shield = 40 x 0.40 = 16 PV(TaxShield) = 16/0.08 = 200 (3) Value of levered company: V L = 1,440 + 200 = 1,640 (4) Market value of equity: L = V L - = 1,640-500 = 1,140 22
WACC and leverage Assume (to simplify the presentation): Perpetuities NOPAT = net operating profit less adjusted taxes In perfect market with tax (and perpetual debt) NOPAT = Net Income + Interest - Tax Shield = (BIT r ) (1 T C ) + r - T C r = Net Income for all-equity-firm = BIT (1 T C ) V L = NOPAT / WACC r r (1 T ) BIT (1 T ) NOPAT C C WACC r r (1 TC ) V V L L In our example (perpetual debt): NOPAT = 144 WACC = 10.53% x 0.69 + 8% x 0.60 x 0.31 = 8.78% V L = NOPAT / WACC = 144 / 8,78% = 1,640 23
What does WACC do? The WACC includes all impacts from the financial structure (which all goes into the denominator of the present value calculation) The WACC decreases with leverage, only because of the tax shields WACC is the discount rate used to calculate directly the market value of the levered firm by discounting the NOPAT (which is, by definition, independent from the financial structure) V = BIT*(1-T c )/ WACC Market value of levered firm BIT is independent of leverage If value of company varies with leverage, so does WACC in opposite direction 24
The WACC in perfect market with tax: an interpretation General definition (in perfect market, with corporate tax): In perfect market with tax WACC r r (1 TC ) V V L L All financing items: the average financing cost of the levered company With perpetual debt: VU WACC ra ra V L In perfect market with tax (and perpetual debt) Cost of assets = the expected return of the same company if entirely equity financed In our example: V L = 1,640 WACC = 10.53% x 0.69 + 8% x 0.60 x 0.31 = 8.78% < r A = 10% 25
Unlevered Vs Levered Values r A is the cost of equity of an all-equity firm, i.e. the cost of assets It is the discount rate that allows to compute the unlevered (i.e. all-equity ) company value in one single calculation: V U = BIT(1-T C )/r A r A does not embed any effect from the financial structure (it is independent from the financial structure) The Weighted Average Cost of Capital (WACC) is the discount rate that allows to compute the total levered company value in one single calculation: V L = BIT(1-T C )/WACC As such, the WACC embeds the effects from the financial structure if any (those are not embedded in the numerator of the PV formula, as NOPAT are independent from the financial structure) 26
What about the cost of equity? In perfect market with tax (and perpetual debt) 1) Cost of equity increases with leverage: r r ( r r ) (1 T ) A 2) Beta of equity increases A ( )(1 T ) A A C C Proof: ( BIT r ) (1 T r But V U = BIT(1-T C )/r A and = V U + T C Replace and solve C ) In our example (perpetual debt): r = 10% +(10%-8%)(1-0.4)(500/1,140) = 10.53% or r = iv/ = 120/1,140 = 10.53% 27
MM and the cost of equity (with tax) In perfect market with tax (and perpetual debt) The expected return on equity is still a growing function of the leverage ratio r ra ( ra r ) (1 TC ) The WACC is now a decreasing function of the leverage (due to tax shields only) r r A r Additional cost of equity due to leverage r A WACC Observable Implicit 0.25 r / 28
Conclusion on our initial issue Question: What happens when the firm increases leverage? MM (perfect capital markets) MM (with taxes) To the company value? (V L ) Unchanged Increases To the equity value? () Unchanged Increases To the cost of capital? (WACC) Unchanged ecreases To the cost of equity? (r ) Increases Increases (less) 29
What about Personal Taxes? Suppose operating income = 1 If paid out as Interest quity income Corporate tax 0 T C Income after corporate tax 1 1 - T C Personal tax T P T P (1-T C ) Income after all taxes 1- T P (1-T P )(1-T C ) 30 With T C corporate Tax, T P personal tax on interest income, T P, personal tax on equity income. NB: Marginal Rates!
PV(TaxShield) with corporate and personal taxes At the investor level, tax advantage of debt is positive if: 1-T P >(1-T C )(1-T P ) PV( TaxShield ) (1 TC )(1 TP) [1 ] (1 T ) P Note: if T P = T P, then PV(TaxShield) = T C NB: Tax advantages may heavily change from one country to the other because taxation differs! But also whitin country => function of the situation of each investor 31
Where does the PV(TaxShield) formula come from? After taxes income for Total Stockholders ebt holders ( BIT r )(1 TC )(1 TP) r ( 1 TP ) ( BIT r )(1 TC )(1 TP) r (1 TP ) This can be written as: BIT (1 T C )(1 T P ) r (1 T P (1 TC )(1 T ) (1 (1 T ) P P ) Market values V u 32
What about the real world? Huge differences regarding leverage Industry influence Cash balances (and thus reflection to have in terms of net debt) Low amount of debt for some industries puzzle? If PV(Tax Shield) >0, why not 100% debt? Or a high figure well above 50% for example? Several explanations have been suggested Limits to tax benefits of debt => need to have taxable earnings (not really the case for start-ups or new high tech companies). Optimally, in theory, from tax savings perspective BIT = interest payments => 0 tax! But there are limits to this! 33
What about the real world mpirical vidence => Internationally low level of leverage (20%-40%) firms do not seem to exploit the full benefits of leverage Graham (2000) estimates that tax benefits of interest deductibility represent 9.7% of market value for a typical firm Two counterbalancing forces: cost of financial distress As debt increases, probability of financial problem increases agency costs Conflicts of interest between shareholders and debtholders Interest payments MUST be made... There is obviously more flexibility regarding dividends => firms with unstable earning may be more reluctant to use leverage at a high level 34
Market value What if we add bankruptcy and agency costs? Trade-off theory PV(costs of financial distress and agency costs) PV(Tax Shield) Value of all-equity firm 35 Optimal ebt ratio = ratio of debt which maximizes the company value ebt ratio 35