Capital Structure (How Much Debt?) MSBC 5060 Chapter 16 Capital Structure (How Much Debt?)

Capital Structure Chapter Overview We looked a the return required by a company’s investors It is the same as the company’s cost It is the required return on the company’s investments WACC = WERE + WDRD(1 - T) WE and WD are the Percentages of Equity and Debt RE and RD are the Costs of Equity and Debt

βEquity = βAssets [1 + D/E(1-T)] Chapter Overview We also looked (in the context of the CAPM) at the effects of debt on Equity Risk βEquity = βAssets [1 + D/E(1-T)] For a given risk of the firms assets (βAssets) A function of cyclicality and operating leverage How does the choice of debt (D/E) change the risk of equity (βEquity)? So the Question is: How much Debt should a firm have? What should be the firm’s Capital Structure? Capital Structure is defined by WE and WD or D/E

Aside: Compare WD = D/V to D/E If WD = D/V = 20% then calculate D/E: E/V = 1 - D/V = 80% D/E = (D/V)/(E/V) = 0.20/0.80 = 0.25 If WD = D/V = 50% then calculate D/E: E/V = 1 - D/V = 50% D/E = (D/V)/(E/V) = 0.50/0.50 = 1.00 If WD = D/V = 60% then calculate D/E: E/V = 1 - D/V = 40% D/E = (D/V)/(E/V) = 0.60/0.40 = 1.50

Chapter Overview WACC is the discount rate for all the firm’s projects The lower the rate, the higher the value of the projects A firm is the sum of its projects So the higher the value of the firm So how does WACC (and therefore firm value) change as WE and WD (or D/E) change?

Definition: Adding Financial Leverage Issue bonds to finance an expansion Issue bonds and use the proceeds to buy back stock Examine what happens with additional leverage: To the Value of the company Value Unlevered (VU) versus the Value Levered (VL) To the Required Return on the Assets (RA) To the Required Return on the Equity (RE) First assume no taxes Second look at the effects of taxes

A = Assets or 0 = An All Stock firm Notation: D = Debt or B = Bond and E = Equity or S = Stock A = Assets or 0 = An All Stock firm

Modigliani & Miller These theories, formulas and propositions were developed by Franco Modigliani and Merton Miller MM I (without Taxes) “Changing how the pie is sliced does not make it any bigger.” A firm’s total value is not affected by its capital structure: VL = VU MM II (without Taxes) Changing capital structure does increase equity risk and equity return but does not change the WACC since a Bigger RE is offset by smaller WE RE = RA + (RA – RD)D/E MM I (with Taxes): With taxes, adding debt does increase firm value. Firm value does depend on its capital structure: VL = VU + TC x D MM II (with Taxes): With taxes Leverage increases equity risk and equity return and does decrease WACC. RE = RA + (RA – RD)(1 – TC)D/E

Again: Without Taxes With Taxes: Changing capital structure does increase equity risk and equity return but does not change the WACC since a Bigger RE is offset by smaller WE RE = RA + (RA – RD)D/E A firm’s total value is not affected by its capital structure: VL = VU With Taxes: With taxes debt does increase equity risk and equity return and does decrease WACC. RE = RA + (RA – RD)(1 – T)D/E With taxes, adding debt does increase firm value. VL = VU + T x D

We start with D/E and end with Firm Value The Progression (Derivation): Firm Value is the sum of the NPVs the projects or products: Value = NPV1 + NPV2 + NPV3 + … For each project or product, NPV is the PV of CFs less the Cost: NPV = CF0 + CF1/(1+R) +…+ CFN/(1+R)N WACC is the R for each of the company’s projects: WACC = WE RE + WD RD(1 - T) RD is the YTM on existing debt RE is from the CAPM and is a function of βE RE = Rf + βE[E(RM) – Rf] βE is a function of three things: The Cyclicality of the product (steel vs. soap) The Degree of Operating Leverage (FC vs. VC) Financial Leverage (the amount of debt or fixed vs. variable financing) Cyclicality and DOL give the Asset Beta: (βA) Debt/Equity (financial Leverage) gives the Equity Beta: βE βE = βA(1 + D/E)(1-T) We start with D/E and end with Firm Value

So how does the Amount of Debt change Value? How Does Debt Change Company Value? Cyclicality of the product and the method of production (DOL) gives Asset Beta (βA) Given βA, the Amount of Debt gives the Equity Beta (βE) βE = βA[1 + D/E(1-T)] Given the βE, the CAPM gives the cost of equity capital (RE) RE = Rf + βE[E(RM) – Rf] Given βA, Amount of Debt gives the cost of debt capital (RD) The Amount of Debt, RE and RD give the WACC WACC = E/V RE + D/V RD(1 - T) The WACC (which is R) gives the NPV for each project or product NPV = CF0 + CF1/(1+R) +…+ CFN/(1+R)N The sum of the NPVs is the Value of the company. So how does the Amount of Debt change Value?

So the lower the WACC… The greater the Value! How Does Debt change Company Value? WACC is the discount rate for the NPVs Company Value is the sum of the NPVs So the lower the WACC… The greater the Value!

RE = RA + (RA – RD)(D/E)(1 –T) Derivation: WACC = WERE + WDRD(1 –T) RA = WERE + WDRD(1 –T) RA = (E/V) RE + (D/V) RD(1 –T) RA = E/(D + E)RE + D/(D + E) RD(1 –T) Do a bunch of Algebra: RE = RA + (RA – RD)(D/E)(1 –T) This result is MMII

How Does Debt change WACC and Value? WACC = WE RE + WD RD(1 - T) In generally, RD < RE Why? And RD(1-T) < RE So more Debt  Lower WACC  HIGHER VALUE But adding Debt Increases βE βE = βA(1 + D/E) Increasing βE increases RE RE = Rf + βE[E(RM) – Rf] So more Debt  Higher WACC  LOWER VALUE Which Dominates?

So How Much Debt? Here is the general idea: Start with no debt Adding a little debt can Lower WACC and Increase Value Lower RD and tax benefit offsets higher RE As more debt is added RD Increases But still lower than RE So WACC is still lower and value increases As more and more debt is added RD (and after tax RD) is greater that RE As debt increases, cost of borrowing and default costs increase WACC increases and value decrease

Determinants of the Amount of Debt Volatility of EBIT Cyclicality of the product DOL (FC vs. VC - Method of Production) Measured by βAssets Assets Needed by the business High vs. Low capital requirements Airlines – high debt Software – low debt So low volatility, high capital industries tend to have more debt Also the nature of the assets: Are the assets easily marketable?

Now to Capital Structure What does adding Leverage do to: The Required Return on the Equity (RE) The Required Return on the Assets (RA) The Value of the Company Value Unlevered (VU) versus the Value Levered (VL)

ValueLevered = ValueUnlevered First Results (no Taxes): ValueLevered = ValueUnlevered VL = VU The value of the firm does not increase with the addition of leverage Changing the way the pie is sliced does not increase the slice of the pie People can borrow just as easily as the company Result: A company can’t create value just by replicating what people can do on their own This result is know as MM I

ValueLevered = ValueUnlevered + PV of Tax Shield Now with Taxes: Taxes create a benefit for debt. So the pie gets bigger: ValueLevered = ValueUnlevered + PV of Tax Shield VL = VU + T x D Result: A company can create value by adding debt: This result is know as MM I with Taxes

How does firm value change when D/E changes? Start by valuing an unlevered company: Value Unlevered = VU Make heroic simplifying assumption about the business: EBIT will be constant forever – a perpetuity So value is the PV of a Perpetuity: Value = CF/R CF = EBIT(1 –T) We don’t have to do this! We can model any CF’s we want. We did this earlier in the semester. But doing this this lets us focus on the discount rate Value Unlevered = VU = EBIT(1 – T)/R So how does R change D/E changes? What does this do to Value?

How does firm value change when D/E changes? Value Unlevered = VU = EBIT(1 – T)/R For an unlevered company R = RE = RA VU = EBIT(1 – T)/RA EBIT = $100 T = 30% RE = RA = 10% VU = EBIT(1 – T)/RA = $100(1 – 0.30)/0.10 = $70/0.10 = $700 Note Tax Exp = $30 per year forever Since this is an unlevered company, the value of the company is the value of the equity: VU = E = $700 Now add debt!

How does firm value change when D/E changes? VU = $700 Now Issue $200 of 5% debt and buy back $200 in equity Int Exp = 5% X $200 = $10 EBT = EBIT – Int Exp = $100 - $10 = $90 Tax Exp = $90 x 30% = $27 So a $3 savings in taxes Tax Shield = D x RD x T = $200 x 5% x 30% = $3 So adding debt saves the company $3 per year forever Now calculate the PV of the Tax Shield: We will discount at the cost of debt RD PV of the Tax Shield = Tax Shield/RD = (D x RD x T)/RD PV of the Tax Shield = D x T = $200 x 30% = $60

How does firm value change when D/E changes? VU = $700 Adding Debt saves the firm $3 per year forever The PV of that at 5% is $60 So adding $200 of 5% debt with a tax rate of 30% adds (D x RD x T)/RD =D x T = $200 x 30% = $60 Value Levered = VL = VU + T x D = $700 + $60 = $760

With Taxes, Adding Debt Increases Firm Value Debt Creates a Tax Shield Unlevered: Total CFs = EBIT(1 – T) = $70 Levered: Total CFs = EBIT(1 – T) + TRDD = $70 + $3 = $73 TRDD is the annual increase in Total CFs from adding debt Assume T, Debt and RD are constant forever Then the Tax Shield is a perpetuity At what rate should we discount the perpetuity? Assume the tax savings has the same risk as the debt So discount the annual Tax Shield at RD So if Tax Shield is a perpetuity discounted by RD, Then the PV of the Tax Shield is: PV of Tax Shield = TRDD/RD = TD MM I with Taxes: VL = VU + TC x D (Recall MM I without Taxes: VL = VU) With Taxes, Adding Debt Increases Firm Value

What Happens to Equity Risk and Equity Return with Taxes? Without Taxes: βEquity = βAssets (1 + D/E) With Taxes: βEquity = βAssets [1 + (1 - T)D/E] Equity Return: Without Taxes: RE = RA + (RA – RD)D/E With Taxes: RE = RA + (RA – RD)(1 – T)D/E

Example Continued: An Unlevered Firm with 100 shares of stock priced at $7.00 earns $100 of EBIT per year forever Calculate the RE and WACC: Unlevered means D/E = 0 No Interest Expense So EBIT = EBT = $100 Taxes = 30% NI = EBIT(1 – T) = $100(1 – 0.30) = $70 The firm has 100 shares of stock EPS = $70/100 = $0.70 Price per share = $7.00 RE = $0.70/$7.00 = 10% WACC = RA = WERE + WDRD(1 - T) = 1.00(10.00%) + 0 = 10.00% Value = Price per share x Shares = $7.00 x 100 = $700 The firm issues $200 of 5% debt and repurchases $200 of stock What does this do to the firm’s value (VL versus VU)? What does this do to the firm’s cost of equity (RE)? What does this do the firm’s WACC?

With Taxes, Adding Debt Increases Firm Value What does this do to the firm’s Value? Unlevered Value (VU) is the PV of the after-tax EBIT T = 30% D = $200 RD = 5% VU = EBIT(1 – T)/WACC = $100(1 – 0.30)/0.10 = $700 VL = VU + PV of Tax Shield Recall: Annual Tax Shield = Tax Rate x Interest Expense = RD x D x T PV of Annual Tax Shield = (RD x D x T)/RD = TD VL = VU + TD VL = $700 + $200 x 0.30 = $700 + $60 = $760 With Taxes, Adding Debt Increases Firm Value

Leverage increases the Equity’s risk so RE Increases What does this do to the firm’s cost of equity (RE)? Calculate the New RE: for the Levered Firm: RE = RA + (RA – RD)(1 – T)D/E RA = 10.00% RD = 5.00% T = 30% Value = $760 D = $200 E = $760 - $200 = $560 D/E = 200/560 = 0.3571 = 10% + (10% - 5%)(1- 0.30)0.3571 = 11.25% Unlevered RE = 10.00% Levered RE = 11.25% Leverage increases the Equity’s risk so RE Increases

Leverage Lowers the Cost of Capital! What does this do to the firm’s WACC? Before the Leverage: RE = 10.00% WE = 1.00 Taxes = 30% WACC = WERE + WDRD(1 - T) WACC = 1.00(10.00%) + 0 = 10.00% If the firm issues $200 of 5% debt and repurchases $200 of stock: RE = 11.25% WE = $500/$760 = 0.7368 RD = 5.00% WD = $200/$760 = 0.2632 T = 30% WACC = 0.7368(11.25%) + 0.2632(5.00%)(1 – 0.30) = 9.21% Leverage Lowers the Cost of Capital!

With Taxes, Adding Debt Lowers WACC And this Increases Firm Value One More Look at Value – Lowering the WACC Unlevered WACC was 10% VU = EBIT(1 – T)/WACC VU = $100(1 – 0.30)/0.10 = 70/0.10 = $700 Levered WACC is 9.21% VL = EBIT(1 – T)/WACC VL = $100(1 – 0.30)/0.0921 = $70/0.0921 = $760 With Taxes, Adding Debt Lowers WACC And this Increases Firm Value

Cost of Equity (RE) Consider the CAPM: RE = Rf + βEquity[E(RM) – Rf] For the Market: E(RM) – Rf = 8.33% Rf = 5.00% RE for the Unlevered Firm: βEquity = 0.60 RE = Rf + βEquity[E(RM) – Rf] = 5.00% + 0.60[8.33%] = 10.00% Also: βEquity = βAssets [1 + (1 - T)D/E] 0.60 = βAssets [1 + (1 - T)0/E] βAssets = 0.60

Firm’s Cost of Equity (RE) For the Levered Firm D/E = 200/560 = 0.3571 βAssets = 0.60 βEquity = βAssets [1 + (1 - T)D/E] = 0.60[1 + (0.70)(0.3571)] βEquity = 0.60[1 + 0.25] = 0.60(1.25) = 0.75 RE = Rf + βEquity[E(RM) – Rf] = 5.00% + 0.75[8.33%] = 11.25% This is the same RE as we got from MM II: RE = RA + (RA – RD)(1 – T)D/E = 10% + (10% - 5%)(1- 0.30)0.3751 = 11.25%

Recap: With Taxes: Leverage Increases Equity Risk (βEquity) βEquity = βAssets [1 + (1 - T)D/E] βEquity from 0.60 to 0.75 Leverage Increases Equity Return (RE) RE = RA + (RA – RD)(1 – T)D/E RE from 10.00% to 11.25% Leverage Decreases WACC WACC from 10.00% to 9.21% Leverage Increases Value VL = VU + TD Value from $700 to $760

How Firms Establish Capital Structure Most corporations have low Debt-Asset ratios. Changes in financial leverage affect firm value. Firm value increases with leverage This is consistent with M&M with taxes. Another interpretation is that firms signal good news when they lever up Differences in capital structure across industries. Evidence that firms behave as if they had a target Debt-Equity ratio

Factors in Target D/E Ratio Taxes Since interest is tax deductible, highly profitable firms should use more debt (i.e., greater tax benefit). Types of Assets The costs of financial distress depend on the types of assets the firm has. Airplanes vs. Fixed Assets Uncertainty of Operating Income Cyclicality and Operating Leverage Even without debt, firms with uncertain operating income have a high probability of experiencing financial distress

Some Debt to Value Ratios

Some Debt to Value Ratios

Other Industries Goto Spreadsheet “Damodaran Corporate Financial Leverage.xlsx” 