UGBA 103 –Introduction to Finance

Dmitry Livdan

Walter A. Haas School

Fall 2017

Dmitry Livdan (Haas) UGBA 103 Fall2017 1/124 II. Financing Decisions

Dmitry Livdan (Haas) UGBA 103 Fall2017 2/124 II. Financing Decisions

Dmitry Livdan (Haas) UGBA 103 Fall2017 3/124 Introduction

So far we have focused on the …rm’sinvestment decisions. In this part of the course we take the investment decisions as given and look at the …rm’s(long-term) …nancing decisions. In part III, we will look at the interactions between investment and …nancing decisions. Finally, we study options in part IV. This will give you the opportunity to return to the …rm’sinvestment and …nancing decisions using new tools in elective courses.

Dmitry Livdan (Haas) UGBA 103 Fall2017 4/124 II.1 Debt Policy

Readings: Berk and DeMarzo Chapters 14-15.

Dmitry Livdan (Haas) UGBA 103 Fall2017 5/124 Big Picture: Why Do We Care?

Debt policy is the second of the two major components of a …rm’s …nancing decisions – Ine¢ ciently high leverage can prevent a company from undertaking pro…table investment opportunities, lead a company to undertake excessive risk, and ultimately bankrupt it – Ine¢ ciently low leverage can allow a …rm to make wasteful investments – Maintaining a suboptimal may lead to the …rm being taken over and current management being …red (e.g. hostile LBOs) Corporate …nance: can a …rm (or its …nancial advisors) add value by changing its debt policy? If so, what factors determine a …rm’s optimal capital structure? Investments: if a …rm deviates signi…cantly from its optimal capital structure, traditional investors may sell it; activist investors may take a large stake and try to change the company’scapital structure – in the extreme, they may take it over

Dmitry Livdan (Haas) UGBA 103 Fall2017 6/124 Leverage Is Irrelevant in Perfect Capital Markets

The modern theory of capital structure dates back to a 1958 paper by Modigliani and Miller. Their Proposition I states that in a perfect capital market, …rm value is una¤ected by changes in capital structure. The intuition is simple. The level of debt determines only how the cash ‡ows of a …rm’sassets are split between bondholders and equityholders. The total cash ‡ows are unchanged, so …rm value must be unchanged. This is an application of the principle of value additivity:

The value of a pie is independent of how it is sliced.

Equivalently (and more technically), we can say that the expected return rA on the …rm’sassets is una¤ected by leverage.

Dmitry Livdan (Haas) UGBA 103 Fall2017 7/124 Leverage Is Irrelevant in Perfect Capital Markets: Intuition I

Suppose that the assets of an all-equity …rm are worth VU = $100m. – The total wealth of the shareholders is then $100m, all coming from the equity value. – This is depicted in the left portion of the …gure on the next slide. Now suppose that the …rm raises $25m in cash from new debt to buy back $25m worth of equity. – The bondholders will only provide $25m in cash in return for a $25m debt stake in the …rm (they are not fooled). – The rest of the …rm ($75m) belongs to the shareholders. – This is depicted in the right portion of the …gure on the next slide.

Dmitry Livdan (Haas) UGBA 103 Fall2017 8/124 Leverage Is Irrelevant in Perfect Capital Markets: Intuition II

Are shareholders better o¤? No: in addition to their equity worth $75m, they now have $25m in cash from the repurchased shares. Their total wealth remains at $100m, so they should be indi¤erent. This result is hardly surprising, as the …rm’sassets (which were optimized by capital budgeting) are exactly the same, no matter how they are …nanced.

Dmitry Livdan (Haas) UGBA 103 Fall2017 9/124 Practice Problem Ch 14.

Dmitry Livdan (Haas) UGBA 103 Fall2017 10/124 Practice Problem Ch 14.

Dmitry Livdan (Haas) UGBA 103 Fall2017 11/124 Practice Problem Ch 14.

Dmitry Livdan (Haas) UGBA 103 Fall2017 12/124 Leverage and Expected Returns: Useful Formulas

Expected return of the …rm’sassets - expected return on a portfolio of all the company’ssecurities or weighted average : D E WACC = r + r . V D V E     MM’sProposition I: VL = VU , i.e. rA independent of leverage and thus equal to WACC. MM’sProposition II: D rE = rA + (rA rD ). E   The increase in the expected return on equity when leverage increases re‡ects the impact of …nancial leverage on betas:

D β = β + (β β ) E A E A D  

Dmitry Livdan (Haas) UGBA 103 Fall2017 13/124 A Common Mistake

MM’sproposition is now widely accepted, but it seemed revolutionary at the time. The prevailing argument went as follows. The value of a …rm equals the discounted value of its future cash ‡ows. The appropriate discount rate is the …rm’s weighted average cost of capital rA, which is the expected return on a portfolio of all the company’ssecurities:

D E D rA = rD + rE = rE (rE rD ). V V V      

Therefore, as long as rE > rD , leverage decreases the WACC and hence increases …rm value:

rE >rD D rA value of …rm since it is less discounted. " ) #) " What is wrong with this argument?

Dmitry Livdan (Haas) UGBA 103 Fall2017 14/124 How Leverage A¤ects Expected Returns

Bonobos is an all equity …rm, which is expected to generate a constant level of earnings and dividends per share of $1.50 in perpetuity. Assume for simplicity that the corporate tax rate is zero. The company currently has 1,000 shares outstanding, which trade for a price of $10:

VU = 1,000 $10 = $10,000, and  total yearly earnings = 1,000 $1.50 = $1,500.  Since the …rm expects to produce a level stream of earnings in perpetuity, the expected return on Bonobos’sequity equals the E/P ratio, 15%: E E E 1.50 P0 = = rE = rA = = = 15%. rE rA ) P0 10

Dmitry Livdan (Haas) UGBA 103 Fall2017 15/124 How Leverage A¤ects Expected Returns (cont’d)

In an attempt to increase EPS, Bonobos’smanagers are considering issuing $5,000 of debt at 10% to repurchase half of the outstanding shares. – Shares outstanding after repurchase: 1,000 500 = 500. – Since the yearly earnings will be used to pay the interest on the debt, the net earnings will be $1,500 $5,000(10%) = $1,000, and the $1,000 earnings per share are now 500 = $2.00 > $1.50. From the calculations on the previous page, it is tempting to conclude E 2 that the price should go up: P0 = = = 13.33 > 10.00. rE 0.15 What is wrong with this argument? EPS went up from 1.50 to 2.00 but the risk of earnings also went up (increasing rE ). This is …nancial risk. D E $2 r 0 = rA + (rA rD ) = 20% P0 = = = $10 E E ) r 0.2   E0

Dmitry Livdan (Haas) UGBA 103 Fall2017 16/124 How Leverage A¤ects Expected Returns (cont’d)

In reality, as D/E rises, rD will also rise owing to the greater risk of D default. This slows the increase in rE = rA + E (rA rD ), as shown in the following graph: 

Dmitry Livdan (Haas) UGBA 103 Fall2017 17/124 Practice Problem Ch 14.

Dmitry Livdan (Haas) UGBA 103 Fall2017 18/124 Practice Problem Ch 14.

Dmitry Livdan (Haas) UGBA 103 Fall2017 19/124 Where to Look for Violations of MM’sPropositions

MM’sproposition is important not because we believe in the assumption of perfect markets, but because it tells us that an optimal capital structure can only arise from market imperfections. – By showing what does not matter, MM also show what does The following imperfections have been suggested as potentially relevant: – taxes; – bankruptcy costs; – agency costs; – asymmetric information. We will now examine each of these imperfections in turn.

Dmitry Livdan (Haas) UGBA 103 Fall2017 20/124 The E¤ect of Corporate Taxes

Debt has an important tax advantage over equity: interest payments are tax-deductible, while dividends and retained earnings are not. Assume that the …rm now has debt in the form of a perpetuity:

value of debt = DL interest payment in year t : It = rD DL. interest on debt = rD ! 

The corporate tax rate is denoted by tc .

Value of 1 year’stax shield is rD tc DL. In perpetuity, this is worth rD tc DL = tc D , which yields rD L

VL = VU + tc DL

Conclusion: The value of the levered …rm is equal to that of the unlevered …rm plus the PV of the tax shields on the debt.

Dmitry Livdan (Haas) UGBA 103 Fall2017 21/124 The E¤ect of Corporate Taxes: Intuition

Suppose that the assets of an all-equity …rm are worth $100m before (corporate) taxes, and that the corporate tax rate is equal to 25% (tc = 25%). – The total after-tax wealth of the shareholders is then $75m, all coming from the after-tax equity value. – This is depicted in the left portion of the …gure on the next page. Now suppose that the …rm decides to issue $25m worth of debt in order to buy back $25m worth of equity. – The bondholders are now e¤ectively given a fraction of the …rm worth $25m, which is not taxed given the tax deductibility of debt. – The rest of the …rm ($75m) belongs to the shareholders, who will receive $56.25m after paying corporate taxes of $18.75m (25% 75). – This is depicted in the right portion of the …gure on the next page.

Dmitry Livdan (Haas) UGBA 103 Fall2017 22/124 The E¤ect of Corporate Taxes: Intuition (cont’d)

After taxes, the shareholders now have $56.25m in equity, and $25m in cash from the sale of their shares. Their total wealth has therefore increased from $75m to $81.25m. This increase corresponds to the on the debt:

rD tc DL tax shield = = tc DL = 25% 25 = 6.25. rD  Since shareholders are better o¤ in this second situation, the …rm should increase its D/E ratio. This will increase the after-tax value of the …rm’sassets by the tax shield on the debt.

Dmitry Livdan (Haas) UGBA 103 Fall2017 23/124 Corporate Taxes: Values and Discount Rates

What do we discount at what rate to get what?

Example for Discount Cash ‡ows perpetual …rm at Result

CFs to shareholders (1 tc )(EBIT r D) rE E D CFs to bondholders rD D rD D After-tax CFs of assets (1 tc )EBIT rA VU After-tax CFs of assets (1 tc )EBIT WACC U VU After-tax CFs of assets (1 tc )EBIT WACC L VL plus yearly tax shield tc r D D rD VL

Dmitry Livdan (Haas) UGBA 103 Fall2017 24/124 Leverage, Expected Returns, and Taxes: Useful Formulas

Expected return of the …rm’sassets: D E r = r + r . A V D V E     MM’sProposition I with taxes:

VL = VU + tc DL.

MM’sProposition II with taxes: D rE = rA + (1 tc )(rA rD ). E   Appropriate discount rate: D E D WACC = (1 tc ) rD + rE = rA 1 tc . VL VL VL      

Dmitry Livdan (Haas) UGBA 103 Fall2017 25/124 Corporate Taxes: An Example

Intel’sassets generate operating pro…t (before interest and taxes) of $102,000 per year in perpetuity. It currently has $130,000 of perpetual debt outstanding, paying a coupon of 12%, and 50,000 shares trading at $6.11 each. Goldman Sachs proposes that Intel could issue $130,000 of subordinated perpetual debt to repurchase some equity. Since the will be junior to the existing debt, it will require a coupon of 14%. Before going ahead with the , Intel’s CFO would like to answer the following questions:

1 What is the value of the …rm after the recapitalization? 2 What is the new expected return on equity? 3 Are shareholders better o¤, and why? 4 What is the new WACC? Assume a tax rate of 35%

Dmitry Livdan (Haas) UGBA 103 Fall2017 26/124 Corporate Taxes: An Example (cont’d)

1 We can use VL0 = VU + tc DL0 to …nd the value of the …rm after the recapitalization, where the primes denote “after”. We know tc = 35% and DL0 = $260, 000, but we need to …nd VU . We can calculate VU by examining the …rm prior to the recapitalization Current …rm value is

VL = DL + EL = 130, 000 + 50, 000 6.11 = $435, 500  which yields

VU = VL tc DL = 435, 500 35% 130, 000 = $390, 000.  Thus, new …rm value is given by

V 0 = VU + tc D0 = 390, 000 + 35% 260, 000 = $481, 000. L L 

Dmitry Livdan (Haas) UGBA 103 Fall2017 27/124 Corporate Taxes: An Example (cont’d)

2. We can calculate rE0 by the formula

(1 tc )(X rD0 DL0 ) EL0 = rE0 Note that there are two tranches of debt with two di¤erent interest rates, which must be considered separately. The new value of equity is given by

E 0 = V 0 D0 = 481,000 260,000 = 221,000 L L L and so (1 0.35)[102,000 (0.12)(130,000) (0.14)(130,000)] r 0 = E 221,000 = 20.1%. 3. Shareholders are better o¤ because their wealth increases from 50, 000 6.11 = $305, 500 (in equity only) to $351, 000 ($221, 000 in  equity, and $130, 000 in cash from the debt issue).

Dmitry Livdan (Haas) UGBA 103 Fall2017 28/124 Corporate Taxes: An Example (cont’d)

4. The new WACC can be calcualated in two ways. First, we can use the standard formula, modi…ed for the inclusion of two types of debt: 130,000 130,000 WACC0 = (1 tc )(12%) + (1 tc )(14%) 481,000 481,000 221,000 + r = 13.8%. E0 481,000 Second, we can use the fact that …rm value equals post-tax earnings (but before deduction of interest, i.e. earnings to all investors) discounted at the WACC:

(1 tc )X (1 0.35)102,000 VL0 = WACC0 = = 13.8%. WACC0 , 481,000

Dmitry Livdan (Haas) UGBA 103 Fall2017 29/124 Sanity Check: Do We Understand Anything? PE Mini Case

General Everything Co. (G.E.) is a large conglomerate with total value of equity of $500 million, and total value of debt (paying the riskless rate of 6%) of $300 million. Its returns are closely correlated with the market and the …rm’sshares have a P/E ratio of 10. The e¤ective rate of corporate income tax for G.E. is 40%. General Everything is considering buying Practically Nothing, Inc. (P.N.), a relatively small …rm which manufactures nightwear. Since the amount of nightwear sold increases when people turn down their heat, and people turn down their heat when times are bad, the returns to P.N. are negatively correlated with the market. P.N. is an all-equity …rm, with current market value of $210 million, an e¤ective tax rate of 30% and a P/E = 25. The terms of the merger have been hammered out as follows: G.E. will buy all shares of P.N. for a total cash value of $250 million and will issue that amount of bonds to raise the money for purchase. Accountants estimate that the e¤ective tax rate of the of the merged …rms (which have no production or market synergies) will be 38%. Bonds of the merged …rms will continue to be riskless. Dmitry Livdan (Haas) UGBA 103 Fall2017 30/124 Sanity Check: Do We Understand Anything? PE Mini Case Continued

Q1: Assuming to keep things simple that the debt will be carried in perpetuity (equivalently, that it will be renewed on the same terms at maturity) and that neither company is growing through new investments, do you think the merger is a good deal for G.E.? Q2: What will be the market value of the merged …rm? The equity value? The PE ratio?

Dmitry Livdan (Haas) UGBA 103 Fall2017 31/124 Sanity Check: Do We Understand Anything? PE Mini Case Solution

Dmitry Livdan (Haas) UGBA 103 Fall2017 32/124 Corporate Taxes: Conclusion

The above analysis somewhat overstates the advantage of borrowing, since we have implicitly assumed that the tax shield of debt is not lost if the operating income in a given year is not su¢ cient to cover the interest payment. However the point remains that if corporate taxes were the only deviation from MM’sideal world, then all …rms should be 100% debt …nanced. Two reasons have been given to explain why …rms do not borrow so much: – The …rst, due to Miller, focuses on personal taxes. – The second is based on bankruptcy and agency costs.

Dmitry Livdan (Haas) UGBA 103 Fall2017 33/124 Practice Problem Ch 15.

Dmitry Livdan (Haas) UGBA 103 Fall2017 34/124 Practice Problem Ch 15.

Dmitry Livdan (Haas) UGBA 103 Fall2017 35/124 Practice Problem Ch 15.

Dmitry Livdan (Haas) UGBA 103 Fall2017 36/124 Practice Problem Ch 15.

Dmitry Livdan (Haas) UGBA 103 Fall2017 37/124 The E¤ect of Personal Taxes (Miller)

In what follows, we will assume di¤erent (personal) tax rates for interest income (tD ) and equity income (tE ). In many countries (including the U.S.), investors are taxed at a lower rate on their capital gains income than on the rest of their income. – Interest income is treated as regular income. – Equity income consists of dividends (usually taxed at the regular income rate) and capital gains (usually taxed at a lower rate). Moreover, the realization of capital gains can be delayed, making the present value of the capital gains tax even lower t < t . ) E D Intuitive argument: When a dollar in pre-tax earnings is paid to a – shareholder, he/she receives (1 tE )(1 tc ); – bondholder, he/she receives (1 t ) (because tax deductible). D Therefore, the tax advantage of debt in the presence of both corporate and personal taxes becomes

(1 tE )(1 tc ) t = 1 1 tD Dmitry Livdan (Haas) UGBA 103 Fall2017 38/124 Firm Value in the Presence of Personal Taxes (cont’d)

The value of a levered …rm now becomes

VL = VU + tDL

Conclusion: The levered …rm is more valuable if t > 0, i.e. if pre-tax earnings are worth more to bondholders than shareholders. In 2013 top regular income tax bracket went back to 1994 level ( tD = 39.6%) while corporate rate remained at tc = 35% so that 1 0.35 t = 1 (1 tE ) = 0.08 + 1.08tE . 1 0.396 – If tE < 0.08/1.08 = 0.074, then t < 0 and equity had an advantage over debt. – In 2013 top capital gains rate went up to pre-1986 level (20%)- 100% debt …nancing is optimal. But we don’tsee this in reality. What have we not taken into account?

Dmitry Livdan (Haas) UGBA 103 Fall2017 39/124 E¤ective vs. Statutory Tax Rates

So far we assumed that the …rm was always able to take advantage of the tax shield. But tax losses can only be carried forward for a limited time. If a …rm shows losses for several years, it loses the interest tax shield forever. In this case, the e¤ective (a.k.a. expected / marginal) tax shield is less than the statutory rate t. The more the …rm borrows, the higher the probability of loss and the lower the expected tax shield.

Dmitry Livdan (Haas) UGBA 103 Fall2017 40/124 The E¤ect of Bankruptcy Costs

Besides reducing the chance of the …rm being able to take advantage of the interest tax shield, leverage also increases the probability of bankruptcy. However, bankruptcy in and of itself need not be costly if the value of the …rm is e¢ ciently transferred to the bondholders. But this is generally not the case; there are numerous ine¢ ciencies/costs that can result from …nancial distress. – Direct costs. * Payments to third parties (lawyers, consultants). * “Wasted”time and e¤ort. * Selling assets at below-market values (i.e., …re sales). – Indirect costs. * Impaired ability to conduct business. * Foregone opportunities. * Suppliers may leave or demand cash payment. * Loss of customers (e.g., Chrysler, GM). * Loss of (key) employees.

Dmitry Livdan (Haas) UGBA 103 Fall2017 41/124 The E¤ect of Bankruptcy Costs (cont’d)

Of course, investors are aware that increased leverage increases the probability of bankruptcy and take the expected cost of default into account when evaluating the …rm. Thus

V = VU + PV(tax shield) PV(bankruptcy costs) The following …gure shows how the trade-o¤ between tax bene…ts and the cost of distress a¤ects the optimal capital structure

Dmitry Livdan (Haas) UGBA 103 Fall2017 42/124 Agency Costs

Agency costs play a role similar to bankruptcy costs in counterbalancing the tax advantage of increased leverage. Until now, we have assumed that bondholders had e¤ectively protected themselves, so that shareholders could only increase the value of their equity by increasing the value of the …rm. We have also implicitly assumed that shareholders will be able to retain the entire bene…t of any new positive NPV project they take on.

Dmitry Livdan (Haas) UGBA 103 Fall2017 43/124 Agency Costs (cont’d)

There are cases where these assumptions are not reasonable. – In some cases equity-holders may be able to reduce the …rm’sassets serving as collateral for the existing debt. For example, shareholders could pay themselves a nifty dividend or issue additional debt. – Another possibility is that the shareholders will be able to increase the risk of the …rm’sassets (by undertaking riskier investments), which makes them better o¤ at the expense of debt-holders (overinvestment). – Shareholders may also be tempted to reject positive NPV projects whose value will accrue to the debt-holders (underinvestment).

Dmitry Livdan (Haas) UGBA 103 Fall2017 44/124 Agency Costs (cont’d)

To protect themselves, debt contracts include covenants to limit investment. These may force the …rm to forgo good investments. The value of the …rm re‡ects these costs:

V = VU + PV(tax shield) PV(bank’ycosts) PV(agency costs)

The above are agency cost of debt. There are also agency costs of equity

Dmitry Livdan (Haas) UGBA 103 Fall2017 45/124 The Trade-O¤ Theory of Capital Structure

The joint e¤ect of taxes, bankruptcy costs and agency costs leads to a trade-o¤ theory of capital structure. The …rm’starget debt-equity ratio depends on a trade-o¤ between – Tax advantage of debt and agency costs of equity – Bankruptcy costs and agency costs of debt. The implications of the theory are as follows: – Pro…table …rms should borrow more than unpro…table …rms. – Firms holding tangible assets should borrow more than …rms holding specialized, intangible assets or valuable growth opportunities. – Safer …rms should borrow more than riskier …rms. Real-world evidence: – Firms holding valuable intangible assets tend to borrow less than …rms holding mostly tangible assets – Risky …rms (…rms with high asset betas) borrow less than safer …rms – But, more pro…table companies have less debt.

Dmitry Livdan (Haas) UGBA 103 Fall2017 46/124 The Pecking-Order Theory of Capital Structure

To explain the inverse relationship between pro…tability and debt ratios, an alternative (complementary) theory has been proposed. This theory is based on the e¤ect of issue costs and information asymmetry between investors and the managers of the …rm. The conclusions of the theory are as follows. – In an attempt to minimize issue costs, …rms prefer to …nance new investments with retained earnings. – If external …nancing is required, …rms prefer …nancing to equity …nancing. The reason is that with asymmetric information between managers and investors new equity issues are interpreted as bad news on the prospects of the …rm, and therefore a¤ect stock prices negatively.

Dmitry Livdan (Haas) UGBA 103 Fall2017 47/124 The Pecking-Order Theory of Capital Structure (cont’d)

The theory implies that there is no well-de…ned target debt equity mix, since there are two kinds of equity, internal and external, one at the top and one at the bottom of the pecking order. – Taken to its limit, this implies that …rms’observed capital structures should appear more or less random, since they will depend mostly on past realizations of cash ‡ows. The theory is consistent with the fact that roughly 90% of gross real investments in the U.S. are …nanced by retained earnings. Moreover, it can also explain why more pro…table …rms generally borrow less. However, it fails to explain the aforementioned evidence that is consistent with the trade-o¤ theory.

Dmitry Livdan (Haas) UGBA 103 Fall2017 48/124 Survey Evidence: Debt Policy Factors

Dmitry Livdan (Haas) UGBA 103 Fall2017 49/124 Challenging Practice Problem

Merck’s“simpli…ed”balance sheet is currently as follows:

Book Value Market Value Assets: NWC $1,473 $1,473 LTA $14,935 $51,212 Liabilities: LTD $5,269 $5,269 Equity $11,139 $47,416

Suppose that Merck decides to move to a 50% book debt-to-value ratio by issuing debt and using the proceeds to repurchase shares. The corporate tax rate is 40%; consider only corporate taxes. Now construct Merck’sbalance sheet (with market values only) to re‡ect the new capital structure, making sure to add an item called “PV(additional tax shields)”on the asset side of the balance sheet. Before it changes its capital structure, Merck has 1,248 million shares outstanding. What is the stock price before and after the change? Dmitry Livdan (Haas) UGBA 103 Fall2017 50/124 Key Takeaways: Debt Policy

MM1: rA and …rm value are independent of leverage. VL = VU D MM2: rE = rA + (rA rD ) E With corporate taxes: D – rE = rA + E (1 tc )(rA rD ) D E – rA = V rD + V rE remains independent of leverage D E D – WACC = (1 tc ) r + r = WACC 1 tc . Discount rate L V D V E U V is no longer a constant rA but depends on leverage  – VL = VU + tc DL. Firm value rises with leverage With corporate and personal taxes: D E – WACCL = (1 tc ) V rD + V rE because rD , rE are before personal taxes (1 tE )(1 tc ) – VL = VU + tDL where t = 1 1 t D Other determinants of leverage: e¤ective vs. statutory tax rate, bankruptcy costs, agency costs, information asymmetry

Dmitry Livdan (Haas) UGBA 103 Fall2017 51/124 Checkpoint: Debt Policy

Material relevant to this section: Berk and DeMarzo: Chapter 14. – Practice problems: 1-4, 6, 8, 13, 15-17 Berk and DeMarzo: Chapter 15. – Practice problems: 1, 3, 6, 8, 14, 18, 19 What is next? Berk and DeMarzo: Chapter 18.

Dmitry Livdan (Haas) UGBA 103 Fall2017 52/124 II. Interaction of Investment and Financing Decisions

Dmitry Livdan (Haas) UGBA 103 Fall2017 53/124 III. Interaction of Investment and Financing Decisions

Readings: Berk and DeMarzo: Chapter 18.

Dmitry Livdan (Haas) UGBA 103 Fall2017 54/124 Big Picture: Why Do We Care?

I discussed investment decisions taking …nancial decisions as given II considered …nancing decisions taking investment decisions as given. – In an MM world, this would be the whole story: capital structure does not a¤ect the value of the …rm, so investment decisions are independent of …nancing decisions III reconsiders capital budgeting when …nancing decisions are not irrelevant and can a¤ect the value of the …rm. – Project NPV must include the value contributed by …nancing decisions. There are two ways to do this: – Calculate an adjusted NPV (APV): the sum of the NPV of the project (i.e. the NPV for an all-equity …rm) and the NPV of the …nancing decisions caused by the project’sacceptance. – Or, discount the project’scash ‡ows using an adjusted cost of capital that takes into account its …nancing as well as risk.

Dmitry Livdan (Haas) UGBA 103 Fall2017 55/124 The Adjusted Present Value Rule

Recall that we can write the value of a levered …rm as the value of an otherwise identical all-equity …rm and the value of its …nancing decisions: V = VU + NPV (…nancing decisions). It is then obvious to de…ne the APV of a project as the sum of its NPV to an all-equity …rm and the PV of the associated …nancing decisions:

APV = ∆V = ∆VU + ∆NPV (…nancing decisions) = NPV (unlevered project) + NPV (change in …nancing decisions)

Separating the APV of a project into its NPV to an all-equity …rm and the value of the associated …nancing decisions should be generally useful for the …nancial manager.

Dmitry Livdan (Haas) UGBA 103 Fall2017 56/124 A Comparison of WACC and APV

Features/advantages of WACC. – WACC accounts for tax shield bene…t of interest in discount rate. – WACC is widely adopted by practitioners and is easy to use. – WACC is applicable when D/E remains essentially constant through project life. – WACC is most appropriate when the project is “typical” of the …rm’s traditional businesses (i.e., same risk), or “scale enhancing”. Features/advantages of APV. – APV accounts for tax shield bene…t of interest in cash ‡ows (not discount rate). – APV was introduced by academics and is slowly being adopted in practice. * 11% of …rms always or almost always use it. – APV often requires/accommodates knowledge of a particular debt repayment schedule. – APV (as opposed to WACC) is suited for situations where the debt to equity ratio is changing signi…cantly over time (capital intensive projects and LBOs). Dmitry– LivdanAPV (Haas) can handle “side e¤ects”:UGBA 103 tax shield, issue costs, bankruptcyFall2017 57/124 costs, etc. The Adjusted Present Value Rule: An Example

Boeing is considering building a new plane: – The plane costs $10m to manufacture, payable immediately – It o¤ers an after-tax cash ‡ow of $1.8m per year for 10 years – The …rm will use $3m of debt to …nance the project. It will …x the debt at $3m for the lifetime of the project. After 10 years, the debt is fully repaid. The cost of debt is 8% and issue costs are 1.5% of the debt value – The opportunity cost of capital (determined by the business risk of Boeing’sassets) is 12% – There are no personal taxes; the corporate tax rate is 20% We solve this in two steps – First, calculate the NPV under all-equity …nancing – Second, calculate the NPV of the change in capital structure

Dmitry Livdan (Haas) UGBA 103 Fall2017 58/124 The Adjusted Present Value Rule: An Example (cont’d)

First step: NPV under all-equity. rA = 12%, so

10 1,800,000 NPV = 10,000,000 + ∑ t = 170,401. t=1 (1.12) Second step: NPV of …nancing side-e¤ects. Two components: – Issue costs are 1.5% $3, 000, 000 = $45, 000 – Annual tax shield is 

tc r 3,000,000 = (0.20)(0.08)(3,000,000) = 48,000.  D  Overall NPV of the change in capital structure is 48,000 1 NPV (…nancing) = 45,000(1 0.20) + 1 0.08 (1.08)10   = 286,084.

Therefore, the APV is $170,401 + $286,084 = $456,485.

Dmitry Livdan (Haas) UGBA 103 Fall2017 59/124 The Adjusted Present Value Rule: An Example (cont’d)

Why don’tinterest payments on the debt (8% $3m) appear as cash ‡ows?  – Because capital markets are e¢ cient (the debtholders get what they pay for), the NPV of this transaction is zero: 3M NPV (loan) = 3M 0.08 3M a10 0.08 10 = 0   j 1.08 What would change if the government subsidized this loan? For example, suppose that it o¤ered the $3m at 6%. – The yearly tax shields are smaller than before, (0.20)(0.06)(3,000,000) = 36,000 < 48,000, and NPV (tax shield) = 36, 000a10 0.08 = 241, 563. j – However, the loan itself now has a positive NPV: 3M NPV (loan) = 3M 0.06 3M a10 0.08 10 = 402, 605.   j 1.08

Dmitry Livdan (Haas) UGBA 103 Fall2017 60/124 Adjusted Present Value: Example (cont’d)

The APV can accommodate debt repayment schedules. – Useful when the …rm’sdebt-to-value ratio will change in predictable ways. – Example: LBOs. In our example, suppose instead that the …rm intends to raise $5 million in debt …nancing for the project. – The principal will be repaid in equal installments over the next 10 years. – The interest rate is 8%. – Assume that the issue costs are zero.

Dmitry Livdan (Haas) UGBA 103 Fall2017 61/124 Adjusted Present Value: Example (cont’d)

The debt repayment schedule (in 000’s)is as follows: End of Year 0 1 2 ... 9 10 Debt outstanding 5,000 4,500 4,000 ... 500 0 Interest payment 400 360 ... 80 40 Principal payment 500 500 ... 500 500 Total payment on the debt 900 860 ... 580 540 Interest tax shield 80 72 ... 16 8

We can now discount the tax shields to …nd 80,000 72,000 16,000 8,000 NPV (…nancing) = + + + + 1.08 (1.08)2    (1.08)9 (1.08)10 = 328,992, for an adjusted present value of APV = 170,401 + 328,992 = 499,393.

Dmitry Livdan (Haas) UGBA 103 Fall2017 62/124 The Adjusted Cost of Capital Rule

While the APV approach is very ‡exible and takes into account di¤erent side e¤ects of accepting a project (e.g. issue costs, taxes), many …rms use a simpler procedure that focuses on the tax impact alone. This procedure discounts the project cash ‡ows at an adjusted cost of capital which re‡ects both the project’srisk and …nancing tax e¤ects. Unfortunately, there is no simple, universally correct method of calculating the adjusted cost of capital, but only some approximate shorthand formulas. We will look at two of these formulas: – the weighted-average cost of capital formula (“debt rebalanced”); – Modigliani and Miller’sformula (“debt …xed”).

Dmitry Livdan (Haas) UGBA 103 Fall2017 63/124 The Adjusted Cost of Capital Formulas

The WACC formula assumes the project maintains a constant D/V over time:

D E WACC = (1 tc )rD + rE V V     The MM formula assumes that the project supports a permanent additional debt ∆D issued at rD . ∆D ∆D rMM = rA(1 tc L) where L = = APV + CF0 PV (project) represents the project’scontribution to the …rm’sdebt capacity as a proportion of the project’smarket value. This is MM’sformula. D Analogous to WACC = WACCU 1 tc for entire …rm V  Dmitry Livdan (Haas) UGBA 103 Fall2017 64/124 The Adjusted Cost of Capital Formulas (cont’d)

Strictly speaking, MM’sformula only applies when – the project provides a level, perpetual cash ‡ow; – the new debt is kept constant forever, whatever happens to the project. Myers (1974): if these don’thold, errors are only 2–6%. You may use

rMM for this course. Steps to use it: – Find rA using the CAPM and the project’sasset β. This would be the appropriate rate for an all-equity …rm. – To re‡ect tax shields, adjust the rate to rMM = rA(1 tc L). – Discount the cash ‡ows of the project at that rate to get APV.

Dmitry Livdan (Haas) UGBA 103 Fall2017 65/124 The Full Picture: An Example

Inditherm is a British producer of heat-conducting polymers. The …rm is currently all-equity. Although it is public, its stock is highly illiquid so it is di¢ cult to obtain a direct estimate of its own beta Cytec, an American specialty chemicals company, is considering acquiring Inditherm. In particular, Cytec is interested in knowing the maximum price that it should bid. Cytec is publicly traded. It is currently …nanced with 800,000 shares, each worth $65 (i.e., $52m of equity), and $15m worth of debt. It has

βE = 1.8 and βD = 0.2. The expected risk premium of the market is currently 8%, and the yield on a 10-year treasury bond is 5%. The corporate tax rate is 34%. We will consider three scenarios: – Debt rebalanced, target has same risk as acquirer – Debt amortized, target has same risk as acquirer, APV method – Debt rebalanced, target has di¤erent risk from acquirer

Dmitry Livdan (Haas) UGBA 103 Fall2017 66/124 The Full Picture: An Example (cont’d)

Cytec’schief …nancial o¢ cer estimates that the expected after-tax cash ‡ows for Inditherm will be as follows.

End of Year 1 2 3 4 5 (1) OperatingIncome 2,620 3,436 3,671 3,976 4,336 (2) TaxonoperatingIncome 891 1,168 1,248 1,352 1,474 (3) After-taxoperatingincome 1,729 2,268 2,423 2,624 2,862 (4) +Depreciation 449 475 475 475 475 (5) -Capitalexpenditures 522 512 525 538 551 (6) -Changeinworkingcapital -203 -275 200 225 250 (7) + proceeds from asset sales 3,545 1,805 (8) After-taxcash‡ows 5,404 4,311 2,173 2,336 2,536

The CFO also estimates that these after-tax cash ‡ows will grow at an annual rate of 3% after year 5.

Dmitry Livdan (Haas) UGBA 103 Fall2017 67/124 The Full Picture: An Example (cont’d)

Assume that, after the acquisition, Cytec will maintain its current D/E ratio and that Inditherm’soperations are similar to Cytec. We can then use Cytec’sWACC to discount Inditherm’scash ‡ows. – First, we can calculate

r = r + (rm r )β = 0.05 + 0.08(0.2) = 6.6%; D f f D r = r + (rm r )β = 0.05 + 0.08(1.8) = 19.4%. E f f E – The weighted average cost of capital is then D E WACC = (1 tc )r + r D V E V     15 52 = (1 0.34)(0.066) + (0.194) = 16.0%. 15 + 52 15 + 52

5,404 4,311 2,173 2,336 2,536 1 APV = + + + + 1.160 (1.160)2 (1.160)3 (1.160)4 0.160 0.03 (1.160)4 = 21,275.

Dmitry Livdan (Haas) UGBA 103 Fall2017 68/124 The Full Picture: An Example (cont’d)

To get a clearer picture of Inditherm’svalue, Cytec’sCFO decides to calculate the adjusted PV in two parts: the value of Inditherm’s unlevered assets plus the value of the tax shields of the new debt. She also decides to be more precise about the exact nature of the extra debt capacity resulting from the acquisition. – To …nance the acquisition, Cytec will be able to borrow £ 8m at 6.6% for the acquisition of Inditherm. The rest will be …nanced in cash using last year’searnings. – The debt contract is a …ve-year contract, during which Cytec is expected to repay the bank in …ve equal end-of-year installments of 8,000 8,000 x = = = 1, 930. a5 6.6% 1 1 1 j 0.066 (1.066)5 h i – Under this scenario, the CFO conservatively assumes that Cytec will not be able to take on more debt.

Dmitry Livdan (Haas) UGBA 103 Fall2017 69/124 The Full Picture: An Example (cont’d)

First, the value of Inditherm’sassets is obtained by discounting the after-tax cash ‡ows at the appropriate rate for the risk. Since Inditherm is not publicly traded, the CFO decides to use the expected rate of return for Cytec’sassets (i.e., the rate at which we would discount the …rm’sassets if it were all-equity …nanced). We know that

WACCL 0.160 rA = WACCU = D = 15 = 17.4%, 1 tc 1 0.34 V 15+52 so that 5,404 4,311 2,173 2,336 2,536 1 NPV = + + + + 1.174 (1.174)2 (1.174)3 (1.174)4 0.174 0.03 (1.174)4 = 19, 620.

Dmitry Livdan (Haas) UGBA 103 Fall2017 70/124 The Full Picture: An Example (cont’d)

To calculate the PV of tax shields, we must …gure out the interest payment each year. This is done in the following table:

End of Year 1 2 3 4 5 Debt Outstanding 6,598 5,103 3,509 1,811 0 Payments on the debt 1,930 1,930 1,930 1,930 1,930 Interest paid @ 6.6% 528 435 337 232 120 Principal paid 1,402 1,495 1,593 1,699 1,811 Interest tax shield 180 148 115 79 41

The PV of the tax shield is therefore 180 148 115 79 41 PV (tax shields) = 1.066 + (1.066)2 + (1.066)3 + (1.066)4 + (1.066)5 = 484, so that APV = NPV + PV (tax shields) = 19,620 + 484 = 20, 104.

Dmitry Livdan (Haas) UGBA 103 Fall2017 71/124 The Full Picture: An Example (cont’d)

Upon further consideration, the CFO decides that Inditherm’s operations are actually somewhat di¤erent from those of Cytec. – First, Inditherm is mainly a¤ected by the UK economy, whereas Cytec is mainly a¤ected by the US economy – Furthermore, Inditherm focuses on plastics, whereas Cytec produces general chemicals Instead, Inditherm’soperations are deemed more comparable to another British plastics …rm, Victrex, which is publicly traded and liquid. – Victrex is currently …nanced with £ 18m of equity and £ 5m (…xed) of debt. – The beta of Victrex’sequity is 2.1, and that of its debt is 0.3. Assume Cytec will …nance the acquisition using debt equal to 30% of the present value of Inditherm

Dmitry Livdan (Haas) UGBA 103 Fall2017 72/124 The Full Picture: An Example (cont’d)

For Victrex, we can calculate

rD = rf + (rm rf )β = 0.05 + 0.08(0.3) = 7.4%; D rE = rf + (rm rf )β = 0.05 + 0.08(2.1) = 21.8%. E Victrex’sweighted average cost of capital is then given by

D E WACCL = (1 tc )rD + rE V V     5 18 = (1 0.34)(0.074) + (0.218) = 18.1%, 5 + 18 5 + 18 so that the expected return on its unlevered assets is

WACCL 0.181 rA = WACCU = D = 5 = 19.5%. 1 tc 1 0.34 V 5+18

Dmitry Livdan (Haas) UGBA 103 Fall2017 73/124 The Full Picture: An Example (cont’d)

Since Victrex and Inditherm have the same business risk, Inditherm’s rA is also 19.5%

We now relever Inditherm’s rA of 19.5% to take into account the 30% debt …nancing. Using MM’sformula, the CFO …nds an adjusted cost of capital of

r  = rA(1 tc L) = 0.195(1 0.34 0.3) = 17.5%. MM  The value of Inditherm’sassets for Cytec is then 5,404 4,311 2,173 2,336 2,536 1 APV = + + + + 1.175 (1.175)2 (1.175)3 (1.175)4 0.175 0.03 (1.175)4 = 19,462.

Dmitry Livdan (Haas) UGBA 103 Fall2017 74/124 WACC: Assumptions and Shortcomings

We have argued that, in calculating the value of a project, we can account for the interest tax shields that the project can support by either – adjusting the discount rate (from rA to WACC) applied to the unlevered free cash ‡ows, or – in the APV approach, by explicitly/separately calculating the tax shields, discounting them at the appropriate rate (typically rD ), and adding the result to the unlevered value of the project. The WACC approach is more of “denominator” adjustment, whereas the APV is more of a “numerator” adjustment. When using WACC to calculate the present value of a project, it is implicitly assumed that the …rm borrows a constant fraction of the project’svalue at all times. Indeed, because a project’svalue is likely to ‡uctuate through time, the debt that it can “a¤ord” will also ‡uctuate. – Project value goes up: issue more debt. – Project value goes down: buy back (retire) debt. Dmitry Livdan (Haas) UGBA 103 Fall2017 75/124 WACC: Assumptions and Shortcomings (cont’d)

The problem is that our levering/unlevering formulas, D rE = rA + (1 tc )(rA rD ) E   D D E and WACC = 1 tc rA = (1 tc )rD + rE , V V V       assume that the changes in debt levels have the same risk as the debt itself. Because the changes in debt levels will be related to the performance of the project, part of the tax shields share the risk of the project’s assets. As a result, it turns out that WACC is precisely correct only when – the project provides a level, perpetual annual cash ‡ow, so that – the project’sexpected value and outstanding debt are constant through time. Myers (1974): using WACC to calculate the value of projects with limited lives or irregular CFs typically results in errors of only 2–6%. Dmitry Livdan (Haas) UGBA 103 Fall2017 76/124 Risk Adjusted Discount Rate (RADR)

How should we lever up rA to correctly account for changing debt levels and associated interest tax shields? Miles and Ezzell (1980) have worked out the formula for the correct a risk adjusted discount rate (RADR):

1 + rA rRADR = rA tc rD L , 1 + rD   where L is the target debt-to-value (D/V ) ratio for the project. As opposed to the WACC approach to levering, RADR is valid for arbitrary cash ‡ow patterns and project lives.

Dmitry Livdan (Haas) UGBA 103 Fall2017 77/124 Target Ratios: Empirical Evidence

In a survey of 392 CFOs, Graham and Harvey (2001) …nd the following

Dmitry Livdan (Haas) UGBA 103 Fall2017 78/124 Discounting Methods: Example

Consider a one-year project that has the following characteristics. – The expected pre-tax cash ‡ow from the project is 23,980. – The corporate tax rate is 40%. – The cost of capital for the (unlevered) project is 21%. – The project will expand the …rm’sborrowing power by 25% of its value. – The …rm can borrow at a rate of 10%. – The project does not necessitate any investment in working capital and no asset will be depreciated. First, let us use APV to …nd the project’svalue V . – The …rm will be able to borrow D = 0.25V . – The value of the project is therefore

C1 tc r D 23,980(1 0.40) (0.40)(0.10)0.25V V = + D = + . 1 + rA 1 + rD 1.21 1.10 – Solving for V , we …nd V = 12,000.

Dmitry Livdan (Haas) UGBA 103 Fall2017 79/124 Discounting Methods: Example (cont’d)

We can also use RADR to …nd this value. – The appropriate risk-adjusted discount rate is

1 + rA r  = r tc r L RADR A D 1 + r  D  1.21 = 0.21 (0.40)(0.10)(0.25) = 19.9%. 1.10   – Consistent with APV, we …nd a project value of

23,980(1 0.40) V = = 12,000. 1.199 Because the debt is 25% of the project’svalue, we have

D = 0.25 12,000 = 3,000, and  E = 12,000 3,000 = 9,000.

Dmitry Livdan (Haas) UGBA 103 Fall2017 80/124 Discounting Methods: Example (cont’d)

Suppose that we tried to use our usual WACC formula to value this project.

– First, we need to lever up rA to …nd rE : D r = r + (1 tc )(r r ) E A E A D   0.25 = 0.21 + (1 0.40)(0.21 0.10) = 23.2%. 0.75   – We can then compute the weighted average cost of capital: D E WACC = (1 tc )r + r V D V E     = (0.25)(1 0.40)(0.10) + (0.75)(0.232) = 18.9%. – The project’svalue is then calculated to be 23,980(1 0.40) V = = 12,101. 1.189

Dmitry Livdan (Haas) UGBA 103 Fall2017 81/124 Discounting Methods: Example (cont’d)

Because the levering formula assumes constant perpetual cash ‡ows, it gives us an incorrect rE and, as a result, an incorrect WACC and a slightly in‡ated project value. – The e¤ect on project value is small: about 0.84%. How can we reconcile WACC with the other two approaches? – Recall that the equity is worth 9,000 today. – The equity-holders can expect to receive the following amount at the end of the year:

E1 = [23,980 r D] (1 tc ) D D = [23,980 (0.10)(3,000)] (1 0.40) 3,000 = 11,208. – Thus their expected return is r = 11,208 1 = 24.533333%. E 9,000

Dmitry Livdan (Haas) UGBA 103 Fall2017 82/124 Discounting Methods: Example (cont’d)

The correct weighted average cost of capital is then

D E WACC = (1 tc )rD + rE V V     = (0.25)(1 0.40)(0.10) + (0.75)(0.24533333) = 19.9%. Clearly, the value of the project is again

23,980(1 0.40) V = = 12,000. 1.199

Dmitry Livdan (Haas) UGBA 103 Fall2017 83/124 Practice Problem Ch 18.

Dmitry Livdan (Haas) UGBA 103 Fall2017 84/124 Challenging Practice Problem

The Leoj Yllib (LY) Corporation is a …rm …nanced with a $200 million perpetual debt, and with 29 million shares each worth $10. The expected return on the debt is 5%. If the …rm were all-equity …nanced, the expected return of the …rm (i.e. of the assets, or of the equity) would be 10%. The corporate tax rate is 42%. Assume that LY only has one current project which generates perpetual annual earnings before taxes and interest (EBIT) of X. Ignore personal taxes. (a) What is X? (b) What is the weighted average cost of capital for LY Corp.? (c) What is the current expected return on the equity of the …rm?

Dmitry Livdan (Haas) UGBA 103 Fall2017 85/124 Challenging Practice Problem (Continued 1)

Now, suppose that LY is considering a second project. This project requires an initial investment of $105 million, and will generate an annual pre-tax cash ‡ow of $25 million in perpetuity. The risk of the project is the same as that of the …rm’s…rst project. (d) If this project were entirely …nanced with new equity, what would its be?

Dmitry Livdan (Haas) UGBA 103 Fall2017 86/124 Challenging Practice Problem (Continued 2)

Suppose instead that the project will be partly …nanced with new debt. More precisely, suppose that the …rm feels that it can issue additional perpetual debt (also at a rate of 5%) worth 50% of the new project’svalue (note: this is not 50% of the initial investment). Also, this new debt will be rebalanced every year in order to keep the debt to value ratio of the project constant. (e) What is the adjusted net present value of this project? (f) Calculate the adjusted rate of return for this project, and show how you could have obtained the same adjusted net present value of the project using this rate. (g) What is the new expected return on the overall equity of the …rm?

Dmitry Livdan (Haas) UGBA 103 Fall2017 87/124 Key Takeaways: Interaction of Investment and Financing Decisions

Two ways to consider e¤ect of …nancing on project value

1 APV: calculate project NPV under all-equity, and add …nancing side e¤ects – treats project and …nancing separately; – takes …nancing (debt tax shields, transaction costs, etc.) into account exactly; – always accurate, as it is more ‡exible. 2 Discount project cash ‡ows at an adjusted rate to re‡ect …nancing. D E 1 WACC = (1 tc ) r + r D V E V * Debt rebalanced * Project with exactly the same risk and …nancing as rest of …rm 2 r = r (1 tc L) (MM’sformula)  * Debt …xed * Only perfectly accurate for perpetual project with constant cash ‡ows.

1+rA 3 r  = rA tc rD L RADR by Miles and Ezzell (1980) RADR 1+rD Dmitry Livdan (Haas)  UGBA 103 Fall2017 88/124 Deriving RADR

To see how the RADR formula is derived, let us consider a project with the following characteristics. – The project is expected to generate an unlevered free cash ‡ow of Ct in year t. – With all-equity …nancing, these cash ‡ows should be discounted at rA. – The project supports a debt-to-value ratio L that will be kept …xed over the life of the project. That is, every year, the debt is rebalanced according to the project’scurrent value. – The corporate tax rate is tc (which is assumed to be the …rm’sMTR). Suppose that we are at the end of year t, and we seek to calculate the project’s(levered) value (Vt ) at that time. – We estimate that the project’sexpected value at the end of next year is V¯t+1. – The “project’sdebt” is rebalanced to Dt = LVt . The adjusted present value of the project at t is

Ct+1 + V¯t+1 tc rD Dt Ct+1 + V¯t+1 tc rD LVt Vt = + = + . (1) 1 + rA 1 + rD 1 + rA 1 + rD Dmitry Livdan (Haas) UGBA 103 Fall2017 89/124 Deriving RADR (cont’d)

We want to …nd a rate r  at which we can discount next year’s unlevered free cash ‡ow and expected project value to …nd the same current value as in (1):

Ct+1 + V¯t+1 Vt = . (2) 1 + r 

We can solve for Ct+1 + V¯t+1 in (1) and (2):

1 + rA (1) Ct+1 + V¯t+1 = Vt (1 + rA) tc rD LVt ; ) 1 + rD (2) Ct+1 + V¯t+1 = Vt (1 + r ). ) If we set these two expressions equal and solve for r , we …nd

1 + rA r  = rA tc rD L , 1 + rD   as originally derived by Miles and Ezzell (1980).

Dmitry Livdan (Haas) UGBA 103 Fall2017 90/124 Checkpoint: Interaction of Investment and Financing Decisions

Material relevant to this section: Berk and DeMarzo: chapter 18. – Practice problems: 4, 6-9. What is next? FINAL EXAM.

Dmitry Livdan (Haas) UGBA 103 Fall2017 91/124 Proof that Leverage Is Irrelevant in Perfect Capital Markets

MM proved Proposition I using a no-arbitrage argument. Consider two …rms that generate the same stream of operating income (X˜ t in year t) and di¤er only in their capital structure:

– Firm U is unlevered: VU = EU . – Firm L is levered: VL = EL + DL. Now compare the following two investment strategies:

1 buy a fraction a of the shares of …rm U; 2 buy a fraction a of both the debt and equity of …rm L.

The …rst strategy has a cost of aEU = aVU and yields a cash ‡ow of aX˜ t at time t, where X˜ t denotes the …rm’soperating income.

Dmitry Livdan (Haas) UGBA 103 Fall2017 92/124 Proof that Leverage Is Irrelevant in Perfect Capital Markets (cont’d)

For the second strategy, letting It be the promised payment to bondholders at time t, we have:

Investment Cost CF if solvent CF if default ˜ Debt aDL aIt aXt Equity aEL a(X˜ t It ) - ˜ ˜ Total a(EL + DL) = aVL aXt aXt

Since both strategies o¤er the same cash ‡ows, they must have the same cost (price) in a well-functioning market:

aVL = aVU VL = VU ) Conclusion: The value of the levered …rm must equal the value of the unlevered …rm. Things of equal value trade at equal prices.

Dmitry Livdan (Haas) UGBA 103 Fall2017 93/124 How Leverage A¤ects Expected Returns (cont’d)

The following table shows how Bonobos’searnings per share would be a¤ected by the increased leverage No Leverage 50% Leverage (1,000 shares) (500 shares) Outcome Bad Medium Good Bad Medium Good Probability 1/3 1/3 1/3 1/3 1/3 1/3 Operating Income 500 1,500 2,500 500 1,500 2,500 Interest 0 0 0 500 500 500 Earnings 500 1,500 2,500 0 1,000 2,000 EPS 0.50 1.50 2.50 0.00 2.00 4.00 Hence, leverage increases both the expected value and the risk of EPS. Is leverage bene…cial to shareholders? No: the increase in expected EPS is exactly o¤set by an increase in the expected return on equity (the E/P ratio) from 15% to 20%, so that the stock price is unchanged.

Dmitry Livdan (Haas) UGBA 103 Fall2017 94/124 How Leverage A¤ects Expected Returns (cont’d)

We can be more precise on how leverage a¤ects rE . Let rA denote the expected return on the …rm’sassets. By MM’s Proposition I, this is una¤ected by leverage. Since the …rm’sassets are a portfolio of its debt and equity, we must have:

D E D rA = rD + rE rE = rA + (rA rD ) V V () E       This is MM’sProposition II. An increase in the debt/equity ratio results in an increase in the expected return on equity. The WACC is una¤ected by changes in leverage. The increase in the expected return on equity when leverage increases re‡ects the impact of …nancial leverage on betas. In fact, we have

D β = β + (β β ) E A E A D  

Dmitry Livdan (Haas) UGBA 103 Fall2017 95/124 How Leverage A¤ects Expected Returns: Graphical Exposition

Dmitry Livdan (Haas) UGBA 103 Fall2017 96/124 Corporate Taxes: A Summary

Here is a simple list of all the rates used so far:

rA Expected after-taxes rate of return on assets (if assets were all-equity …nanced) rE Expected rate of return on the …rm’s equity rD Expected rate of return on the …rm’sdebt WACC Discount rate for after-tax cash ‡ows of assets (WACC = rA for an all equity …rm) A useful way to picture the levered …rm is as follows:

Value of unlevered …rm: VU Debt: D Tax Shield: tc D Equity: E With perfect capital markets, increasing D/E did not have an e¤ect on the left-hand-side of the above balance sheet. With corporate taxes, increasing D/E increases the left-hand side. Since the bondholders receive what they pay for (they receive a claim worth D in exchange for D in cash), the shareholders’wealth increases by the tax shield. Dmitry Livdan (Haas) UGBA 103 Fall2017 97/124 Leverage, Expected Returns, and Taxes: Graphical Exposition

Dmitry Livdan (Haas) UGBA 103 Fall2017 98/124 Firm Value in the Presence of Personal Taxes (Miller)

Consider again our two identical …rms (one unlevered, one levered).

Every year, assuming a debt level of D paying rD , the …rm’s shareholders expect to receive

(EBIT rD D)(1 tE )(1 tc ), The bondholders expect to receive

rD D(1 tD ) The total cash ‡ow reaching investors is therefore

(EBIT rD D)(1 tE )(1 tc ) + rD D(1 tD ) = EBIT(1 tE )(1 tc ) + rD D [(1 tD ) (1 tE )(1 tc )] (1 tE )(1 tc ) = EBIT(1 tE )(1 tc ) + rD D(1 tD )[1 ] 1 tD VU D t  | {z } | {z } Dmitry Livdan (Haas) UGBA 103 | {zFall2017 99/124} Real World: Personal Tax Rates

Does taking personal taxes into account explain why …rms do not adopt extreme leverage ratios? It is easy to do some back-of-the-envelope calculations. Before the 1986 Tax Reform Act, the corporate tax rate was 46%, while ordinary income was taxed at rates up to 50%. The top capital gains rate was 20%, even though the e¤ective rate was less than 20%, since capital gains can be deferred. The relative advantage of debt depended on the e¤ective tax rate on equity:

(1 tE )(1 tc ) 1 0.46 t = 1 = 1 (1 tE ) = 0.08 + 1.08tE . 1 tD 1 0.50

– If tE < 0.08/1.08 = 0.074, then t < 0 and equity had an advantage over debt. – If the tax rate on equity for the marginal investor was exactly 7.4%, then leverage was again a matter of indi¤erence, just as in the absence of taxes. This was the outcome predicted by Miller.

Dmitry Livdan (Haas) UGBA 103 Fall2017 100/124 Real World: Personal Tax Rates (cont’d)

The TRA of 1986 reduced the corporate rate to 34%, while the highest tax rate on ordinary income dropped to 28%. – Therefore, from 1986 to 1994, 1 0.34 t = 1 (1 t ) = 0.08 + 0.92t . 1 0.28 E E – Even if we assume that equity gains escape taxation entirely (tE = 0), there is still an obvious tax advantage to debt (at least for …rms with incomes high enough to take advantage of the tax shield).

In 1994, the rates changed to tc = 35% and tD = 39.6%, so that 1 0.35 t = 1 (1 tE ) = 0.08 + 1.08tE . 1 0.396 In 2003, the tax rates on both dividend income and capital gains have been both reduced to 15%, while the top regular income tax bracket is taxed at 35% tc = tD = 35% so t = tE . In 2013 top regular) income tax bracket goes back to 1994 level (39.6%) while top capital gains rate goes up to pre-1986 level (20%).

Dmitry Livdan (Haas) UGBA 103 Fall2017 101/124 WACC with Corporate and Personal Taxes

The expressions for the WACC now take the following forms:

DL DL EL WACCL = WACCU 1 t = (1 tc )rD + rE VL VL VL      

where rD and rE are before-personal-tax rates of return. Recall that t < tc as long as tE < tD , and that in the current tax regime t is likely to be positive.

The above formula implies that, if t > 0, an increase in leverage reduces the WACC and increases …rm value. It seems that 100% debt …nancing is optimal – But we don’tsee this in reality. What have we not taken into account?

Dmitry Livdan (Haas) UGBA 103 Fall2017 102/124 Corporate and Personal Taxes: A Summary

What do we discount at what rate to get what?

Example for a Discounted Cash ‡ows perpetual no-growth …rm at Result Pre-tax CF to shareholders (1-tc )(EBIT-rD DL) rE EL After-tax CF to shareholders (1-tE )(1-tc )(EBIT-rD DL) (1-tE )rE EL Pre-tax CF to bondholders rD DL rD DL After-tax CF of bondholders (1-tD )rD DL (1-tD )rD DL After-corp-tax CF of assets (1-tc )EBIT WACCL VL

Dmitry Livdan (Haas) UGBA 103 Fall2017 103/124 Bankruptcy Costs: An Example

Assume that, next year, Acme Chemical will have a cash ‡ow of $550 1 1 with probability 2 (the bad state) and $1,650 with probability 2 (the good state), after which it will cease to operate. For simplicity, the discount rate is 10% for all cash ‡ows (i.e., debt or equity). With no debt, the value of the …rm/equity is

0.5(550) + 0.5(1,650) V = = 1,000. 1.10

Dmitry Livdan (Haas) UGBA 103 Fall2017 104/124 Bankruptcy Costs: An Example (cont’d)

Now assume that the …rm issues a discount bond with a face value of $1,100 payable in one year, and uses the proceeds to repurchase equity. The debt introduces a probability of default/bankruptcy. However, let us …rst assume that bankruptcy is costless, that is, all assets are e¢ ciently transferred to the debt-holders following default. Because the …rm can only a¤ord $550 in the bad state and the bondholders get what they pay for, we have 0.5(550) + 0.5(1,100) D = = 750. 1.10 This means that the equity is worth 0.5(0) + 0.5(550) E = = 250. 1.10 and the …rm’svalue is still V = D + E = 750 + 250 = 1,000. Default/bankruptcy has no e¤ect on …rm value.

Dmitry Livdan (Haas) UGBA 103 Fall2017 105/124 Bankruptcy Costs: An Example (cont’d)

Now suppose that the bankruptcy process is costly. – Third party claims (lawyer fees) and indirect costs will total $110 if the …rm defaults. This means that the …rm e¤ectively only has $440 in the bad state. Because the bondholders get what they pay for and can anticipate the loss of $110 in the low state, we now have 0.5(440) + 0.5(1,100) D = = 700. 1.10 The equity is worth 0.5(0) + 0.5(550) E = = 250. 1.10 and the …rm’svalue is V = D + E = 700 + 250 = 950. Expected bankruptcy costs are $1,000 $950 = $50. Who bears this cost? How?

Dmitry Livdan (Haas) UGBA 103 Fall2017 106/124 Agency Costs: Overinvestment Example

Monte Carlo, Inc. currently has $300 in cash and projects that, in one year, will generate cash ‡ows of 1 – $550 with probability 2 (the bad state), and 1 – $2,970 with probability 2 (the good state). After that, the …rm will cease to operate. The discount rate for all cash ‡ows is 10%. Monte Carlo’scash is also invested at that rate of 10%. – It will accumulate to $300(1.10) = $330 at the end of the year. – So the …rm as a whole will have * $550 + $330 = $880 to distribute to investors in the bad state, and * $2,970 + $330 = $3,300 in the good state. Monte Carlo has $1,100 face value of discount bonds outstanding to be paid o¤ in one year.

Dmitry Livdan (Haas) UGBA 103 Fall2017 107/124 Agency Costs: Overinvestment Example (cont’d)

Next year, payo¤s for the debt-holders and equity-holders will therefore be as follows.

Bad Good Debt 880 1,100 Equity 0 2,200 Total 880 3,300

1 1 2 (880)+ 2 (1,100) The debt is worth D = 1.10 = 900. 1 (880)+ 1 (1,100) – The expected return on this debt is r = 2 2 1 = 10%. D 900 – The promised (or contractual) is i = 1,100 1 = 22%. D 900 The equity is worth 1 (0)+ 1 (2,200) E = 2 2 = 1,000. 1.10 The total value of the …rm is V = D + E = 900 + 1,000 = 1,900.

Dmitry Livdan (Haas) UGBA 103 Fall2017 108/124 Agency Costs: Overinvestment Example (cont’d)

Now assume that the …rm has the opportunity to take a new one-year project requiring an initial investment (at time 0) of $300 (i.e., all of Monte Carlo’scash). In one year, this project will generate a cash ‡ow of – $110 in the bad state, and – $440 in the good state. That is, if undertaken the …rm will be left with – $550 + $110 = $660 in the bad state, and – $2,970 + 440 = $3,410 in the good state. This is clearly a negative-NPV project:

1 (110) + 1 (440) NPV = 2 2 300 = 50. 1.10 Will the shareholders undertake this project?

Dmitry Livdan (Haas) UGBA 103 Fall2017 109/124 Agency Costs: Overinvestment Example (cont’d)

Consider the new payo¤ structure if the project is undertaken.

Bad Good Debt 660 1,100 Equity 0 2,310 Total 660 3,410

1 1 2 (0)+ 2 (2,310) The shareholders’equity is now worth E 0= 1.10 = 1,050. Since this is greater than E = 1,000, they will want to undertake the project. This is at the expense of the bondholders, whose debt is now worth 1 1 2 (660)+ 2 (1,100) D0= 1.10 = 800. Thus, the shareholders will overinvest to increase the riskiness of the …rm (and debt). – E¤ectively, the shareholders “stole” $50 from the bondholders, but also made the bondholders su¤er the $50 NPV. – The value of the …rm is now only V 0= D0+E 0= 800 + 1,050 = 1,850, i.e., it is reduced by the $50. Dmitry Livdan (Haas) UGBA 103 Fall2017 110/124 Agency Costs: Underinvestment Example

Let us return to the original setup. Let us now assume that Monte Carlo has the opportunity to invest in a new one-year project requiring an initial investment of $400. For the investment, – Monte Carlo will use all of its cash ($300), and – it will raise an additional $100 from the shareholders. This project is completely riskless. It will generate a cash ‡ow of $473 in either state. This is clearly a positive-NPV project: 1 (473) + 1 (473) NPV = 2 2 400 = 30. 1.10 Also, if the project is undertaken, the …rm will have – $550 + $473 = $1, 023 in the bad state, and – $2,970 + 473 = $3,443 in the good state. Will the shareholders want to undertake this project?

Dmitry Livdan (Haas) UGBA 103 Fall2017 111/124 Agency Costs: Underinvestment Example (cont’d)

With this new project, the payo¤ structure is as follows. Bad Good Debt 1,023 1,100 Equity 0 2,343 Total 1,023 3,443

1 1 2 (0)+ 2 (2,343) The shareholders’equity is now worth E 00 = 1.10 = 1,065. – Although, this is greater than E = 1,000, the increase of $65 in their equity is not worth the initial $100 that the shareholders must contribute for the project to be undertaken (i.e., they would lose $35). – Thus they will want to reject the project (despite its positive NPV). Other other hand, the value of the debt would increase from D = 900 to 1 1 2 (1,023)+ 2 (1,100) D00 = 1.10 = 965. – The bondholders would capture the positive NPV of $30 and also take $35 in value from the shareholders. So having risky debt can cause the …rm to avoid some positive-NPV projects Dmitrywhen Livdan these (Haas) projects would makeUGBA the 103…rm’sdebt less risky. Fall2017 112/124 The E¤ect of Agency Costs

These costs reduce the value of debt both directly and indirectly because of costly measures taken to avoid these costs. – To protect themselves, debt contracts include covenants limiting the ‡exibility of the …rm to pay dividends, to issue new debt, to undertake risky investments, etc. – These covenants are costly both to negotiate and to enforce, and they might force the …rm to forego good investment opportunities. Note that agency costs are also more likely to be prevalent when …rms are close to …nancial distress, so these costs complement the more traditionally de…ned bankruptcy costs.

Dmitry Livdan (Haas) UGBA 103 Fall2017 113/124 The Trade-O¤ Theory of Capital Structure (cont’d)

As the following …gure (taken from Berk and DeMarzo) shows, …rms in safer industries with tangible assets tend to borrow more.

Dmitry Livdan (Haas) UGBA 103 Fall2017 114/124 The Pecking-Order Theory: Example

Suppose that an all-equity …rm has $5 in cash (and no other asset) and will operate for one year. Clearly, the equity is currently worth $5. Assume that the discount rate for all cash ‡ows is zero, and that there are no corporate taxes. A new one-year project requiring an initial investment of $10 will generate cash ‡ows of $5 (bad state) or $25 (good state) with equal probabilities next year. – The net present value of the project is 1 1 NPV = 10 + (5) + (25) = 5 > 0. 2 2 – To …nance the project, however, the …rm must raise $5 by issuing claims against its end-of-year cash ‡ows.

Dmitry Livdan (Haas) UGBA 103 Fall2017 115/124 The Pecking-Order Theory: Example (cont’d)

Suppose that the …rm chooses to issue some debt to …nance the $5. – After raising the $5 and investing the company’sexisting cash in the project, the …rm will be worth either $5 or $25 with equal probabilities at the end of the year. – Because the project always generates at least $5, the …rm can promise the debtholders $5 in both states of the world. Indeed, these investors are willing to pay $5 for a claim worth 1 1 PV = (5) + (5) = 5. 2 2 The existing shareholders’equity is then worth 1 1 E = (5 5) + (25 5) = 10. 2 2 Their wealth has gone up by $5, the NPV of the project.

Dmitry Livdan (Haas) UGBA 103 Fall2017 116/124 The Pecking-Order Theory: Example (cont’d)

Suppose now that the …rm chooses to issue more equity to …nance the $5. – As before, after raising the $5 and investing the company’sexisting cash in the project, the …rm will be worth either $5 or $25 with equal probabilities at the end of the year. – Because the …rm’svalue (which is its expected end-of-year cash ‡ow) is 1 1 V = (5) + (25) = 15, 2 2 the …rm must promise one third of the equity to new shareholders for it to raise the required $5. The existing shareholders’equity is then worth 2 1 1 E = (5) + (25) = 10. 3 2 2   Again, their wealth has gone up by $5, the NPV of the project.

Dmitry Livdan (Haas) UGBA 103 Fall2017 117/124 The Pecking-Order Theory: Example (cont’d)

Now suppose that the …rm’sCEO has some positive information about the project and that this information is not publicly available. 3 – The CEO knows that the true probability of the good state is 4 , and so he knows that the project’snet present value is really 1 3 NPV = 10 + (5) + (25) = 10. 4 4 1 – The public still thinks that the probability of the good state is 2 and that the project’sNPV is 5. If the project is …nanced by issuing $5 worth of debt, the CEO knows that the equity will be worth 1 3 E = (5 5) + (25 5) = 15, 4 4 that is, the shareholders’sequity goes up by 10, the (privately-known) NPV of the project.

Dmitry Livdan (Haas) UGBA 103 Fall2017 118/124 The Pecking-Order Theory: Example (cont’d)

Because the public does not know that the probability of the good 3 1 state is 4 , it is still the case that the …rm must promise 3 of its equity to new shareholders in order to raise $5. – Indeed, from the perspective of these new shareholders, this new equity 1 1 1 is worth their investment of $5 as 3 2 (5) + 2 (25) = 5. However, the CEO knows that the existingh equity willi then be worth only 2 1 3 E = (5) + (25) = 13.33. 3 4 4   – That is, the shareholders’sequity goes up by only 8.33, not by the (privately-known) project’sNPV of 10. – This is because the new equity issue raises $5, but is really worth

1 1 3 E = (5) + (25) = 6.67. 0 3 4 4  

Dmitry Livdan (Haas) UGBA 103 Fall2017 119/124 The Pecking-Order Theory: Example (cont’d)

As shown by the previous example, the use of debt …nancing allows the CEO to create more shareholder wealth when his private information about future outcomes is positive. Similarly, it is easy to verify that issuing equity becomes optimal when the CEO’sprivate information about future outcomes is negative. – Of course, knowing this, investors will react negatively to equity issues. – For example, for a given amount that the …rm seeks to raise, the new investors will require a larger portion of the …rm’sequity. – To avoid this possibility, CEOs with negative information will pool with those who have positive information by issuing debt (if they can), as this will be cheaper on average. This is how debt becomes the preferred form of …nancing when managers know more about their …rm than investors do. Of course, all these asymmetric information issues are avoided (along with all issuance costs) when the …rm can …nance internally.

Dmitry Livdan (Haas) UGBA 103 Fall2017 120/124 The Pecking-Order Theory of Capital Structure - Summary

This theory is based on information asymmetry between managers and investors: – In an attempt to minimize issue costs, …rms prefer to …nance new investments with retained earnings. – If external …nancing is required, …rms prefer bond …nancing to equity …nancing. When managers issue stock, investors infer that they have private information that the stock is overvalued and so the stock price falls. (This is comparable to the sale of a second-hand car, or anything where there is asymmetric information). The theory implies that there is no well-de…ned target debt equity mix, since there are two kinds of equity, internal and external, one at the top and one at the bottom of the pecking order. Real-world evidence: – 90% of investment in the U.S. is …nanced by retained earnings – More pro…table …rms generally borrow less.

Dmitry Livdan (Haas) UGBA 103 Fall2017 121/124 Summary of Key Takeaways

Dmitry Livdan (Haas) UGBA 103 Fall2017 122/124 Key Takeaways: Debt Policy

MM1: rA and …rm value are independent of leverage. VL = VU D MM2: rE = rA + (rA rD ) E With corporate taxes: D – rE = rA + E (1 tc )(rA rD ) D E – rA = V rD + V rE remains independent of leverage D E D – WACC = (1 tc ) r + r = WACC 1 tc . Discount rate V D V E U V is no longer a constant rA but depends on leverage  – VL = VU + tc DL. Firm value rises with leverage With corporate and personal taxes: D E – WACC = (1 tc ) r + r because r , r are before personal taxes V D V E D E (1 tE )(1 tc ) – VL = VU + tDL where t = 1 1 t D Other determinants of leverage: e¤ective vs. statutory tax rate, bankruptcy costs, agency costs, information asymmetry

Dmitry Livdan (Haas) UGBA 103 Fall2017 123/124 Key Takeaways: Interaction of Investment and Financing Decisions

Two ways to consider e¤ect of …nancing on project value

1 APV: calculate project NPV under all-equity, and add …nancing side e¤ects – treats project and …nancing separately; – takes …nancing (debt tax shields, transaction costs, etc.) into account exactly; – always accurate, as it is more ‡exible. 2 Discount project cash ‡ows at an adjusted rate to re‡ect …nancing. D E 1 WACC = (1 tc ) r + r D V E V * Debt rebalanced * Project with exactly the same risk and …nancing as rest of …rm

2 r = r (1 tc L) (MM’sformula)  * Debt …xed * Only perfectly accurate for perpetual project with constant cash ‡ows.

Dmitry Livdan (Haas) UGBA 103 Fall2017 124/124