2 Financing a Firm with Equity You are examining an investment project.For a current investment of $400, the project will generate cash flow of either $800 or $300 next year, depending on whether the economy is strong or weak, respectively. Both scenarios are equally likely.Project Cash FlowsTime 0Time 1BoomBust$400$800$300
3 Financing a Firm with Equity The project cash flows depend on the overall economy and thus contain market risk. Therefore, you demand a risk premium over the current risk-free interest rate of 4% to invest in this project.The cost of capital for this project is 10%. The expected cash flow in one year is:½($800) + ½($300) = $550.The NPV of the project is:
4 Financing a Firm with Equity Suppose you currently have no cash. Does this mean you should pass up the investment?No, of course not. You simply raise capital.If you finance this project using only equity, how much should investors be willing to pay for 100% of the equity?If you raise $500 by selling equity in the firm, after paying the investment cost of $400, you can keep the remaining $100, the NPV of the project, as a profit. Alternatively you can sell less than 100% of the equity.
5 Financing a Firm with Equity Unlevered Equity: Equity in a firm with no debtAre those who purchase the equity getting a fair deal?Because there is no debt, the cash flows of the unlevered equity are equal to those of the project.The expected return of 10% is appropriate for the risk shareholders are taking.Payoffs and Returns for the Unlevered EquityTime 0Time 1 PayoffsTime 1 ReturnsInitial ValueStrong EconomyWeak EconomyUnlevered Equity$500$800$30060%-40%
6 Financing a Firm with Debt and Equity Suppose instead, you decide to borrow $100 initially, in addition to selling equity.Because the project’s cash flow will always be enough to repay the debt, the debt is risk free and you can borrow at the risk-free interest rate of 4%. You will owe the debt holders:$100 × 1.04 = $104 in one year.Levered EquityEquity in a firm that also has debt outstanding
7 Financing a Firm with Debt and Equity Given the firm’s $104 debt obligation, your shareholders will receive only $696 ($800 – $104 = $696) if the economy is strong and $196 ($300 – $104 = $196) if the economy is weak.Value and Payoff for Debt and Levered EquityTime 0Time 1 PayoffsInitial ValueStrong EconomyWeak EconomyDebt$100$104Levered Equity---$696$196Firm$500$800$300
8 Financing a Firm with Debt and Equity What price E should the levered equity sell for?Which is the best capital structure choice (levered or unlevered) for the entrepreneur?Modigliani and Miller argued that with perfect capital markets, the total value of a firm should not depend on its capital structure.They reasoned that the firm’s total cash flows still equal the cash flows of the project, and therefore have the same present value.Because the cash flows of the debt and equity sum to the cash flows of the project, by the Law of One Price the combined values of debt and equity must be $500.Therefore, if the initial value of the debt is $100, the value of the levered equity must be $400.
9 Financing a Firm with Debt and Equity Because the cash flows of levered equity are smaller than those of unlevered equity, levered equity will sell for a lower price ($400 versus $500).However, the entrepreneur is not worse off. He/She/You will still raise a total of $500 by issuing both debt and levered equity. Consequently, you would be indifferent between these two choices for the firm’s capital structure.
10 The Effect of Leverage on Risk and Return Leverage increases the risk of the equity of a firm.Therefore, it is inappropriate to discount the cash flows of levered equity at the same discount rate of 10% that you used for unlevered equity. Investors in levered equity will require a higher expected return to compensate for the increased risk.Levered and Unlevered Equity ReturnsTime 0Time 1 PayoffsTime 1 ReturnsInitial ValueStrong EconomyWeak EconomyExpected ReturnDebt$100$1044%Levered Equity$400$696$19674%-51%11.5%Unlevered Equity$500$800$30060%-40%10%
11 The Effect of Leverage on Risk and Return The returns to equity holders are very different with and without leverage.Unlevered equity has a return of either 60% or –40%, for an expected return of 10%.Leverage increases the risk of the equity, levered equity has a return of either 74% or –51%.To compensate for the increased risk, levered equity holders receive a higher expected return: 11.5%.Note that the firm’s average cost of capital with leverage is , the same as the unlevered firm and the project.
12 Modigliani-Miller IIn a perfect capital market, the total value of a firm is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure.Investors and firms can trade the same set of securities at competitive market prices equal to the present value of their future cash flows.There are no taxes, transaction costs, or issuance costs associated with security trading.A firm’s financing decisions do not change the cash flows generated by its investments, nor do they reveal new information about them.
13 MM and the Law of One Price MM established their result with the following argument:In the absence of taxes or other transaction costs, the total cash flow paid out to all of a firm’s security holders is equal to the total cash flow generated by the firm’s assets.Therefore, by the Law of One Price, the firm’s securities and its assets must have the same total market value.
14 Modigliani-Miller II Leverage and the Equity Cost of Capital MM Proposition II:The cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value debt-equity ratio.Cost of Capital of Levered Equity (the relations above must hold for expected returns as well as actual returns)
15 Modigliani-Miller II: The Example Leverage and the Equity Cost of CapitalRecall from above:If the firm is all-equity financed, the expected return on unlevered equity is 10%.If the firm is financed with $100 of debt, the expected return of the debt is 4%.Therefore, according to MM Proposition II, the expected return on equity for the levered firm is:
16 Capital Budgeting and the Weighted Average Cost of Capital If a firm is unlevered, all of the free cash flows generated by its assets are paid out to its equity holders.The market value, risk, and cost of capital for the firm’s assets and its equity coincide and, therefore:
17 Capital Budgeting and the Weighted Average Cost of Capital If a firm is levered, project cost of capital, rA, is equal to the firm’s weighted average cost of capital.Weighted Average Cost of Capital (No Taxes)With perfect capital markets, a firm’s WACC is independent of its capital structure and equals its unlevered equity cost of capital, which matches the cost of capital of its assets.
19 Levered and Unlevered Betas The effect of leverage on the risk of a firm’s securities can also be expressed in terms of beta:Unlevered beta is a measure of the risk of a firm as if it did not have leverage, which is equivalent to the beta of the firm’s assets.If you are trying to estimate the unlevered beta for an investment project, you should base your estimate on the unlevered betas of firms with comparable investments.
20 Levered and Unlevered Betas We rearrange this to find:In the case of risk free debt this simplifies to:Both equations demonstrate that leverage serves to amplify the market risk of a firm’s assets, βU, raising the market risk of its equity, βE, above βU. This increase in risk is what causes the increase in the cost of equity capital that results from increased leverage.
21 The Interest Tax Shield and Firm Value MM Proposition I with TaxesThe total value of the levered firm exceeds the value of the firm without leverage due to the present value of the tax savings from debt.
22 The Interest Tax Shield with Permanent Debt Typically, the level of future interest payments is uncertain due to changes in the marginal tax rate, the amount of debt outstanding, the interest rate on that debt, and the risk of the firm.For simplicity, we will consider the special case in which the above variables are kept constant.
23 The Interest Tax Shield with Permanent Debt Suppose a firm borrows debt D and keeps the debt permanently. If the firm’s marginal tax rate is c , and if the debt is riskless with a risk-free interest rate rf , then the interest tax shield each year is c × rf × D, and the tax shield can be valued as a perpetuity.
24 The Weighted Average Cost of Capital with Taxes With tax-deductible interest, the effective after-tax borrowing rate is rD(1 − c) and the weighted average cost of capital becomes
26 The Cost of Equity Capital As the picture indicates the cost of equity capital has the same relationship to the unlevered cost of capital, rU, and the debt to equity ratio as in the case without corporate taxes.In chapter 18 the text demonstrates formally that this relation holds as long as the firm acts to maintain a fixed debt to equity ratio (a common but not universal policy).Clearly:
27 The Interest Tax Shield with a Target Debt-Equity Ratio When a firm adjusts its leverage to maintain a target debt- equity ratio, we can compute its value with leverage, VL, by discounting its free cash flow using the weighted average cost of capital.The value of the interest tax shield can be found by comparing the value of the levered firm, VL, to the value of the unlevered firm, VU, the present value of the free cash flow discounted at the firm’s unlevered cost of capital, the pretax WACC.
28 Bankruptcy and Capital Structure With perfect capital markets, Modigliani-Miller (MM) Proposition I applies: The total value to all investors does not depend on the firm’s capital structure.There is no disadvantage to debt financing, and a firm will have the same total value and will be able to raise the same amount initially from investors with either choice of capital structure.Bankruptcy shifts the ownership of the firm from equity holders to debt holders without changing the total value available to all investors.In reality, bankruptcy is rarely simple and straightforward. It is often a long and complicated process that imposes both direct and indirect costs on the firm and its investors.It is the costs of bankruptcy that imply a disadvantage to the use of debt financing in an imperfect capital market.
29 Direct Costs of Bankruptcy The bankruptcy process is complex, time-consuming, and costly.Costly outside experts are often hired by the firm to assist with the bankruptcy process.Creditors also incur costs during the bankruptcy process.They may wait several years to receive payment.They may hire their own experts for legal and professional advice.
30 Direct Costs of Bankruptcy The direct costs of bankruptcy reduce the value of the assets that the firm’s investors will ultimately receive.The average direct costs of bankruptcy are approximately 3% to 4% of the pre-bankruptcy market value of total assets.Workouts and pre-packaged bankruptcies may help reduce these small costs as well.
31 Indirect Costs of Financial Distress While the indirect costs are difficult to measure accurately, they are often much larger than the direct costs of bankruptcy.Loss of CustomersLoss of SuppliersLoss of EmployeesLoss of Management’s TimeLoss of ReceivablesFire Sale of AssetsDelayed LiquidationCosts to CreditorsThe indirect costs of financial distress have been estimated to be substantial: 10% to 20% of firm value
32 The Tradeoff TheoryThe firm picks its capital structure by trading off the benefits of the tax shield from debt against the costs of financial distress and agency costs.According to the tradeoff theory, the total value of a levered firm equals the value of the firm without leverage plus the present value of the tax savings from debt, less the present value of financial distress costs.
33 Optimal LeverageFor low levels of debt, the risk of default remains low and the main effect of an increase in leverage is an increase in the interest tax shield.As the level of debt increases, the probability of default increases.As the level of debt increases, the expected costs of financial distress increase, acting to reduce the value of the levered firm.The rate at which the costs and benefits change are different across firms and across industries.
34 Optimal LeverageThe tradeoff theory states that firms should set their leverage to the level at which firm value is maximized.At this point, the tax savings that result from increasing leverage are perfectly offset by the increased probability of incurring the costs of financial distress.The tradeoff theory helps explain why firms choose debt levels that are too low to fully exploit the interest tax shield (due to financial distress costs)And helps explain differences in the use of leverage across industries (due to differences in the magnitude of distress costs and the volatility of cash flows)
35 Debt-to- Value Ratio [D / (E + D)] for Select Industries
36 Historical View of Dividends Illustrated by the arguments of Gordon (1959) - more dividends = more valueFollows from the discounted dividend approach to valuing a firm:
37 Historical ViewGordon argued that retained earnings rather than current dividends made the cash flow stream for the shareholder riskier.This would increase the cost of capital.The future dividend stream would presumably be higher due to the investment of retained earnings (+NPV).He argued the first effect would be the dominant one.Now called the “bird in the hand fallacy.”
38 Along Came M&MBasic Point: Firm value is determined by its investment policy, net dividends are simply the residual of earnings after investment.Dividend IrrelevanceIn perfect capital markets, holding fixed the investment policy of a firm, the firm’s choice of dividend policy is irrelevant and does not affect the initial share price.
39 Dividend Irrelevance Example Consider the case of Ralph Inc.Currently (time 0) Ralph Inc. is expected to survive another year in business (till time 1). At which time the firm will liquidate and all value will be distributed to claimants.The firm is presently all equity financed with 50,000 shares outstanding. The cash flow of the firm is risk free and it is common knowledge that Ralph Inc. will receive $1 million immediately and another $1 million at time 1.The current dividend policy is for Ralph Inc. to payout its entire cash flow as dividends as it is received. So $20 per share now and at time 1.The risk free rate in the economy is 5%. And the firm has no positive NPV projects available.
40 Dividend Irrelevance Example Ralph, the CEO of Ralph Inc. is convinced that an alternative dividend policy would increase the current stock price.The current value of the firm and the price per share is:V0 = Div0 + Div1/(1.05) = $1m + $1m/(1.05) = $1,952, or P0 = $39.05 per share.The share price will drop to $19.05 after the time 0 dividend is paid.Ralph wants you to evaluate the impact on the current stock price of an increase or a decrease of the current dividend of $2 per share.
41 Dividend Irrelevance Example $2 per share dividend increase:A $2 per share dividend requires $1,100,000 in total so the firm must raise $100,000 to accomplish this policy change.The firm can issue risk free bonds to raise $100,000 today they must promise to repay $105,000 (5% risk free rate) in one year.This will leave only $895,000 in total dividends, or $17.90 per share, for the existing shareholders at time 0.The time zero stock price will then be:P0 = $22 + $17.90/(1.05) = $39.05 (??). The price will drop to $ $22 = $17.05 when the time 0 dividend is paid.
42 Dividend Irrelevance Example $2 per share dividend decrease:With an $18 per share dividend today this leaves an extra $100,000 in cash within the firm.Because the firm has no positive NPV projects it does the next best thing and makes a zero NPV investment, buying t-bills.With a risk free rate of 5%, the t-bills will return $105,000 at time 1. This implies a total dividend of $1,105,000 or $ per share at time 1.The current stock price is:P0 = $18 + $22.10/(1.05) = $39.05
43 Dividend Irrelevance Example What made this example work?Two things were critical:We fixed the cash the firm will receive and assumed they had no positive NPV projects. This is just an extreme version of the assumption that the dividend policy will not alter the investment policy of the firm.We assumed no taxes or transactions costs.Several were not:The one year time frame.The risk free cash flows.The fact that the firm was all equity financed to begin with.The use of debt to finance the increase in dividends.
44 Dividend Irrelevance Example The insight this example is supposed to bring to you is that under the irrelevance assumptions a change in dividend policy results in the company simply moving money across time.Using the capital markets (so the NPV is zero) ensures that no value is created or destroyed by this movement. Thus the current stock price is not changed.Moving money across time is also what the capital markets allow individual investors to do. Therefore, a change in dividend policy doesn’t do anything for the investors they couldn’t do themselves. Again no price change is the result.