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.
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% (beta is 1.0 and market risk premium is 6%). The expected cash flow in one year is: • ½($800) + ½($300) = $550. • The NPV of the project is:
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. Or it might be good to sell less than 100% of the equity.
Financing a Firm with Equity • Unlevered Equity: Equity in a firm with no debt • Are 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 is 10% which is appropriate for the risk shareholders take on since it was appropriate for the project.
Financing a Firm with Debt and Equity • Suppose instead, you decide to borrow $100 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 Equity • Equity in a firm that also has debt outstanding
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.
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.
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 selling 100% of the (now) levered equity. • Consequently, the entrepreneur would be indifferent between these two choices for the firm’s capital structure. • Nor are the equity holders worse off. The cash flow received by equity holders has dropped but so has the price.
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.
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%. • The risk of the equity increases even when there is no risk of default. • Note that the firm’s average cost of capital with leverage remains , the same as the unlevered firm and the project.
Modigliani-Miller I • In 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.
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.
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
Modigliani-Miller II: Our Example • Leverage and the Equity Cost of Capital • Recall 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%. • With $100 of debt the expected return of the levered equity was 11.5%. • From the MM Proposition II, the expected return on equity for the levered firm is calculated as:
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 unlevered equity coincide and, therefore:
Capital Budgeting and the Weighted Average Cost of Capital • If a firm is levered, the cost of capital of the assets, 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.
Example • Honeywell International Inc. (HON) has a market debt-equity ratio of 0.5. • Assume its current debt cost of capital is 6.5%, and its equity cost of capital is 14%. • If HON issues equity and uses the proceeds to repay its debt and reduce its debt-equity ratio to 0.4, it will lower its debt cost of capital to 5.75%. • With perfect capital markets, what effect will this transaction have on HON’s equity cost of capital and its WACC?
Example • Solution • Current WACC • New Cost of Equity
Example • Solution (continued) • New WACC • The cost of debt capital falls from 6.5% to 5.7% and the cost of equity capital falls from 14% to 13.8% however, the WACC is unchanged. Note the use of the “new” costs of equity and debt capital in the calculation of the “new” WACC. It is a common mistake to ignore the change on the cost of equity capital of the reduced use of debt.
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 assets.
Levered and Unlevered Betas • We rearrange the above equation to find: • In the case of risk free debt this simplifies to (why?): • 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 causes the increase in the cost of equity capital that results from increased leverage. Our example:
The Interest Tax Shield and Firm Value • When we explicitly recognize corporate taxes the story gets a bit more complicated but the reasoning remains the same. • MM Proposition I with Taxes • The 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. • Note that now the way a firm chooses its capital structure does influence its after tax cash flows generated.
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. • As a really simple example consider the special case in which the marginal tax rate, the amount of debt, the interest rate on the debt, and the risk of the firm are all kept constant. • This allows us to see a quick estimate of the magnitude of the value of the debt tax shields.
The Interest Tax Shield with Permanent Debt • Suppose a firm borrows D dollars (present value) of 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. • In this case, tax shield can be valued as a risk-free perpetuity: • Every $1 in interest debt holders receive costs equity holders $(1-τC): Net benefit is $1 - $(1-τC) = τC
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
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. • In chapter 18 your textbook demonstrates formally that this relation holds as long as the firm acts to maintain a fixed debt to equity ratio (a common practice). • Clearly:
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 then be found by comparing the value of the levered firm, VL, to the unlevered value, VU, of the free cash flow discounted at the firm’s unlevered cost of capital, the pretax WACC.
Personal Taxes • The cash flows to investors are typically taxed twice. Once at the corporate level and then investors are taxed again when they receive their interest or dividend payment. • For individuals: • Interest payments received from debt are taxed as income. • Equity investors also must pay taxes on dividends and capital gains.
Including Personal Taxes in the Interest Tax Shield • The amount of money an investor will pay for a security depends on the cash flows the investor will receive afterall taxes have been paid. • Personal taxes reduce the cash flows to investors and can offset some of the corporate tax benefits of leverage. • The actual interest tax shield depends on both corporate and personal taxes that are paid. • To determine the true tax benefit of leverage, the combined effect of both corporate and personal taxes needs to be evaluated.
Effective Tax Advantage of Debt under Personal Taxes • In general, every after tax$1 received by debt holders from interest payments costs equity holders $(1 − *) on an after-tax basis, where: • When there are no personal taxes (i = e= 0) or when the personal tax rates on debt and equity income are the same (i = e ), the formula reduces to * = c. • When equity income is taxed less heavily than debt income (e is less than i), then * is less than c. • Now: is the net benefit
Valuing the Interest Tax Shield with Personal Taxes • With personal taxes and permanent debt, the value of the firm with leverage becomes • If * is less than c, the benefit of leverage is reduced in the presence of personal taxes.
Limits to the Tax Benefit of Debt • The optimal level of leverage from a tax saving perspective is where interest equals EBIT. • At the optimal level of leverage, the firm shields all of its taxable income and it does not have any tax-disadvantaged excess interest. • However, it is unlikely that a firm can predict its future EBIT precisely. • If there is uncertainty regarding EBIT, then there is a risk that interest will exceed EBIT. As a result, the expected tax savings for high levels of interest falls, possibly reducing the optimal level of interest/debt.
The Low Leverage Puzzle • It would appear that firms, on average, are under-leveraged. However, it is hard to accept that most firms are acting suboptimally. • In reality, there is more to the capital structure story than discussed so far. • A key item missing from the analysis thus far is that increasing the level of debt increases the probability of bankruptcy. • If bankruptcy is costly, these costs might offset the tax advantages of debt financing. It’s all in the frictions!
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 any choice of capital structure.
The Costs of Bankruptcy and Financial Distress • With perfect capital markets, the risk of bankruptcy is not a disadvantage of debt, rather bankruptcy simply shifts the ownership of the firm from equity holders to debt holders without changing the total value available to all contributors of capital. • 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.
Direct Costs of Bankruptcy • The bankruptcy process is complex, time-consuming, and costly. • Top management time is consumed by the process. • 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.
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-bankruptcymarket value of total assets. • Workouts and pre-packaged bankruptcies may help reduce these small costs as well.
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 Customers • Loss of Suppliers • Loss of Employees • Loss of Management’s Time (pre-bankruptcy) • Loss of Receivables • Fire Sale of Assets • Delayed Liquidation • Costs to Creditors • It is estimated that the potential loss due to financial distress (or the threat of distress) is 10% to 20% of firm value
The Tradeoff Theory • The firm picks its capital structure by trading off the benefits of the tax shield from debt against the expected 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.
Optimal Leverage • For 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, ultimately reducing the value of the levered firm. • The rate at which the costs and benefits change are different across different firms and across industries.
Optimal Leverage • The 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 expected 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) and firms
Exploiting Debt Holders: The Agency Costs of Leverage • Agency Costs • Costs that arise when there are conflicts of interest between the firm’s stakeholders • Managers are presumed to make decisions that increase the value of the firm’s equity. When a firm uses leverage, managers may make decisions that benefit shareholders but harm the firm’s creditors and lower the total value of the firm. • This implies that the amount of debt in the firm may affect the assets (and the cash flow generated by those assets) that the firm owns.
Over-Investment • Big Trouble Corp. (BTC) owes its creditors $5 million, due in six months. • BTC has liquidated its assets because it could not operate profitably. Its remaining asset is $1 million cash. • Big Bill, the lone shareholder and general manager is considering two possible actions. • (1) Buy six month T-bills that earn 1% interest. • (2) Go to Vegas and wager the entire $1 million on a single spin of the roulette wheel. • Why might Bill consider the second “investment”? • Would he have considered it in the absence of high leverage?
Under-Investment • Slight Trouble Corp. (STC) has a small but significant chance of bankruptcy in the next few years. Its debt is trading far below par. • Managers are evaluating an investment project that will cost $1 million to undertake. The alternative is to pay $1 million out as dividends. • While the NPV of the project is positive it may be that the shareholders are better off with the dividend than if the project is taken. • The reason is that while shareholders pay all the costs of the project, they will have to share its value with bondholders. The value of the project will, in part, serve to raise the value of the bonds.
Disciplinary Power of Debt • “On the other hand” as economists are fond of saying, debt can be a disciplinary device. • It is well recognized that an owner works harder and makes better decisions than an employee. • High leverage helps managers become significant shareholders. • This was an often cited justification for the LBO wave of the mid 80’s and early 90’s. • Similarly, one of the most contentious issues between managers and shareholders is the payout of excess cash. Consider Hollinger International and Conrad Black’s behavior or Enron, and the list goes on. • Debt allows managers to commit to the payout in a way that cannot be accomplished with a dividend policy.