Debt/Equity
Definition The mix of securities that a firm uses to finance its investments is called its capital structure. The two most important such securities are debt and equity
Debt Firm s assets Common Equity
Project 1 Project 2 Project 3 Debt Project 4 Project 5 Project 6 Common Equity
Overview Overview of lecture Capital structure - basics Debt Equity Miller and Modigliani view of financial structure Taxes traditional picture Balancing bankruptcy costs Incentive problems - conflicts shareholders and creditors. Evaluating levered investments APV FTE WACC
Definition Definition: Capital Structure: The mix of securities that a firm uses to finance its investments. Purpose: Design the firms capital structure to maximise the value of the firm. What are the factors that are important in determining the firm s capital structure? Limitation: We concentrate on the choice between debt and equity. (Understanding debt and equity a prerequisite to understand other alternatives.)
Capital structure irrelevance. In 1958, Franco Modigliani and Merton Miller, proposed their theory of capital structure. In a perfect capital market the value of the firm must be invariant to its capital structure choice. To understand when capital structure will matter, we must first understand under what conditions it will not matter. We therefore begin our study of capital structure with a look at the MM theory.
Miller and Modigliani I Assumpions: No Taxes. Perfect capital markets. Result: (MM proposition I ) In a perfect capital market, the value of the firm is independent of its capital structure.
Showing the MM proposition I. Consider two firms: Generating the same stream of operating income. Differ only in their capital structure. Firm U is unlevered. Firm L is levered, it has debt in its capital structure. Value of stock(equity): E L. Value of debt: D L.
Firm Value: Unlevered firm: Value of equity E U, same as the total value of the firm, V U. Levered firm: Total value of the firm is V L = E L + D L. We want to show that the capital structure does not affect firm value.
Suppose you buy a fraction α of the shares of firm U. This costs you αv U and entitles you to α X of the profits. Investment αv U Cash flow α X Whatever the cashflows are, they flow to equity.
Definition of debt: Debt is issued for one period. Due to pay I, the sum of interest and principal.
Payment of debt Outcomes for debt: The earnings X for the firm are larger than I. The bondholders get I. Stockholders get X I. The earnings X are not enough to cover debt service. The firm goes bankrupt. Bondholders receive all earnings X. Stockholders get nothing.
Investment in Levered firm. Alternative strategy to investing in equity of unlevered firm: Purchase a fraction α of both the debt and the equity of firm L. Investment Cash flow αd L α min[ X, I ] αe L α max[ X I, 0] Total Payoff αv L α X
Compare the two investments. Investment Cash flow Unlevered αv U α X Levered αd L α min[ X, I ] αe L α max[ X I, 0] αv L α X Both investment strategies offer the same payoff, α X.
No arbitrage. We now appeal to what we call a no-arbitrage argument: In well-functioning capital markets, two investments that offer identical future cash flows must have the same value today. Both investment strategies give future cashflows αx. Therefore, they have the same values today, αv U = αv L ( = αe L + αd D ). The value of the levered firm must equal the value of the unlevered firm, V U = V L. That was what we wanted to show: Result: (MM proposition I) In a perfect capital market, the value of the firm is independent of its capital structure.
Miller Modigliani proposition II. r E = r + (r r D ) D E This equation is MM s proposition II. Required return r E r r D Risk free Risky
Expected return on the firm s assets is a weighted average of the expected returns on the firm s securities. The beta of the firm s assets a weighted average of the betas of the firm s securities: β = D V β D + E V β E Rearrange this in term of β E : β E = β + (β β D ) D E This is why investors require higher return on levered equity. The required return simply rises to match the increased risk.
Recall the basic accounting identity. Real Debt Assets Equity The risk of the real assets will not be affected by the debt-equity combination. the weighted average of debt and equity is constant. Only changing terms on the right side, do not change left side. Hence net result fo changing right side null.
Adjusting for Corporate Taxes. Debt financing has one important advantage under the current US corporate income tax system. The interest that the company pays on debt is tax deductible. Dividends and retained earnings, the cash flows to equity holders, are not tax deductible.
Example Firm U, an unlevered firm. Firm L, a levered firm with $10,000 of 10% debt. Both firms (U and L) have the same earnings before interest and taxes of $5,000.
Example ctd Income statement Firm U Firm L EBIT 5000 5000 Interest 0 1000 Taxable income 5000 4000 Tax (34%) 1700 1360 Net income 3300 2640 Total income to bondholders and 3300 3640 stockholders Income to the government 1700 1360
The cash flows to security holders of firm L: higher than those to the security holders of firm U by an amount equal to the interest rate tax shields, The interest tax shields are τ c I, where Get: I are the interest payments. τ c is the corporate tax rate. Cash flow to levered firm = Cash flow to unlevered firm + Interest tax shield CF L = CF U + τ c I
For our example: CF U + τ c I = 3300 + 0.34 1000 = 3640 = CF L Take present value of both sides of cash flow identity: Find the value of the levered firm, V L : PV (CF L ) = PV (CF U ) + PV (τ c I ) V L = V U + τ c PV (I )
The present value of the interest payment, I, can be found by discounting the expected interest payment, E[I ], by the required rate of return on the firm s debt, r D. Assume that the firm s debt is perpetual: PV (I ) = E[I ] r D = D L Consequently, V L = V U + τ C D L Note: PV (I ) is less than D L if the firm does not plan to borrow permanently, or the interest tax shields cannot be utilised at some point in the future. (Losses).
Example Assume r = 20%. All cash flows are perpetual. V L = V U + τ c D = 3300 + 0.34 10, 000 0.20 = 16, 500 + 3, 400 = 19.900 The value of the firm s equity is: E L = V L D L = 19, 900 10, 000 = 9, 900
Thus, if firm U issued $10,000 of debt, it could increase its market value by $3,400. The increase in firm value flows through directly to the old stockholders. They receive a $10,000 dividend at the time the debt is issued and are left with equity worth $9,900. This represent an increase in wealth of $3,400: Wealth of equity holders = (10, 000 + 9, 900) 16, 500 = $3, 400 = τ c D L
Since the value of the firm increases as the level of debt increases, the optimal debt to value ratio for all firms is D/V = 99.9%. This is obviously unrealistic, but it does serve as an important reminder of how important taxes can be in determining a firm s leverage ratio. The corporate tax code favors debt over equity. Thus, it should not be surprising that higher levels of debt are often used following successful takeovers or management buyouts. In fact, the purpose of many takeovers is to simply get the firm to use more debt financing so that the tax payments made to the government are minimised.
Adjusting for taxes in costs of capital. Maximising the value of the firm is equivalent to minimising the firm s cost of capital. Therefore, it should not be surprising that the cost of capital for a levered firm, r, is less than the cost of capital for an identical unlevered firm, r. In particular, the cost of capital for a levered firm can be estimated as follows: r = r (1 τ c D V ) = r E E V + r D(1 τ c ) D V Rearrange this equation to obtain an expression for r E : r E = r + (r r D )(1 τ c ) D E The firms asset beta is given by
Continuing our example, Estimate the cost of capital for firm L, (r): from: the cost of capital for firm U, r, and firm L s debt-to-value ratio, D/V. r = r (1 τ c ) D ( V ) 10, 000 = 0.20 1 0.34 19, 900 = 16.6%.
The cost of equity capital for firm L is: r E = r + (r r D )(1 τ c ) D E 10, 000 = 0.2 + (0.2 0.1) (1 0.34) 9, 990 = 26.7%. Assuming: β = 1.0, β D = 0 Levered firm s equity beta is: β E = β + (β β D )(1 τ c ) D E 10, 000 = 1.0 + 1.0(1.0 0.34) 9, 000 = 1.67
Non-debt Tax shields. In the previous the value of a levered firm found by assuming that the corporate tax shield was equal to the corporate tax rate, τ c, for each dollar of interest, regardless of the amount borrowed. In reality the interest tax shield is earned only if the interest expense can be used to offset taxable income. If a firm shows a loss and cannot carry the loss back against past taxes, its interest tax shields must be carried forward with the hope of using it later. In the meantime, the firm loses the time value of money while it waits. If tax losses continue in the future, the wait may be permanent, and the interest tax shield lost forever.
Alternatives to borrowing as tax shields. Borrowing is not the only way to shelter income from taxes. In addition to interest payments, firms also have a variety of non-debt tax shields. 1. Depreciation expenses. 2. Tax loss carry forwards 3. Pension contributions 4. Charitable contributions The more a firm shields income in these other ways, the lower the expected tax shield from borrowing. Firms with higher amounts of non-debt tax shields, should use less debt.
Bankruptcy costs. In reality, a firm that borrows more increases its chances of encountering financial distress. Sometimes financial distress leads to bankruptcy. Sometimes it simply means that the firm is having difficulty in meeting its fixed obligations. In any case, financial distress may be costly. These costs do not affect the firm only in the event of financial distress, however. Rather, the expected costs of financial distress are reflected in current market prices. That is, V L = V U + PV (Tax shields) PV (Expected costs of financial distress)
The expected costs of financial distress depend on the probability of distress and the magnitude of the costs encountered if the event occurs. Firm value PV(bankruptcy cost) PV(tax shields) V U ( D E ) Balancing of tax shields and bankruptcy costs. D E
The costs of bankruptcy include both the direct costs Legal fees (lawyers) Administrative fees. Indirect Costs e.g. lost business because of customer uncertainty or the unwillingness of suppliers to accept credit.
Month Cost as % o Name 0-12 -36-60 -84 change in va Chicago and Nortwestern 2.7 1.4 2.5 0.6 0.6 0.7 Chicago, Indianapolis and Louisville 6.6 9.4 1.9 1.6 1.6 2.2 Chicago, Milwaukee, St.Paul & Pacific 3.8 2.1 3.7 0.8 0.4 0.4 Denver and Rio Grande Western 1.7 1.9 0.4 0.4 0.6 0.8 Eerie Railroad 3.9 1.1 1.3 2.5 1.0 1.4 Minneapolis, St.Paul & SSM 9.1 2.9 3.7 3.2 1.0 1.2 Missouri Pacific 3.3 1.7 0.6 0.8 1.3 2.1 New York, New Haven and Hartford 1.9 2.2 1.5 1.1 0.6 0.8 St.Louis San Francisco Railway 6.0 9.8 0.8 0.6 0.9 1.0 Western Pacific 8.8 6.5 5.9 2.3 1.5 1.8 High 9.1 9.8 5.9 3.2 1.6 2.1 Low 1.7 1.1 0.4 0.4 0.6 0.4 Mean 5.3 4.0 2.5 1.4 1.0 1.3 ICC reported bankruptcy cost as a percentage of market value.
In table, Warner(1977) provides evidence on the direct costs of bankruptcy for 11 bankrupt railroads. The average cost was about two million dollars spread over an average of 13 years. On average the costs of bankruptcy were only 5.3% of the overall market value of the firm at the time the bankruptcy was declared. The costs decline to 1.0% of overall market value estimated 7 years prior to bankruptcy. Thus, the expected costs of bankruptcy are likely to be much smaller. For example, if the probability of bankruptcy is 20%, then the expected bankruptcy costs would be
Expected costs of bankruptcy = Probability Cost of bankruptcy = 0.20 (0.01 Value of the firm) = 0.20 0.01 (Value of the firm) = 0.002 (Value of the firm) Discounting back 7 years at, say, 10%, gives PV (Bankruptcy costs) 0.002 Value of the firm = (1.10) 7 = 0.001 Value of the firm
Misconceptions about bankruptcy. There are some common misconceptions about bankruptcy and bankruptcy costs. 1. The decline in the value of the firms assets is a result of bankruptcy. This is a common misconception, but it has cause and effect mixed up. Firms go bankrupt because their assets have declined in value. Bankruptcy is the result of lower asset values, not the cause. 2. Firms that go bankrupt also go out of business and cease to exist. Most bankruptcies involve reorganizations in which the firm continues to operate. Bankruptcy simply means that the firm has failed to meet its fixed obligations. The stock holders are then forced to give up the ownership of the firms assets to its creditors, who then become the new stock holders.
Bankruptcies are bad because they often times result in the loss of jobs. Remember, bankruptcy is simply the process whereby ownership of the firms assets is transferred from stockholders to bondholders. There is nothing inherently good or bad about this. The fact that parts of the business may be shut down following a bankruptcy is not a result of the bankruptcy. The closing of parts of the business that are no longer profitable would have happened anyway, even if the firm was entirely equity financed.
Example: Risk Shifting. Financial distress can be costly even though the firm is not technically in default or bankrupt. Financial distress can cause the firms shareholders to pursue policies that advance their own self interest at the expense of bondholders. Consider a firm with the following balance sheet (in market values): Cash $100 Debt $500 Fixed assets 500 Equity 100 Total Assets $600 Total liabilities $600 The debt is due in exactly one year, at which time the firm must pay principal plus interest of $800. The equity has a positive value because there is some chance that the value of the firm s assets will exceed $800 at the end of the year.
Now suppose the firm comes across the following investment project. Possible cash flows next year Bad state good state Probability 90% 10% Cash flow 0 800 Cost of project = $100. NPV of project = $100.
Although the NPV of the project is negative, you can see why the shareholders might use the firm s $100 cash to invest in the project. If the project fails, the shareholders are no worse off than they would have been anyway. If the project is successful, the shareholders will have enough to pay off the bondholders and have something left over for themselves. Essentially this project allows the shareholders to gamble with the bondholders money. If the project is undertaken, the new balance sheet might look like the following: Cash $0 Debt $350 Fixed assets 500 Equity 150 Total Assets $500 Total liabilities $500 This is called risk shifting because the shareholders have substituted a risky project (the new investment) for a riskless asset (the cash). In the absence of financial distress, the shareholders would not likely undertake such an investment strategy.
Example Forgoing profitable investments. Now suppose the firm has the following investment opportunity: Cash flow next year $400 (certain) Cost of project $200 NPV of project $150 To undertake the project, the equity holders will be required to invest an additional $100 in the firm. However, they will be reluctant to do so because the cash flows on the project are likely to go to the bondholders, not the stockholders. Thus, the shareholders may actually forego profitable investment projects when the firm is in financial distress.
The new balance sheet for the firm, if the project is undertaken, might look like the following: Cash $0 Debt $750 Fixed assets 850 Equity 100 Total Assets $850 Total liabilities $850
Example Excessive dividends. While shareholders may refuse to contribute additional capital to the firm when it is in financial distress, they certainly have no aversion to taking money out. For example, shareholders would like to use the $100 in cash to pay themselves a dividend. If they do, the new balance sheet might look like: Cash $0 Debt $450 Fixed assets 500 Equity 50 Total Assets $500 Total liabilities $500 Although the value of the equity falls by $50, the shareholders are better off because they now have an additional $100 in their pockets. Essentially the shareholders are taking some of the bondholders money and giving it to themselves.
The existence of these costs of financial distress may reduce the optimal level of debt for the firm. The ability of stockholders to expropriate wealth from bondholders will result in lower prices for the firm s debt, thereby increasing the cost of borrowing. The higher interest rate demanded by bondholders compensates them for the losses they may suffer due to the conflict of interest they may have in the future with stockholders. Thus, the costs of financial distress are really borne by stockholders through lower prices for the firm s debt when it is issued.
Bond covenants constraining activities such as asset sales or mergers are examples of voluntary contracts that can reduce the agency costs stemming from the bondholder-stockholder conflict. The cost reducing benefits of the covenants accrue to the firm s shareholders through the higher price the bonds will command at the time the bonds are issued. If covenants reduce the costs which bondholders incur in monitoring the firm and its activities, these reductions in agency costs are also passed on to stockholders through higher bond prices at issuance.
Choosing the firm s Debt-Equity ratio in practice. 1. Taxes: For firms that are in a tax-paying position, an increase in leverage can reduce the tax burden and thus increase the total cash flows to the firms security holders. This will have the effect of increasing the total market value of the firm. 2. Risk: Financial distress can be costly. Therefore, other things being equal, the higher the business risk of the firm s assets, the lower will be its debt ratio. Firms in stable industries with substantial free cash flow should be more highly levered. 3. Asset type: The costs of financial distress are likely to be greater for firms whose value depends on growth opportunities or intangible assets. Therefore, firms with more intangible assets should on average borrow less than firms with more tangible assets. 4. Financial slack: You want to make sure that your firm has sufficient financial slack so that financing is quickly and readily available when positive-npv projects arise.
Accounting for the tax shields in capital budgeting. If a project supports additional borrowing by the firm, then this is a positive externality conferred by the project on the firm as a whole. It should be recognised as a benefit of the project. The project itself may be financed with debt, equity, or retained earnings. But this should not be important. What is important is the additional debt capacity provided by the project. There are two ways to account for the tax shields. Direct Estimation (Adjust Cashflows.) Adjust cost of capital. Alternatively: Look at what s left to equity
Calculations involving capital structure Cost of capital The most important case where we deal with the capital structure in practice is in investment analysis, because of the MM II result: Due to the tax advanteage of debt, the way an investment is finance can affect whether it is a valuable investment. There has been developed a number of methods for dealing with this issue, and it is important to be aware of them, also because all are not applicable in the Norwegian tax environment. Let us start with establishing a baseline, and looking at how one deal with the issue in cases without taxes.
Different betas for debt and equity. The beta that is used to compute the discount rate or opportunity cost of capital for new investment project is the project s asset beta. Asset betas for a variety of industries are provided in the above table. Unfortunately, asset betas are not directly observable, only equity betas are observable. If the firm is unlevered, (i.e. uses no debt), then its equity beta and asset beta are one in the same. In this case, the required rate of return on the firm s assets is equal to the required rate of return on its equity. r = r E = r f + (r m r f )β E where r is the required return on the firm s assets. r E is the required return on the firms equity, and β E is the firms equity beta.
When a firm has both debt and equity in its capital structure, however, this is no longer the case. In the case where the firm uses leverage, the asset beta β, will be a weighted average of the betas on the firms debt and equity. The asset beta is given by: β = β D D V + β E E V where β D = Beta of the firm s debt. D = Market value of the firm s debt. E = Market value of the firm s equity. V = D + E Thus, the cost of capital for a levered firm is r = r f + (r m r f )β = r D D V + r E E V where r D and r E are the required rates of return on the firm s debt and equity, respectively.
Exercise β Market value Debt 0.05 100 Equity 1.40 200 E[ r m ] = 10% r f = 5% 1. What is the asset beta β? 2. Find the firms cost of capital
The business risk of an asset or firm is measured by its asset beta. The use of debt to finance a portion of the firm s investments adds additional risk to the firm s equity. This additional risk is called financial risk and is measured by the difference between the firm s equity and asset betas.
There is an important question that needs to be answered: Will a particular financing option have cash flow consequences? Typical examples of cases where this is the case Tax savings from debt. (Tax shields) Issue costs when issuing debt/equity. Borrowing at below market interest rates.
To account for taxes in such calculations there are three methods typically employed to make tax adjustment in investment calculations Adjusted present value Flow to equity Weighted Average Cost of Capital
APV If a project supports additional borrowing by the firm, then this is a positive externality conferred by the project on the firm as a whole. It should be recognised as a benefit of the project. The project itself may be financed with debt, equity, or retained earnings. But this should not be important. What is important is the additional debt capacity provided by the project. APV simply estimate and discount the increased cash flow. This is called the Adjusted present value calculation 1. Calculate the net present value of the project as if it is 100% equity financed. 2. Add the present values of the increase in cash flow coming from the financing decision. (Note that the present value is calculated using an interest rate that reflects the risk)
Flow to Equity Here we need to isolate the cash flows that flow to equity holders, only, and discount them at the cost of capital relevant for equity, ie. the equity cost of capital.
Instead of accounting for the tax shields explicitly, as above, one can adjust the discount rate to recognise the tax benefits of borrowing. We call this discount rate the weighted average cost of capital: r = r E E V + r D (1 τ c ) D ( V = r 1 τ c D ) V Using the weighted average cost of capital, the project NPV is: NPV = T t=1 E[C t ](1 τ c ) (1 + r) t C 0
Interaction between capital structure and investment decisions Extended example - showing all three methods.
Exercise The Global Connections Corporation has a current market capitalization of $1 billion. It considers an investment with initial outlay of $100 million. The investment increases the net cash flows by 15 million per year for the indefinite future. GCC faces a tax rate of 30%, has 20% debt in its capital structure which it seeks to maintain in the new project. The firms debt is risk free, at 8%. The relevant interest rate for investment in this line of business is 10%. 1. Calculate the value of the project as if it was all equity financed 2. Use the Adjusted PV method to evaluate the project. 3. Use the Flow to Equity method to evaluate the project 4. Use the WACC method to evaluate the project.
Exercise solution All equity financed Annual after tax cash flow = 15 mill (1 0.3) = 10.50 mill Let k be the cost of capital for the all equity finance project NPV = 10.50 k 100 = 10.50 0.1 100 = 105 100 = 5
Exercise solution ctd The adjusted PV: Need to calculate the value of the debt tax shield, i.e. the savings due to lower taxes from interest payment. Here need to find the increase in debt justified by the project. If we only consider the investment of 100, the debt increases by 0.2 100 = 20 million, and we would calculate APV = NPV all equity project + PV Tax shields But.. = 5 + = 5 + (20 0.08) 0.3 0.08 (20 0.08) 0.3 0.08 = 20 0.3 = 5 + 6 = 11
Exercise solution ctd Adjusted present value APV = NPV all equity project + PV Tax shields (20 0.08) 0.3 = 5 + = 20 0.3 = 5 + 6 = 11 0.08 But that ignores that the value of the firm increases from the present value of the project, so the debt capacity increases by (100 + APV ) 0.2. The calculation must factor that in, and put in (100 + APV ) in the calculation of the debt capacity APV = 5 + ((100 + APV ) 0.2 0.08) 0.3 0.08 APV (1 0.06) = 5 + 6 = 11 APV = 11 = 11.70 mill 0.94
E = 10.50 0.056D = 101.45 0.541D Exercise solution ctd Flows to equity Need to discount the cash flows to equity at the equity cost of capital. Calculate as: k E = k + (1 τ)(k r D ) D E = 0.1 + (1 0.3)(0.1 0.08) 0.2V 0.8V = 10.35% Then figure out the cash flows to equity Let E and D be equity and debt values due to the project, only Cflow equity = (15 0.08 D)(1 τ) = (15 0.08 D)(1 0.3) = 15 0.7 0.08 0.7 D = 10.50 0.056D To be discounted at the cost of capital for equity
Exercise solution ctd Now, this is written in terms of D, the amount of debt issued to finance the project. Since the firm has a target debt ratio of 0.2, we know that 0.2 = D D + E and we can solve for D E = 0.25 hence D = 0.25E which we can plug in instead of D above: E = 101.45 0.541D = 101.45 0.541 0.25 E Solving for E: E(1 + 0.541 0.25) = 101.45 E = 101.45 (1 + 0.541 0.25) = 101.45 1.13525 = 89.36
Exercise solution ctd But this is the value of equity after issuing enough equity to cover the investment needs. To find the added value of equity need to find out how much equity was issued. Since D = 0.25E we find the debt issued as D = 0.25 89.36 = 22.36 Issued equity 100 22.36 = 77.64 The increased value of equity = 89.36 77.64 = 11.72 11.70
Exercise solution ctd WACC Need to calculate a weighted cost of capital that can be used to discount the total cash flows WACC = D D + E (1 τ)r D + E E + D r E = 0.2 (1 0.3) 0.08 + 0.8 0.1035 = 0.094 NPV = 10.5 100 = 11.70 0.094