Theory of Capital Structure

THEORY OF CAPITAL STRUCTURE

Determination of an optimal capital structure has frustrated theoreticians for decades. The early work made numerous assumptions in order to simplify the problem and assumed that both the cost of debt and the cost of equity were independent of capital structure and that the relevant figure for consideration was the net income of the firm. Under these assumptions, the average cost of capital decreased with the use of leverage and the value of the firm (the value of the debt and equity combined) increased while the value of the equity remained constant.

Debt/Equity

Modigliani and Miller showed that this could not be the case. Their contention was that two identical firms, differing only in their capital structure, must have identical total values. If they did not, individuals would engage in arbitrage and create the market forces that would drive the two values to be equal.

Their proof of this proposition was based upon several assumptions (many of which have subsequently been relaxed without changing the results):

· All investors have complete knowledge of what future returns will be

· All firms within an industry have the same risk regardless of capital structure

· No taxes (we will relax this assumption subsequently)

· No transactions costs

· Individuals can borrow as easily and at the same rate of interest as the corporation

· All earnings are paid out as dividends (thus, earnings are constant and there is no growth)

· The average cost of capital is constant

Since no taxes has been assumed, the operating income (EBIT) is equivalent to the net income which is all paid out as dividends. Thus, the value of the firm is equal to

Since the value of the firm is equal to the sum of the value of the debt and equity,

Substituting the last equation into the preceding equation and solving for Ks

Thus, ks must go up as debt is added to the capital structure.

Debt/Equity

To prove their point, they assumed two identical firms, an unlevered firm (all equity) and a levered firm with $4 million of debt carrying an interest rate of 7.5%, both firms generating an operating income (EBIT) of $900,000 annually. They adopted the assumption that stockholders of both firms would have the same required rate of return of 10% which, as previously mentioned, was the standard assumption at the time (that the cost of equity was constant regardless of capital structure).

Unlevered Firm Levered Firm

EBIT $ 900,000 $ 900,000

-Interest 0 300,000

Income $ 900,000 $ 600,000

Since the required rate of return of shareholders is 10% in both cases

Unlevered Firm Levered Firm

Value of Equity =

Value of Debt = $ 0 $ 4,000,000

Total Value of Firm = $9,000,000 $10,000,000

If this were true, then someone who owns 10% of the levered firm would have income of $60,000 ($600,000 * 10%) and could sell it for $600,000 ($6 million * 10%). With this $600,000 the individual could borrow another $300,000 at 7.5% and buy 10% of the unlevered firm for $900,000 ($9 million * 10%). What would this individual’s income be now?

EBIT $ 90,000 ($900,000 * 10%)

-Interest 22,500 ($300,000 * 7.5%)

Income $ 67,500

Thus, the income would be greater by buying the unlevered firm’s stock and borrowing money to finance the purchase. As other individuals see this opportunity, they also will sell the stock of the levered firm (driving its price down) and buy the stock of the unlevered firm (using some borrowed money) and thereby driving the value of the unlevered firm’s stock up. As the price of the unlevered firm is bid up, the value of the unlevered firm increases above $9 million dollars, while the selling of the levered firm’s stock drives the equity value below $6 million (which decreases the total firm value, including the $4 million of debt, below $10 million) until the two firms’ values, in equilibrium, are equal and no opportunity to arbitrage the difference exists. Consequently, if the total value of the two firms is equal, then the average cost of capital must be equal. And if the average cost of capital is equal, then it must be true that the cost of equity rises in such a manner as to exactly offset the increased use of cheaper debt financing (and we end up with the previous graph showing this).

As we previously uncovered when we looked at financial leverage, this is not a surprising result. As a firm increases its use of debt, the risk to the stockholder increases and, as a consequence, the stockholder’s required rate of return will increase. Modigliani and Miller simply defined how the stockholder’s required rate of return should increase with increased financial leverage.

The lesson that is intended by this is that value cannot be created by simply substituting one form of financing for another.

Subsequent to this analysis, it was pointed out that corporate taxes have an impact on the valuation. Without going through the mathematics (which is in your textbook), suffice it to say that the result was that the value of the firm increased with increased leverage. Specifically,

The fact that the government is a “partner” in the business results in a subsidy when debt financing is used and a deductible expense (unlike equity payments). When corporate taxes were taken into account, the average cost of capital was found to decrease with increased leverage:

Ka before-tax

Ka after tax

Kd before-tax

Kd after-tax

Debt/Equity

This implies that a firm should use as much debt as possible. Yet, we do not see companies using 100% debt. It might be pointed out that during the late 1980s there was a considerable amount of substitution of debt for equity among firms, particularly in the case of leveraged buyouts. However, many of those firms subsequently failed (for example, Unocal) and the typical debt/equity ratio today is similar to earlier levels.

So why do we not see more debt employed by companies? The answer to this question has been sought by many and two primary proposals have been put forth. First, bankruptcy costs were invoked as a factor. That is, the more debt a firm uses, the higher the probability that the firm would default and go into bankruptcy. Therefore, the present value of bankruptcy costs had to be deducted from the value of the firm. A second factor was that of “agency” costs, such as the necessity of reporting regularly to lenders (audited financial statements, bank “monitoring” and other bank fees, trustees for debt payments, etc.) that accompany the use of debt. Both of these costs increase in present value of expected costs terms as the proportion of debt increases. Another way of viewing these costs is that the risk of receiving full interest and principal payments increases and thus the required rate of return of lenders increases. (For example, “junk” bonds often yield higher rates of interest than the required rate of return on equity for companies with very little debt.) Consequently, the cost of debt increases and the average cost of capital will ultimately increase.

Ka after-tax

Kd after-tax

Debt/Equity

As can be observed from the graph, a minimum average cost of capital exists, but exactly where it should be has yet to be determined within a theoretical framework.

So what are the insights that we can gain from this theoretical view of capital structure? First, we should note that, while debt financing is “cheap” in the sense that required rates of return on equity will always be higher than the interest rate on debt, there is a “hidden” cost in that the cost of equity rises as we utilize more debt financing. This is one reason that using the average cost of capital in valuing a project or company is more appropriate, even if we intend to borrow all of the money to finance it. While we may use cheap debt to finance a project, the increased risk to shareholders from increasing our financial leverage results in an increase in the cost of equity. The average cost of capital reflects both the cost of debt as well as the cost of equity and thus will reflect the increased cost of equity associated with the use of more debt financing.

The second important concept is that tax-deductible debt financing results in a tax subsidy by the government. This subsidy adds value to the firm. For example, what is the “advantage” of being a home owner with a mortgage rather than leasing a home? It is the taxes that you will save. The reason that Congress eliminated the deductibility of credit card interest is that it did not want to encourage, through a tax subsidy, the financing of purchases purely for consumption. On the other hand, the purchase of a home (which is still tax-deductible) is an “investment”, not to mention the political consequences of voting to end the subsidy of the American Dream of home ownership.

Current Thoughts on the Effect of Leverage on the Cost of Capital

The evidence quoted in the textbook suggests that the costs of an increased probability of bankruptcy and the increasing agency costs associated with debt increase at such a rate as to (approximately) just offset the tax advantage of using increasing amounts of cheap, tax-deductible debt. Thus, on an after-tax basis, the weighted average cost of capital remains relatively stable and is roughly the same as the required return on equity for a firm that does not utilize any leverage.

Ka after-tax

Kd after-tax

Debt/Equity

Note that there is no effect on the cost of equity. The incremental costs associated with increased bankruptcy risk and the agency costs imposed on the firm can be reflected as a cost of using additional debt financing.

As an example, consider a California firm that was in violation of its existing bank loan covenants of maintaining a specified quick ratio and debt service coverage ratio. Naturally, the bank would prefer not to pursue bankruptcy proceedings since its recovery would be minimal. Instead, the bank was willing to accept roughly 50% of the funds owed to it plus preferred stock payable over a five-year period at a 10% (low) dividend yield. Overall, the bank "foregave" approximately 25% of what was owed to it (which resulted in extraordinary income for the firm). In order to generate the funds to pay the bank, a second bank was found that was willing to make both a term loan and a revolving line of credit secured by inventories and receivables. While the new loans had no covenants regarding ratios, the bank charged a minimum $30,000 per month of bank fees which included the interest on the debt as well as a fee based upon the amount of inventories and receivables available (but not necessarily borrowed against) for the revolver. The conclusion of the firm was that the optimal debt policy was to pay down the new loan only to the extent that the interest and fees amounted to $30,000 per month since any additional pay down would yield no decrease below the minimum $30,000 per month of charges. It was estimated that the effective rate of interest on the loan was in the neighborhood of 24% even under the optimal policy. Thus, some lenders are willing to make high-risk loans, but the cost is incorporated under various guises of interest, bank and commitment fees, resulting in an effective rate of interest that borders on usurious (i.e, above legal limits).

As the risk rises for lenders as more debt is employed, so does the risk to the stockholders. The textbook derives a relationship based upon the assumption of a risk-free corporate debt, although there is no such thing. Alternatively, one can consider the fact that the cost of debt reflects the market's assessment of the risk to lenders and that the cost of equity should include an additional risk-premium based upon the fact that an equity position is more risky than that of debt even for a highly levered firm. With this perspective, and referring back to the review on risk and the Capital Asset Pricing Model, Hamada has shown that the beta of the leveraged firm is a function of the extent to which debt is used relative to equity.

Of course, the factor (1-t) reflects the fact that increased profitability from the use of leverage is reduced by the "partnership" that the firm has with government in that increased profits are reduced by their taxation. Similarly, increased losses are offset by tax-loss carrybacks and carryforwards. Moreover, substituting for the definition of beta shows that this relationship is true with respect to total risk as well as systematic risk since the correlation between the market and an unlevered firm is the same as the correlation between the market and a levered firm.

Thus, CAPM gives us insight into the manner in which leverage affects risk, and hence required rates of return, regardless of whether total risk or systematic risk is of more concern to the decision-maker. As will be seen in the textbook, the unleveraging of corporate betas and averaging in order to derive an industry unlevered beta and using the CAPM to yield an industry required return on unlevered equity as a proxy for the average cost of capital is central to the text’s approach of valuing the firm as a whole.

To see the more applied implications, consider the effect on a firm’s cost of equity resulting from a change in capital structure. As an example, reconsider the firm from the Cost of Capital handout in which the weighted average cost of capital was calculated. Suppose the company intended to issue an additional $200,000 of debt and use the proceeds to repurchase $200,000 of common stock. (For simplicity, assume that there are no transactions costs involved.) In addition, assume that the cost of debt rises from the market rate of 9% to 10% as a result of the higher amount of leverage. Assume also that the required return for preferred stockholders increases from 8% to 8.4% as a result of the higher leverage as well. Finally, assume that the repurchase of shares is estimated to result in driving the price per share up to $11.41 each.