Capital Structure

Broadly, a firm can finance its assets with either debt or equity. The proportion of debt relative to equity used, is known as the firm"s capital structure (also sometimes referred to as its capital stack).

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A method to determine the best capital structure for a given firm is not known (either in theory or practice).

However an understanding of the implications of given structures, will allow financial managers to strike a reasonable balance between debt and equity.


Modifying A Capital Structure

Before we talk about the firms choice of capital structure, it is useful to know that firms can change their capital structure (known as capital restructuring).

To increase the debt-to-equity ratio, the firm can issue debt, and use the proceeds to buy back stock.

Conversely, to decrease the debt-to-equity ratio, the firm can issue stock, and use the proceeds to buy back debt.

Note these restructurings do not affect the firm"s assets. This highlights the fact that:

The capital structure decision is independent of the investment decision.


The Goal of Financial Management

Remember, the goal of financial management is to maximize the value of the firm"s equity. So the firm should seek a capital structure which does this.

Interestingly, maximizing the value of equity will be equivalent to maximizing the value of the whole firm. We"ll usually state our goal as the latter.

Further, the value of the firm will be maximized when the firm"s weighted-average cost of capital (WACC) is minimized. So central in our discussion will be the effect of changing the firm"s capital structure on the firm"s cost of financing.


Financial Leverage

Leverage refers to the use of debt in the firm"s capital structure—the analogy being debt magnifies returns like mechanical leverage magnifies force.

In what follows we"ll demonstrate the effect of leverage on the return on equity.

An Example of Leverage

Say your firm, PA Solar, has assets with a market value of $10 million. The firm is all equity financed, and has 50,000 shares outstanding, at $200 per share ($10 million / 50,000).

Your firm is considering a restructuring that will add $5 million in debt to the firm"s capital structure. The debt will pay 10%.

The proceeds from issuing $5 million in debt can be used to buy back 25,000 shares of stock ($5 million / $200). There will then be 25,000 shares left outstanding.

The firm will be financed with 50% debt, and 50% equity after the restructuring. This means the debt-to-equity ratio is 1.

The stock price is unchanged by the restructuring, `\frac{\$5,000,000}{25,000} = \$200`. Note, we have ignored any impact of the restrucutring on taxes.


Below is a table showing the current and restructured capital structures.

CurrentRestructured
Assets$10,000,000$10,000,000
Equity$10,000,000$5,000,000
Debt$0$5,000,000
Share Price$200$200
Shares Outstanding50,00025,000

The Effect of Capital Structure

Here we investigate the effect of differing capital structures on the return on equity (ROE) and earnings per share (EPS). We do so in three future scenarios—recession, normal, and expansion.

In the recession and expansion, EBIT will be 50% and 150% of the EBIT in the normal scenario respectively.

Current (No Debt)

RecessionNormalExpansion
EBIT$600,000$1,200,000$1,800,000
Interest$0$0$0
Net Income$600,000$1,200,000$1,800,000
ROE6%12%18%
EPS$12$24$36

Restructured

RecessionNormalExpansion
EBIT$600,000$1,200,000$1,800,000
Interest$500,000$500,000$500,000
Net Income$100,000$700,000$1,300,000
ROE2%14%26%
EPS$4$28$52

The Effect of Leverage

The above examples show the effect of leverage is to increase the variability of ROE and EPS as a function of EBIT. That is, leverage magnifies gains and losses.

In the following interactive app, you can set the percent that EBIT will be increased/decreased in the expansion/recession scenarios.

It will then calculate ROE and EPS in each scenario, given EBIT.


EPS, EBIT, and Debt

The following interactive app will plot EPS as a function of EBIT in both cases with debt and no debt.

What this app shows is how EPS benefits from debt if EBIT is above a certain point, however is lowered if EBIT is below that point. In short, leverage is good on the upside, and bad on the downside.

Does Capital Structure Matter?

From the above we see that leverage magnifies the returns to equity (on the upside and downside). So it would seem that the capital structure is important for equity investors considering owning the stock?

Interestigly, equity investors may view the capital structure as irrelevant. This is because the equity investors can create any capital structure they want for the firm, by borrowing or lending in their own account. This is referred to as homemade leverage.

In the following example we"ll show how an equity investor can turn a position in the all-equity stock, into a position leveraged with a debt-to-equity ratio of 1.


Creating a Leveraged Position

Assume an investor want to buy $10,000 of the proposed restructured firm (50 shares
$200 per share), however the firm is presently all-equity. The EPS in the restructured case is $4, $28, and $52 in the recession, normal, and expansion cases.

Now assume the investor buys $20,000 of the all-equity firm (100 shares
$200 per share), by using $10,000 of her own money, and $10,000 borrowed at 10%.

In this case the investor"s EPS and ROE will match the EPS and ROE in the restructured case. The investor has replicated the leveraged position herself, and did not need the firm to do it.

The only assumption needed was that the investor can borrow at the same rate as the company, which is reasonable (see margin rates on stock brokerage accounts).

In a similar fashion (through lending) an investor can create an all-equity firm from a leveraged firm.


The Modigliani and Miller (M&M) Propositions

The idea of homemade leverage was introduced my M&M early in their famous work (Nobel Memorial Prize winning) on capital structure. Their groundbreaking propositions are worthy of their own presentation. Be sure to check out that presentation. Briefly, their propositions are:

No Taxes

The value of the leveraged and unleveraged firms are equal (capital structure irrelevance).

The cost of equity is: `R_e = R_u + \frac{D}{E}(R_u - R_d)`, where `R_u` and `R_d` are the required returns on the unlevered firm, and debt respectively.


M&M with Taxes

Taxes

The value of the levered firm is equal to the value of the unlevered firm plus the present value of the interest tax shield.

The cost of equity is: `R_e = R_u + \frac{D}{E}(R_u - R_d)(1 - \tau)`, where `R_u` and `R_d` are the required returns on the unlevered firm, and debt respectively. `\tau` denotes the tax rate.


Adding the Cost of Financial Distress

M&M proposition II with taxes says that the firm"s WACC is decreasing in the debt-to-equity ratio. However, this doesn"t take into account that the more debt the firm has, the greater the probability of financial distress (or ultimate bankruptcy). Remember, interest, unlike dividends, must be paid.

There are costs merely to financial distress, even if bankruptcy does not occur, such as employees leaving, supplier demanding up-front payments instead of allowing credit, and NPV positive investments may not be taken to preserve cash.

Also, bankruptcy itself, if it occurs, is very costly. Legal and administrative expenses alone are substantial.


Optimal Capital Structure

Balancing the benefit of the debt tax shield with the cost of financial distress, implies the existence of an optimal capital structure. That doesn"t mean we have a formula—only that there is evidence that such a capital structure exists.

This is called the static trade-off theory of capital structure. Firms borrow until the marginal gain of the tax benefit equals the cost of the increased probability of financial distress.

At this point, the value of the levered firm is maximized, and simultaneously the WACC is minimized.


Observed Capital Structures


Credits and Collaboration

Click the following links to see the code, line-by-line contributions to this presentation, and all the collaborators who have contributed to 5-Minute Finance via GitHub.

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