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### Understanding Capital Structure

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Capital Structure

- A company can obtain long-term financing in the form of equity, debt or a combination of both.
- Capital structure is the proportion of debt and preference and equity shares on a firm’s balance sheet.

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Capital Structure

- Optimal Capital structure is the capital is the capital structure at which the weighted average cost of capital is minimum and thereby maximum value of the firm.

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Capital Structure

- The relative proportions of debt, equity and other securities that a firm has outstanding constitute its capital structure.
- When corporations raise funds from outside investors, they must choose which type of security issue.

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Capital Structure

- The most common choices are financing through equity alone and financing through a combination of debt and equity.
- So V = B + S = D + E

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Capital Structure

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Capital Structure

- Shareholders are interested in maximizing the value of the firm’s shares.
- A key question is: What is the ratio of debt to equity, if any, that maximizes the shareholder’s value?

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Capital Structure

- As it turns out, changes in capital structure benefit shareholders if and only if the value of the firm increases.
- So we concern ourselves with the question of which proportion of debt versus equity maximizes the overall value of the firm.

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Capital Structure

- We assume perfect capital markets in the following analysis:
- Perfect competition
- Equal access to information
- No transaction costs
- No taxes (later we drop this assumption)
- We also assume that the individual can borrow at the same rate as the firm.

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Example: Capital Structure

- We will compare a firm whose capital structure is all equity, with a firm that is identical, except that it has some debt in its capital structure.

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Example: Capital Structure

- Suppose a firm has 1000 shares, a share price of $10, a market value of $10,000, and operating income as described in the table below.
- This income is a perpetuity, and all earnings are paid out as a dividend to investors. Expected income is $1500 and expected return is 15%.

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Example: Capital Structure

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Example: Capital Structure

- Suppose the firm borrows $5,000 at 10% rate of interest and buys back 500 of its shares to create the following new situation: # shares 500, B = $5000, S = $5000, shares value: $10, annual interest: $500

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Example: Capital Structure

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Example: Capital Structure

- Argument that value has increased: If operating income is greater than $1,000 then the expected Return On Equity increases.
- Since we expect operating income of $1,500, leverage must have added value. Shareholders expect 20% ROE with leverage.

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Example: Capital Structure

- Counter-argument: Suppose an investor takes $10 of his/her own money and borrows $10 at 10% interest and invests the $20 to buy 2 shares of the unlevered firm.

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Example: Capital Structure

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Example: Capital Structure

- Note: Investor gets the same result from borrowing personally as he/she gets from investing in the leveraged firm.
- Therefore, the firm is not doing anything by leveraging that the investor could not do on his/her own.
- This implies VL = VU. This is the famous Modigliani-Miller Proposition I.

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Example: Capital Structure

- So leverage increases the expected earnings per share, but not the share price. How can that be?

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Example: Capital Structure

- Leverage also increases the riskiness of the earnings. We must discount those higher expected earnings at a higher discount rate.
- All equity: 1.50/.15 = $10
- Leveraged: 2.00/.20 = $10
- Recall: The value of a firm = the PV of the future cash flows.

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Example: Capital Structure

- If the firm is all equity financed, then VU = C1/(1+r0) + C2/(1+r0)2 + … where r0 is the cost of capital of an all equity financed firm.
- If there is some debt in the capital structure, the cost of capital is given by:

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Example: Capital Structure

- r = [B/(B+S)]rB + [S/(B+S)]rS where rS is the cost of equity capital of the now leveraged firm.
- and VL = C1/(1+r) + C2/(1+r)2 + ...

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Example: Capital Structure

- Since the value of the company doesn’t change with leverage, VL = VU, and so r must equal r0 – that is, r must be constant as debt is added to the capital structure (remember here we are assuming no taxes etc.).

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Example: Capital Structure

- The idea is that as “expensive” equity is replaced with “cheap” debt, the risk to equity increases, as a result of the increased leverage, and so rS increases.
- The increase in rS just balances against the increased fraction of cheaper debt, so that r stays constant.

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Example: Capital Structure

- r0 = cost of capital for the all equity firm = ra = required/expected return on the assets – reflects business risk – not financial leverage. If we solve:
- r0 = [B/(B+S)]rB + [S/(B+S)]rS for rS, we get rS = r0 +[B/S](r0 – rB)

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Example: Capital Structure

- This is Modigliani-Miller Proposition II.
- In our example above, ra = 1500/10,000 = 15%. If B = S = 5000, then:
- rS = 15% + [5000/5000](15% - 10%) = 20%
- Initially the firm was all equity, had 1,000 shares at $10/share and equity worth $10,000
- V = 1500/.15 = (CF/rS) = $10,000

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Example: Capital Structure

- With $5,000 debt at 10% and $5,000 equity, now rS = 20%, up from 15% and:
- V = 500/.10 + 1000/.20 = interest payment/rB + CF/rS = 5,000 + 5,000 = 10,000

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Example: Capital Structure

- Essentially, we split a single cash flow of 1500/year, discounted at 15% into 2 cash flows of 500 and 1000, the former discounted at 10% and the latter discounted at 20%

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