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` A company can obtain long-term financing in theform of equity, debt or a combination of both.
` Capital structure is the proportion of debt and
preference and equity shares on a firm¶s balancesheet.
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` Optimal Capital structure is the capital is thecapital structure at which the weighted averagecost of capital is minimum and thereby maximum
value of the firm.
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` The relative proportions of debt, equity and other securities that a firm has outstanding constitute itscapital structure.
` When corporations raise funds from outsideinvestors, they must choose which type of securityissue.
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` The most common choices are financing throughequity alone and financing through a combinationof debt and equity.
` So V = B + S = D + E
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` Shareholders are interested in maximizing thevalue of the firm¶s shares.
` A key question is: What is the ratio of debt to
equity, if any, that maximizes the shareholder¶svalue?
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` As it turns out, changes in capital structure benefitshareholders if and only if the value of the firmincreases.
` So we concern ourselves with the question of which proportion of debt versus equity maximizesthe overall value of the firm.
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` We assume perfect capital markets in thefollowing 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 atthe same rate as the firm.
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` We will compare a firm whose capital structure isall equity, with a firm that is identical, except that ithas some debt in its capital structure.
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` Suppose a firm has 1000 shares, a share price of $10, a market value of $10,000, and operatingincome as described in the table below.
` This income is a perpetuity, and all earnings arepaid out as a dividend to investors. Expectedincome is $1500 and expected return is 15%.
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Outcomes
OperatingIncome
500 1000 1500 2000
Earnings PerShare
0.50 1.00 1.50 2.00
Return OnEquity
5% 10% 15% 20%
Expected!
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` Suppose the firm borrows $5,000 at 10% rate of interest and buys back 500 of its shares to createthe following new situation: # shares 500, B =
$5000, S = $5000, shares value: $10, annualinterest: $500
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Outcomes
Operating
Income
500 1000 1500 2000
Interest 500 500 500 500
Equity Earnings 0 500 1000 1500
Earnings Per
Share
0 1 2 3
ReturnOn
equity
0% 10% 20% 30%
Expected
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` Argument that value has increased: If operatingincome is greater than $1,000 then the expectedReturn On Equity increases.
` Since we expect operating income of $1,500,leverage must have added value. Shareholdersexpect 20% ROE with leverage.
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` Counter-argument: Suppose an investor takes $10of 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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Outcomes
Operating
Income
500 1000 1500 2000
Earnings on 2Shares
1 2 3 4
Interest on $10
at 10%
1 1 1 1
Net Earnings on
2 shares
0 1 2 3
Return on $10
Investment
0 10 20 30
Expected
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` Note: Investor gets the same result fromborrowing personally as he/she gets frominvesting in the leveraged firm.
` Therefore, the firm is not doing anything byleveraging 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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` So leverage increases the expected earnings per share, but not the share price. How can that be?
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` Leverage also increases the riskiness of theearnings. 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 futurecash flows.
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` If the firm is all equity financed, then VU = C1/(1+r 0)+ C2/(1+r 0)
2 + « where r 0 is the cost of capital of an all equity financed firm.
` If there is some debt in the capital structure, thecost of capital is given by:
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` Since the value of the company doesn¶t changewith leverage, VL = VU, and so r must equal r 0 ±that is, r must be constant as debt is added to the
capital structure (remember here we are assumingno taxes etc.).
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` The idea is that as ³expensive´ equity is replacedwith ³cheap´ debt, the risk to equity increases, asa result of the increased leverage, and so r S
increases.` The increase in r S just balances against the
increased fraction of cheaper debt, so that r staysconstant.
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` r 0 = cost of capital for the all equity firm = r a =required/expected return on the assets ± reflectsbusiness risk ± not financial leverage. If we solve:
` r 0 = [B/(B+S)]r B + [S/(B+S)]r S for r S, we get r S = r 0+[B/S](r 0 ± r B)
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` This is Modigliani-Miller Proposition II.
` In our example above, r a = 1500/10,000 = 15%. If B = S = 5000, then:
` r S = 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/r S) = $10,000
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` With $5,000 debt at 10% and $5,000 equity, nowr S = 20%, up from 15% and:
` V = 500/.10 + 1000/.20 = interest payment/r B +
CF/r S = 5,000 + 5,000 = 10,000
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` 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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