# Cost of Capital Questions by zee15908

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```									Chapter 10: Cost of Capital.

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INTRODUCTION
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One view of the influence of leverage on the cost of capital is that presented by
Modigliani and Miller. In their view, the cost of debt does not rise with leverage,
and the cost of equity rises linearly as depicted by their Proposition II. Under this
formulation (which assumes no bankruptcy costs), the cost of capital declines
with leverage (and the value of the firm rises). An alternative view holds that with
increased leverage, both debt and equity take on increasing risk (positive
bankruptcy costs are assumed). Under this theory, the cost of capital falls up to
some critical degree of leverage, then begins to rise. Under this view, there is an
optimal capital structure which minimizes the firm's cost of capital (and
maximizes value).

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298d970f-5006-43fb-bccf-99be8e9b8d7d.xls
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QUESTIONS
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1) Assume a world of Modigliani and Miller where the after-tax debt cost does not change with
leverage because there are no bankruptcy costs, and the equity cost function is a straight line
reflecting the equation of Modigliani and Miller's Proposition II, which is
ks = ku +(ku – kb)(B/S)(1-T).

a) What happens to the cost of equity as the debt-to-firm-value ratio at market value, B/V,
rises from 0 to 60 percent in increments of 10 percent? (The before-tax cost of debt is
10 percent, the unlevered cost of equity is 12 percent, and the tax rate is 40 percent.)
HINT: Translate debt-to-value ratios into debt to equity ratios for use in MM Proposition
II. Also view this graphically.

b) What happens to the weighted cost of capital (WCC) as B/V rises? Is there a minimum
weighted cost of capital? (See graph.) What does this imply for the value of the firm?
For optimum leverage?

2) An alternative to the MM world postulates that the cost of debt rises with leverage, and that
the cost of equity rises with leverage curvilinearly, not as a straight line as implied by MM
Proposition II. The following figures reflect this alternative:

Before-Tax
Leverage         Cost of Debt      Cost of Equity
0-10%             10.00%            12.00%
10-20%            10.20%            12.30%
20-30%            10.80%            12.75%
30-40%            11.00%            13.29%
40-50%            12.00%            15.00%
50-60%            16.00%            20.00%
Over 60%           27.00%            30.00%

a) Compare the weighted cost of capital for each alternative capital structure under the
Modigliani-Miller assumptions to the weighted cost of capital with bankruptcy costs.

b) Is there a minimum cost of capital in the non-MM world? What is the optimum capital
structure?

3) Now you are free to change any of the decision variables: Leverage ratio, initial cost of debt,
unlevered cost of equity, tax rate. Note, however, that the costs of debt and equity in the
world with bankruptcy costs are dependent upon the leverage ratio and cannot be changed
independently.

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298d970f-5006-43fb-bccf-99be8e9b8d7d.xls
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COSTS OF CAPITAL UNDER MODIGLIANI-MILLER ASSUMPTIONS
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INPUTS
Leverage (Debt/Assets = B/V)                         80.0%      (Debt/Equity = B/S = 400.0% )
Tax rate                                             40.0%
Unlevered cost of debt (kb )                         10.0%
Unlevered cost of equity (ku )                       12.0%

CALCULATIONS

ks = ku + ( ku – kb ) ( B/S ) ( 1 – T )

= 0.120 + ( 0.120 – 0.100 ) ( 4.000 ) ( 1 – 0.40 ) =     16.80%

WCC = k = kb ( 1 – T ) ( B/V ) + (S/V) ( k s )

= 0.100 ( 1 – 0.40 ) ( 0.800 ) + ( 0.200 ) ( 0.168 ) =   8.16%

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298d970f-5006-43fb-bccf-99be8e9b8d7d.xls
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COMPARISON OF MODIGLIANI-MILLER (MM) & WORLD WITH BANKRUPTCY
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Leverage (Debt/Assets = B/V)                    80%
Tax rate                                        40%

MODIGLIANI-MILLER WORLD:
kb =                                  10.0%
ks =                                 16.8%

Weighted cost of capital = k =       8.16%

WORLD WITH BANKRUPTCY COSTS:
kb =                                    27.0%
ks =                                 30.0%

WCC = k = kb ( 1 – T ) ( B/V ) + (S/V) ( ks )
= 0.270 ( 1 – 0.40 ) ( 0.800 ) + ( 0.200 ) ( 0.300 ) = 18.96%

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298d970f-5006-43fb-bccf-99be8e9b8d7d.xls
GRAPH A: M-M COSTS OF CAPITAL

25%

20%

15%
Costs of Capital

10%

5%

0%
0%   10%   20%   30%         40%           50%     60%        70%          80%           90%
Leverage (B/V)

After-Tax Debt     Equity   WCC

298d970f-5006-43fb-bccf-99be8e9b8d7d.xls
GRAPH B: COSTS OF CAPITAL--BANKRUPTCY
35%

30%

25%
Costs of Capital

20%

15%

10%

5%

0%
0%   10%     20%                    30%            40%               50%                 60%

Leverage
After-Tax Debt         Equity   WCC

298d970f-5006-43fb-bccf-99be8e9b8d7d.xls

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