Question

Assume that two firms, A and B, are identical in all respects except that Firm A is debt free and Firm B has a capital structure that is 50 percent debt and 50 percent equity by market value. Further suppose that the assumptions of the Modigliani & Miller capital structure irrelevance proposition holds (i.e. no taxes or transactions costs, no bankruptcy costs, etc.) and that each firm will have net operating income (EBIT) of $800,000. The required return on assets, r, for these firms is 12.5 percent and the debt yields 5 percent.

Required:

Calculate the following for both Firm A & B:

a. total firm value

b. market value of debt and equity

c. required return on equity.

Answer 1

Solution :-

Return on Assets ( ROA ) = 12.5%

ROA = EBIT / Total Assets

12.5% = 800,000 / Total Assets

Total Assets = $6,400,000

(A)

Value of total Firm = $6,400,000

Firm A Value = $6,400,000

As per MM theory , Value of Levered Firm = Value of Un levered Firm , If there are no taxes

Therefore value of Firm B = $6,400,000

(B)

Market Value of Equity of Firm A = $6,400,000 ( As no debt )

Now in case of Firm B , Equity - 50% and Debt - 50%

Market Value of Equity = $6,400,000 * 50% = $3,200,000

Market Value of Debt = $6,400,000 * 50% = $3,200,000

(C)

Return of Equity ( Firm A ) = EBIT / Equity Value = $800,000 / $6,400,000 = 12.5%

As per MM Approach

ROE ( Levered ) = ROE ( Unlevered ) + ( D/E ) [ ROE unlevered - Return on Debt ]

= 12.5% + [ $3,200,000 / $3,200,000 ] * ( 12.5% - 5% )

= 12.5% + 7.5%

= 20%

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