Solution:-
(a) Since investors are ready to buy 25% of the firm for $5.5 million, it means that value of the firm is as follows:
Market value of the firm= $5.5m/25%= $22 million
(b) A per Modigliani Miller (MM) theorem, the total value of a firm is not impacted by change in capital structure as the market value of a firm is dependent on the earnings potential of a business and not how the assets have been financed. Therefore, in this case the total value of the firm would still be $22 million.
Total value of firm= $22 million
Value of equity + value of debt = 22,000,000
Value of equity + 400,000= 22,000,000
Value of equity= $21,600,000 or $21.6 million
% of equity required to be sold to raise $5.1 million= ($5.1m/$21.6m)*100= 23.61%
(c) % stake remaining for entrepreneur in case (a)= 100%-25%= 75%
% stake remaining for entrepreneur in case (b)= 100%-23.61%= 76.39%
Value of entrepreneur's stake in case (a) = $22,000,000*75%= $16,500,000 or $16.5 million
Value of entrepreneur's stake in case (b) = $22,000,000*76.39%= $16,805,800 or $16.81 million
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