Question

U.i designs is an all equity firm that has 40000 shares of stock outstanding. the company has decided to borrow $1 million to buy out the shares of a deceased stockholder who holds 2500 shares. what is the total value of this firm if you ignore taxes

Answer 1

Answer: The value of the firm is $16 million.

For this question we use the Modigliani-Miller Proposition I which states that the value of the firm is same irrespective of the amount of equity and debt in its capital structure, ignoring taxes.

Amount borrowed for buyback = $1m

No. of shares bought back   = 2500

Value per share                    = $$400 = \frac{1000000}{2500}$

Shares outstanding before buyback = 40000 shares

Shares bought back                           =  2500 shares

Shares outstanding after buyback    = $37500 = 40000-2500$  

Next we calculate the value of the firm before and after buyback of shares.

The value of the firm before buyback comprises of only 40000 equity shares. There is no debt. Hence,

$Value of the firm before buyback = Shares outstanding before buyback * Value per share$

$Value of the firm before buyback = 40000 * 400$

$Value of the firm before buyback = 16000000 or 16 million$

The value of the firm after buyback will be

$Value after buyback = (Shares outstanding after buyback * Value per share) + Value of debt$

$Value after buyback = (37500* 400) + 1000000$

$Value after buyback = 15000000 + 1000000$

$Value after buyback = 16000000 or 16 million$

Since value of the firm before and after buyback of shares is the same, we can say that the Modigliani-Miller Proposition I without taxes holds and the value of the firm is $16 million.