## Question

###### Cargill, Inc. is currently an all equity firm that has 180,000 shares of stock outstanding with...

Cargill, Inc. is currently an all equity firm that has 180,000 shares of stock outstanding with a market price of $50.50 a share. The current cost of equity is 12.6 percent and the tax rate is 25 percent. The firm is considering adding $3.76 million of debt with a coupon rate of 5.5 percent to its capital structure. The debt will be sold at par value. What eis the levered value of the equity? $6,540,000 $6,827,800 $7,142,900 $7,381,470 $6,270,000

## Answers

No of outstanding shares = 180,000

Market Price = $50.50 per share

Value of un-levered firm = 180,000 * 50.50 = $9,090,000

We can solve this problem using the Modigliani-Miller Theorem (M&M):

This theory says that the value of a levered firm is equal to the value of an identical un-levered firm plus the tax benefit it derives from the presence of debt in its capital structure.

Here Tax benefit = Value of Debt * Tax rate

= $3,760,000 * 25%

= $940,000

Therefore, Value of the firm = Value of un-levered firm + Tax benefit

=$9,090,000 + $940,000

= $10,030,000.

Value of levered equity = Value of firm - Value of Debt

= $10,030,000 - $3,760,000

= $ 6,270,000

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