My question is about debt and its effect on the value of equity. Say the EBIT is $5,000, tax rate of 25%, and cost of equity of 10% in an all equity firm. The value of the firm is (5,000 * 0.75)/0.10 = $37,500. Lets say now that the company takes on debt worth of $15,000 at a cost of 5% without repurchasing equity. The value of the firm shoud then increase to: Old Value + Cash from Debt + PV of tax shield i.e. 37,500 + 15,000 + (0.25 * 15,000) = $56,250. Hence, equity value shoud be $41,250
The new cost of equity should be: 10 + (10 - 5)(1-0.25)(15,000/41,250) = 11.36%
EBIT - Interest - Tax = 5,000 - 750 - 1,062.5 = $3,187.5
$3,187.5/cost of equity i.e. 3,187.5/0.1136 = 28,058.97 (why is this value not equal to the equity value of 41,250 calculated above). Where am i going wrong.