Question

Company U and company L are identical in every respect except company U is unlevered and company L has $1,000,000 perpetual debt with an interest rate of 6%. Both companies are expecting to have an EBIT of $300,000 in perpetuity and all earnings will be immediately distributed to common shareholders. Company U has a cost of equity of 10%. Assume that all Modigliani and Miller assumptions are satisfied. Calculate the cost of equity for the levered firm according to MM proposition I without taxes.

Answer 1

Answer:

Company U [NO TAXES]

Since there are no taxes and and debt value is zero, therefore, net income for Company U will be $300,000 for perpetuity and its cost of equity is 10%
Therefore, value of the Company U = 300,000/10% = $3,000,000

Company L [NO TAXES]

Since, both the companies are same in every aspect.
Therefore, value for Company L will also be $3,000,000
Debt value = $1,000,000
Therefore, Equity will be $3,000,000 - $1,000,000 = $2,000,000

Debt Equity Ratio = Debt / Equity = 1,000,000 / 2,000,000 = 0.50

Therefore, cost of equity for the levered firm = unlevered equity + debt equity ratio (unlevered equity - debt rate)

i.e. Re = Ra + D/E (Ra-Rd) ; where Ra is the unlevered equity, Rd is the cost of debt

Cost of equity for levered firm = 10% + 0.50 (10%-6%) = 12%