Question

BB.co is a construction company that at the moment was fully financed with assets. The new manager suggests that shareholders include debt in their financial structure as this increases the value of the company. The company has an EBIT of $100 each year. Their equity is valued (that is, the price of their shares) so that their expected return is 10% and the corporate tax rate is 20%. The company can indebt at the risk-free rate, 4%. Suppose the EBIT is perpetual and a Modigliani-Miller world with taxes. How much would the value of the company increase if BB.co is indebted permanently so that its debt represents 50% of the value of the assets of the company?

Answer 1

Value of the unlevered company will be equal to present value of its unlevered after tax-earnings, discounted at its unlevered cost of equity:

After tax earnings = 100 ( 1 - 0.2) = 80

Since the company is fully financed by equity, the expected return of 10% will also be it's cost of capital.

Value = 80 / 0.1

Value of unlevered company = 800

Cost of equity after introducing debt:

Cost of levered equity = cost of unlevered equity + ( cost of unlevered equity - cost of debt ) ( 1 - tax) debt / equity

Cost of levered equity = 0.10 + ( 0.10 - 0.04) ( 1 - 0.2) ( 0.5 )

Cost of levered equity = 0.10 + 0.024

Cost of levered equity = 0.124 or 12.4%

After tax cost of debt = 0.04 ( 1 - 0.2)

After tax cost of debt = 0.032 or 3.2%

Weighted average cost of capital = weight of debt * cost of debt + weight of equity * cost of equity

Weighted average cost of capital = 0.5 * 0.032 + 0.5 * 0.124

Weighted average cost of capital = 0.016 + 0.062

Weighted average cost of capital = 0.078 or 7.8%

Value of levered firm = Earnings after tax / WACC

Value of levered firm = 80 / 0.078

Value of levered firm = 1,025.64

Increase in the value of company = 1,025.64 - 800 = 225.64