Question

Mega Skate company is focused on maximizing shareholder value. They would like to recapitalize and issue more debt to repurchase common stock. They are considering two alternative capital structures. Use the information provided to complete the calculations.

Their current levered beta is 1.1 and their current capital structure is 10% debt and 90% equity. Their current cost of debt is 7.75%.

Their effective tax rate is 25%.The yield on a 20-year Treasury bond is 2.59%. The expected return on the stock market is 8.09%.

Possible alternative structures (D/E)	Cost of debt (rd)
25%/75%	8.0%
35%/65%	8.5%

1. Find the levered beta for each proposed capital structure given here. Note that the company already has debt in their capital structure, so the existing company beta is a levered beta. You first need to solve for the unlevered beta using the current b_L and current capital structure.
2. Calculate the cost of equity for each capital structure (current and two proposed)
3. Calculate the cost of capital for each capital structure (current and two proposed)
4. Which is the optimal capital structure (consider the current capital structure as well as the proposed structures). Why is this structure optimal (the best)?

Answer 1

a)As Unlevered Beta = Levered Beta / (1+ (1-t)*D/E) from MM proposition of Capital Structure

Unlevered beta of the company = 1.1 / (1+(1-0.25)*10%/90%) =1.015385

Levered Beta for D/E (25%/75%) = Unlevered Beta *(1+ (1-t)*D/E)

=1.015385* (1+(1-0.25)*25%/75%)

=1.269231

Levered Beta for D/E (35%/65%) = Unlevered Beta *(1+ (1-t)*D/E)

=1.015385* (1+(1-0.25)*35%/65%)

=1.425444

b) From Capital Assets pricing model

Cost of equity = Risk free rate + Beta* (Market return - Risk free rate)

Here, Risk free rate = 20 year treasury bond rate = 2.59%

Market Return = 8.09%

For Original structure with D/E (10%/90%)

Cost of equity = Risk free rate + Beta* (Market return - Risk free rate)

= 2.59%+ 1.1* (8.09%-2.59%)

=8.64%

For structure with D/E (25%/75%)

Cost of equity = Risk free rate + Beta* (Market return - Risk free rate)

= 2.59%+ 1.269231* (8.09%-2.59%)

=9.57%

For structure with D/E (35%/65%)

Cost of equity = Risk free rate + Beta* (Market return - Risk free rate)

= 2.59%+ 1.425444* (8.09%-2.59%)

=10.43%

c) Cost of Capital (WACC) for original structure

= weight of debt*cost of debt*(1-tax rate) + weight of equity * cost of equity

= 0.1*7.75%*(1-0.25) + 0.9*8.64%

=8.3573%

Cost of Capital (WACC) for structure with D/E (25%/75%)

= weight of debt*cost of debt*(1-tax rate) + weight of equity * cost of equity

= 0.25*8%*(1-0.25) + 0.75*9.57%

=8.6775%

Cost of Capital (WACC) for structure with D/E (35%/65%)

= weight of debt*cost of debt*(1-tax rate) + weight of equity * cost of equity

= 0.35*8.5%*(1-0.25) + 0.65*10.43%

=9.0108%

d) The optimal capital structure is the one which has the least cost of capital, thereby maximising the firm value

In this case, as the cost of capital is minimum for the original capital structure with D/E (10%/90%) , the Original capital structure is the best (optimal)