Question

Assume that capital markets are perfect. A firm finances its operations via $50 million in stock with required return of 15% and $40 million in bonds with a required return of 9%. Assuming that the firm could issue $10 million in additional bonds at 9% and use the proceeds to reture $10 million worth of equity, what would happen to the firm’s WACC ? What would happen to the required return on the company’s stock ?

Answer 1

Using MM Proposition Formula II.

r_L = r_A + (r_A -r_D )*D/E
where,
r_L = required return on equity = 0.15
r_A = weighted average cost of capital (wacc)
r_D = required return on debt = 0.09
D/E = 40/50 = 4/5

Putting in the equation
0.15 = r_A + (r_A - 0.09) * 4/5
r_{A +} 4/5r_A - 0.072 = 0.15
1.8 r_A = 0.222
r_A = 0.1233
    = 12.33%

wacc of the firm would be 12.33%

To find out the required return on stock we will use the same formula
r_L = r_A + (r_A -r_D )*D/E
now D/E = 50/40 = 5/4
r_L = 0.1233 + (0.1233 - 0.09) * 5/4
    = 0.1233 + 0.04167
    = 16.5%

The new cost of equity would be 16.5%. Hence, the addition of $10 million of debt would cause the equity cost to rise from 15% to 16.5%.