Question

Determine the expected return on equity for a firm with a WACC of 12%, $500,000 in 9% debt, and $800,000 in equity. Both debt and equity are shown at market values, and the firm pays no taxes. How can the expected return on equity be reduced?

Answer 1

WACC= (E/V × Re) + (D/V × Rd)

• Re = cost of equity
• Rd = cost of debt
• E = market value total equity
• D = market value of total debt
• V = total market value of the company (E + D)

Note = if tax rate is given then it has to be deducted from cost of debt i.e. 9% (1 - tax%) . As in question it is mentioned no taxes so no effect of taxes on cost of debt.

So,

0.12= (800,000/1300,000 × Re) + (500,000/1300,000 × 0.09)

0.12 =(8 × Re/13) + (0.45/13)

_{(13 has been taken common on right hand side and in the next step, it is multiplied to left hand side )}

0.12 × 13 =( 8× Re ) + 0.45

1.56 =(8 × Re) + 0.45

8 × Re = 1.56 - 0.45

8 × Re =1.11

Re= 0.13875

Re= 13.875%

The expected return on equity could be reduced by replacing the debt with equity in the capital structure . If debt were replaced totally with equity , the expected return on equity would reach to 12%.

OR (Another way to calculate)

With no taxes, the expected return on assets equals the WACC.

Expected return on equity = expected return on assets + [debt-equity ratio × (expected return on assets - expected return on debt)]=

=0.12 + [0.625 × (0.12 - 0.09)]

=0.12 +[0.625 × 0.03]

=0.12 + 0.01875

=0.13875

=13.875%