# MM cost of equity

Why is the cost of equity different from the unlevered cost of capital i.e. cost of capital if company is 100% equity financed? Also is there an explanation of how we arrive at the formula for cost of equity?
Schweser notes said you could find it using the Wacc formula but I can’t seem to work it out.

It isn’t.

Things behave as they’re supposed to behave.

WACC = \frac{D(1 - T)}{D(1 - T) + E} \times k_d + \frac{E}{D(1-T)+E} \times k_e

Dividing both sides by \frac{E}{D(1-T)+E} :

\frac{D(1-T)+E}{E} \times WACC = \frac{D(1-T)}{E} \times k_d + k_e

k_e = \frac{D(1-T)+E}{E} \times WACC - \frac{D(1 - T)}{E} \times k_d

k_e = \frac{D(1-T)}{E} \times WACC + \frac{E}{E} \times WACC - \frac{D(1 - T)}{E} \times k_d

k_e = WACC + \frac{D}{E} \times (WACC - k_d) \times (1 - T)

When \frac{D}{E} = 0 , then k_e = k_0

k_0 = WACC + 0 \times (WACC - k_d) \times (1 - T)

WACC = k_0

Finally:

k_e = k_0 + \frac{D}{E} \times (k_0 - k_d) \times (1 - T)