Question

r_{equity =} r_unlevered + (r_unlevered - r_debt) * debt/equity

r_equity = 15%

r_debt = 5%

debt/equity ratio = 1

How do I slove this for r_unlevered? I am confused by the algebra.

Answer 1

_{equity =unlevered} + (_unlevered - _debt) * debt/equity

15%= UNLEVERED +(UNLEVERED-5%)*1

15% - UNLEVERED =(UNLEVERED-5%)*1

15% -UNLEVERED =UNLEVERED-5%

15%- 2UNLEVERED =-5%

-2UNLEVERED =-15%- 5%

-2UNLEVERED = - 20%

-UNLEVERED = -20%/2

UNLEVERED= 10%