Beta - Levered & Unlevered


The following is the answer for one of the mock exam questions that i was working on. Would appreciate if somebody could explain to me why the levered beta formula used here not unlevered 0.9 x 1+(1-0.40)130,000/225000 , the tax rate was 40% . Also, why was it not unlevered beta used to calculate the cost of equity ?

In line with the assumptions made in McAlmont’s first comment, calculate the discount rate which should be used to calculate the NPV of the proposed new production facility.

McAlmont’s first comment: I believe that the unlevered beta of companies in our industry to be 0.9 and that any new project would be financed in such a way as to maintain our current capital structure.


Bluetonic’s levered beta = 0.9 x [(1 + 130,000 / 225,000)] = 1.42

Cost of equity = 0.03 + 1.42 x 0.09 = 15.78%

Cost of debt = 6%

WACC = 130 / (130+225) x 6% x (1 – 0.4) + 225 / (130+225) x 15.78% = 11.32%

The formula they use in Level I includes the tax rate while the formula they use in Level II does not.

(There is, or, at least, there used to be, a footnote in Level II that had the formula with the tax rate included.)