If the assets of the firm with value A as a portfolio of unlevered assets with value UA and debt tax shields with value TX,then the beta of the assets is represented by:

Question

Quizplus · Accepted Answer

The formula for the asset beta with unlevered assets and debt tax shields is: 
βA = βU [1 + (1 - TC) * (D/E)]
where βU is the beta of unlevered assets, TC is the corporate tax rate, and D/E is the debt-to-equity ratio. Since the firm has unlevered assets with value UA and debt tax shields with value TX, we can write:
A = UA + TX
Letting D be the value of debt, we have:
A = UA + TX = UA + TC * D
and
D = TX / TC
Plugging this into the formula for βA, we get:
βA = βU [1 + (1 - TC) * (TX / TC) / E]
βA = βU [1 + TX / (E * TC)]
Choice C is the only one with this formula.

If the Assets of the Firm with Value a as a Portfolio