Question

If a firm has $15 million of debt with a debt beta of 0.2 and $40 million of equity with an equity beta of 2.2, then the firm's asset beta is ____.

a) 0.5
b) 1.0
c) 1.5
d) 2.0

Answer 1

To find the asset beta, we take the weighted average of the debt and equity betas based on the firm's capital structure. The firm's asset beta, rounded to the nearest option provided, is 1.0.

Step-by-step explanation:

To calculate the firm's asset beta, we use the weighted average of the equity beta and the debt beta, with weights proportional to the firm's equity and debt in its capital structure. Given that the firm has $15 million of debt with a debt beta of 0.2 and $40 million of equity with an equity beta of 2.2, the asset beta is calculated as follows:

Asset Beta = (Debt Value / Total Value) * Debt Beta + (Equity Value / Total Value) * Equity Beta

Plugging in the numbers:

Asset Beta = ($15 million / $55 million) * 0.2 + ($40 million / $55 million) * 2.2

Asset Beta = (0.2727 * 0.2) + (0.7273 * 2.2) = 0.0545 + 1.6001 = 1.6546

Therefore, the closest answer to the firm's asset beta from the options provided is: b) 1.0