Question

A firm is currently 100% equity financed and the beta of its equity is 0.9. If the firm changes to 20% debt financing and the beta of debt iss 0.1.

What will be the beta of its equity after the change in the capital structure?

Answer 1

To calculate the beta of the equity after the change in capital structure, we can use the following formula:

βE = βU + [βU - βD] × (D/E)

Where:
βE = beta of equity
βU = beta of unlevered firm
βD = beta of debt
D/E = debt-to-equity ratio

First, we need to calculate the unlevered beta of the firm (βU), which represents the risk of the firm's assets without taking into account the effects of financial leverage. We can use the following formula to calculate βU:

βU = βE / [1 + (1 - T) × (D/E)]

Where:
T = tax rate

Since the tax rate is not given in the question, we will assume it to be 35% (a typical corporate tax rate in the US).

βU = 0.9 / [1 + (1 - 0.35) × (0/1)]
βU = 0.9

Next, we can use the given debt-to-equity ratio (D/E) of 20% / 80% = 0.25 to calculate the beta of the levered firm (βL):

βL = βU + [βU - βD] × (D/E)
βL = 0.9 + [0.9 - 0.1] × 0.25
βL = 1.05

Finally, we can use the formula for the beta of equity to find βE:

βE = βL + (βL - βU) × (E/L)
βE = 1.05 + (1.05 - 0.9) × (80%/20%)
βE = 1.20

Therefore, the beta of the equity after the change in the capital structure is 1.20.

the change in the capital structure is 1.20.