An unlevered ﬁrm has a cost of capital of 14% and earnings before interest and taxes of $150,000. A levered ﬁrm with the same operations and assets has both a book value and a market value of debt
Of $700,000 with a 7% annual coupon. The applicable tax rate is 35%. What is the value of the
Levered ﬁrm?
A) $696,429
B) $907,679
C) $941,429
D) $1,184,929
E) $1,396,429

Question

Quizplus · Accepted Answer

To calculate the value of the levered firm, we need to find the unlevered value and the value of the tax shield.

Unlevered Value:
First, we need to find the unlevered value using the equation:

Unlevered Value = EBIT / Cost of capital

Unlevered Value = $150,000 / 0.14 = $1,071,429

Value of Tax Shield: 
Next, we need to find the tax shield value. The interest expense of the levered firm is $49,000 ($700,000 * 7%). The tax shield value is calculated as:

Tax Shield Value = Interest expense * Tax rate

Tax Shield Value = $49,000 * 0.35 = $17,150

Total Firm Value: 
Now, we can calculate the value of the levered firm using the equation:

Levered Value = Unlevered Value + Present Value of Tax Shield

Levered Value = $1,071,429 + ($17,150 / 0.07) = $1,941,429

Therefore, the value of the levered firm is $941,429 (Option C).

An Unlevered ﬁRm Has a Cost of Capital of 14