Question

Suppose that your firm's current unlevered value, V*, is $800,000, and its marginal corporate tax rate is 35 percent. Also, you model the firm's PV of financial distress as a function of its debt level according to the relation: PV of financial distress = 800,000 × ((D/V*)^2). What is the firm's levered value if it issues $200,000 of perpetual debt to buy back stock?

Answer 1

The firm's levered value after issuing $200,000 of perpetual debt and considering the tax shield and PV of financial distress is $820,000.

Step-by-step explanation:

Calculation of Firm's Levered Value

To calculate the firm's levered value, we must consider both the tax shield from debt and the present value (PV) of financial distress costs. The firm's unlevered value (V*) is $800,000 and it plans to issue $200,000 of perpetual debt. The corporate tax rate is 35%, creating a tax shield on the debt. Additionally, the PV of financial distress as a function of the debt ratio (D/V*) is given by the formula: 800,000 × (
`(D/V*)^2`).

First, we calculate the tax shield as follows:
Tax Shield = Debt × Tax Rate = $200,000 × 35% = $70,000.

Next, we calculate the PV of financial distress:
PV of Financial Distress = 800,000 × (
`($200,000/$800,000)^2`) = 800,000 × (
`0.25^2`) = 800,000 × 0.0625 = $50,000.

Finally, we determine the levered value (V) by adding the tax shield to the unlevered value and then subtracting the PV of financial distress:
Levered Value = V* + Tax Shield - PV of Financial Distress = $800,000 + $70,000 - $50,000 = $820,000.

The firm's levered value after issuing $200,000 of debt to buy back stock is $820,000.

Answer 2

$820,000

Step-by-step explanation:

The computation of the firm's levered value is shown below:

Value of levered firm = Value of unlevered firm + Debt × tax -PV (financial distress)

Value of levered firm = $800,000 + $200000 × 35% - $800,0000 × (25%)^2

= $820,000

The 25% is come from

= $200,000 ÷ $800,000

= 25%

We simply applied the above formula to determine the levered value