Galaxy Corp operates in a world with corporate taxes and financial distress costs (only capital markets imperfections). It has 200 shares trading at $25 each and $1,500 in perpetual debt with an interest rate of 6%. Its tax rate is 35%. At its current debt level, the present value of the expected financial distress costs is $200. The firm will issue additional perpetual debt, also with an interest rate of 6%, and use the proceeds to repurchase shares. After this recapitalization the firm will have a total of $2,500 in debt and a total present value of expected financial distress costs of $500.

After the recapitalization, the value of the firm (with one decimal) is:

Question

Galaxy Corp operates in a world with corporate taxes and financial distress costs (only capital markets imperfections). It has 200 shares trading at $25 each and $1,500 in perpetual debt with an interest rate of 6%. Its tax rate is 35%. At its current debt level, the present value of the expected financial distress costs is $200. The firm will issue additional perpetual debt, also with an interest rate of 6%, and use the proceeds to repurchase shares. After this recapitalization the firm will have a total of $2,500 in debt and a total present value of expected financial distress costs of $500.

After the recapitalization, the value of the firm (with one decimal) is:

BlackTom AI · Accepted Answer

We start by clearly restating the given setup and the financial pieces involved, so the deduction that follows uses the concrete numbers provided.

- Current situation before recapitalization:
  - Equity value (200 shares × $25) = $5,000
  - Debt = $1,500
  - Present value of financial distress costs = $200
  - Tax rate = 35%
  - The firm’s value with debt can be connected to an unlevered value plus the tax shield from debt minus the present value of distress costs.

- After the recapitalization:
  - New debt level = $2,500 (additional $1,000 of debt is issued to fund the buyback)
  - The discounting assumption for perpetual debt with a 6% rate implies the annual tax shield from debt is Tax rate × Debt, i.e., 0.35 × Debt.
  - New present value of distress costs = $500
  - The firm uses the $1,000 debt proceeds to repurchase shares, which reduces equity accordingly. For a simplified accounting view, the change in equity value due to the buyback can be tied to the debt raised being allocated to repurchases.

Key step: separate out the unlevered firm value (Vu) from the levered value using the tax shield and distress costs.

- Compute Vu (the value of the firm if it had no debt):
  The pre-recapitalization levered value can be written as:
  V_pre = Vu + (Tax shield_pre) − (Distress_costs_pre).
  Here, Tax shield_pre = 0.35 × $1,500 = $525, and Distress_costs_pre = $200.
  The observed V_pre from market values is Equity + Debt = $5,000 + $1,500 = $6,500.
  Therefore:
  6,500 = Vu + 525 − 200
  Vu = 6,500 − 525 + 200 = 6,175.

- Compute V_post (the value after recap):
  Post-recapitalization, Debt = $2,500 and Distress_costs_post = $500. The new tax shield is 0.35 × $2,500 = $875.
  Using the Vu we just found, the levered value post-recap is:
  V_post = Vu + (Tax shield_post) − (Distress_costs_post)
  V_post = 6,175 + 875 − 500 = 6,550.

Interpretation:
- The recapitalization increases the tax shield by moving from $525 to $875 (an increase of $350).
- It also increases the present value of distress costs from $200 to $500 (an increase of $300).
- Net effect on firm value from these two changes is +$350 − $300 = +$50, applied to the original Vu-based structure, yielding V_post = 6,550 when combined with Vu = 6,175.

Additional consistency check:
- If you instead view value directly as Equity + Debt (and treat distress costs as adjustments to value rather than separate cash flows), the repurchase reduces equity by the amount financed ($1,000), while debt rises by $1,000, so the immediate sum E + D remains at $6,500 before accounting for the updated distress costs and tax shield. The updated tax shield (+$350) and updated distress costs (−$300) then adjust this baseline to the same V_post = $6,550 predicted above.

In summary, after the recapitalization, the firm’s value, accounting for the new debt tax shield and the higher distress costs, comes out to $6,550. The effects are driven by the larger tax shield that debt provides and the higher estimated financial distress costs that accompany the bigger debt load. The numbers explicitly show how the debt level, tax rate, and distress costs interact to determine the levered firm value.

COMM_V 370 101-108 2025W1 COMM 370 - 2025W1 - Final - Requires Respondus LockDown Browser

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