Wicked Corp has 20,000 shares trading at $10 each and no debt. Its tax rate is 35%. It will issue $100,000 in perpetual debt and use the proceeds to repurchase shares. Corporate taxes and bankruptcy costs are the key market imperfections. Wicked Corp's value after the leveraged recapitalization will increase to $215,000.

Calculate the expected financial distress cost (at the new debt level) per share outstanding when the firm announces the recapitalization.

Question

Wicked Corp has 20,000 shares trading at $10 each and no debt. Its tax rate is 35%. It will issue $100,000 in perpetual debt and use the proceeds to repurchase shares. Corporate taxes and bankruptcy costs are the key market imperfections. Wicked Corp's value after the leveraged recapitalization will increase to $215,000.

Calculate the expected financial distress cost (at the new debt level) per share outstanding when the firm announces the recapitalization.

BlackTom AI · Accepted Answer

We start by clearly restating what is given and what is being asked.
- The firm Wicked Corp has 20,000 shares at $10 each, no debt, so pre-announcement equity value is 200,000 and there is no distress cost yet.
- It will issue 100,000 in perpetual debt and use the proceeds to repurchase shares. After the recapitalization, the firm’s value is 215,000.
- We are asked to calculate the expected financial distress cost (at the new debt level) per share outstanding when the firm announces the recapitalization.

Next, translate the leveraged recapitalization into the standard decomposition: the change in firm value from leverage equals the PV of the tax shield from debt minus the expected distress costs.
- The tax shield from debt is tax rate times debt level, assumed here to be perpetual, so PV of the tax shield = 0.35 × 100,000 = 35,000.
- The overall value increase from leverage is final value minus initial value = 215,000 − 200,000 = 15,000.
- Therefore, the expected distress costs must satisfy: PV(distress) = PV(tax shield) − (increase in value) = 35,000 − 15,000 = 20,000.

Now determine per-share distress cost at the time of the announcement.
- Before the recap, there are 20,000 shares outstanding.
- The total expected distress cost is 20,000 (as computed above).
- Distress cost per share at the announcement = total distress cost / number of shares outstanding = 20,000 / 20,000 = 1.

To recap the reasoning in a compact form: the levered value increase (15,000) is less than the tax shield (35,000) because part of the tax shield is offset by expected distress costs; solving 35,000 − distress = 15,000 gives distress = 20,000. Dividing that by the original 20,000 shares yields a per-share distress cost of 1.00.

Key checks and potential pitfalls:
- Ensure you used the correct baseline for “shares outstanding” when computing per-share distress cost (the announcement moment uses the 20,000 shares, not the post-buyback 10,000).
- The assumption that the tax shield is valued at 35,000 hinges on perpetual debt and a stable tax rate; if debt were not perpetual or market conditions changed, the PV of the tax shield could differ.
- If the problem instead asked for distress cost per share after repurchase, you would divide by 10,000, yielding 2.00, but that is not the requested metric here.

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