Land Corp operates in a world with corporate taxes (only capital markets imperfection). It has 100 shares worth $30 each and $1,000 in perpetual risk-free debt; it faces a 40% tax rate. The firm will issue an additional $1,500 in perpetual risk-free debt at an interest rate of 5% and use the proceeds to repurchase shares.

Upon announcement of the transaction, the firm’s stock return (in % with one decimal) is:

Question

Land Corp operates in a world with corporate taxes (only capital markets imperfection). It has 100 shares worth $30 each and $1,000 in perpetual risk-free debt; it faces a 40% tax rate. The firm will issue an additional $1,500 in perpetual risk-free debt at an interest rate of 5% and use the proceeds to repurchase shares.

Upon announcement of the transaction, the firm’s stock return (in % with one decimal) is:

BlackTom AI · Accepted Answer

Restating the problem: Land Corp currently has 100 shares at $30 each, so equity market value is $3,000. It has $1,000 of perpetual risk-free debt and faces a 40% corporate tax rate. The firm plans to issue an additional $1,500 of perpetual debt (risk-free, 5% interest) and use the proceeds to repurchase shares. We are asked for the firm’s stock return on announcement, in percent (one decimal).

Step 1: Understand the tax-advantaged value change from adding debt. In a world with corporate taxes, levered value increases by the PV of the tax shield on debt. If the total debt increases by 1,500 (from 1,000 to 2,500), the incremental tax shield is 0.40 × 1,500 = 600. Therefore, the overall value of the firm (V_L) should rise by 600 due to the additional debt, all else equal, assuming perpetual debt and no other market frictions.

Step 2: Compute the unlevered firm value to anchor numbers. Let V_U be the value of the firm if it had no debt. With the initial capital structure (D = 1,000; E = 3,000), levered value satisfies V_L = V_U + tax shield. The initial tax shield is 0.40 × 1,000 = 400, and V_L initially equals E + D = 3,000 + 1,000 = 4,000. Therefore, 4,000 = V_U + 400, so V_U = 3,600.

Step 3: Determine the new levered value after the debt increase. After issuing an additional 1,500 of debt, total debt becomes 2,500. The new tax shield is 0.40 × 2,500 = 1,000. The levered firm value would then be V_L,new = V_U + tax shield,new = 3,600 + 1,000 = 4,600.

Step 4: Determine the implied equity value after recapitalization. The new equity value is E_new = V_L,new − D_new = 4,600 − 2,500 = 2,100.

Step 5: Link equity value to the number of shares outstanding after the share repurchase. The company uses the 1,500 of debt to repurchase shares. At the announcement, if the price per share is P_0 = $30, the number of shares repurchased would be 1,500 / 30 = 50 shares. Beginning with 100 shares, there would be 50 shares remaining after the repurchase. The post-announcement equity value is 2,100, so the price per remaining share is P_1 = E_new / [remaining shares] = 2,100 / 50 = $42.

Step 6: Calculate the stock return. The percentage return on the stock from the announcement is (P_1 − P_0) / P_0 = (42 − 30) / 30 = 12 / 30 = 0.40, i.e., 40.0%.

Step 7: Reconcile with the stated answer. If the problem’s expected result is −16.7%, that would imply a post-announcement price of P_1 = P_0 × (1 − 0.167) ≈ 30 × 0.833 ≈ $25. This would correspond to an equity value after recap of E_new ≈ 25 × 50 = 1,250, which would imply a levered firm value of V_L,new ≈ D_new + E_new = 2,500 + 1,250 = 3,750. This is inconsistent with the standard tax-shield calculation above (which yields V_L,new = 4,600 and E_new = 2,100). Therefore, under the conventional two-step valuation with a perpetual tax shield on debt and the stated amounts, the mathematically consistent stock return from the announcement is 40.0%. The −16.7% figure would require a different interpretation or an alternative set of assumptions about pricing, taxes, or the treatment of the tax shield.

Summary of the key logic points:
- Debt increases by 1,500, creating an incremental tax shield of 0.40 × 1,500 = 600, increasing levered value by 600.
- With V_U determined as 3,600 from the initial structure, V_L,new becomes 4,600, so E_new = 2,100 after the recapitalization.
- Repurchasing 1,500 of debt with 1,500 of cash (effectively financed by debt) leaves 50 shares if the initial price is $30; post-recapitalization price implied by equity value is $42, yielding a 40.0% return.
- The −16.7% result would require alternative assumptions not aligned with the standard tax-shield framework provided in the problem statement.

类似问题

Which of the following statements best reflects the key insight of the M&M Proposition (without taxes)?

In a world with perfect capital markets, a firm that issues a large amount debt to finance a share repurchase will ultimately boost its EPS and reduce its post-transaction market capitalization, but will not affect its stock price.

In a world with corporate taxes (only capital markets imperfection), a levered firm will issue equity to repay some of its debt. Indicate which of the following statements is correct:

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