We need to determine how much the earnings per share (EPS) will change under the proposed debt financing plan if the economy undergoes a strong expansion. Let's walk through the problem step by step.

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1. Calculate EBIT under different scenarios

• Normal EBIT: $18,000
• Strong expansion EBIT: $18,000 \times (1 + 0.22) = 21,960$
• Recession EBIT: $18,000 \times (1 - 0.35) = 11,700$

Now, let's compute the effect of the proposed debt issue.

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2. Interest Payment on the New Debt

• New debt issue: $50,000
• Interest rate: 7.4%

So, the annual interest expense will be:
$50,000 \times 0.074 = 3,700$

This interest expense will affect the EBIT under the new plan. Now, let's compute the Net Income (after-tax profit) under a strong expansion.

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3. Net Income with and without Debt

Case 1: Strong Expansion (No Debt)

$\text{EBIT} = 21,960$ Since there is no debt, EBIT = EBT (Earnings Before Taxes).
So, the tax payment will be:
$21,960 \times 0.21 = 4,611.60$ $\text{Net Income (without debt)} = 21,960 - 4,611.60 = 17,348.40$

Case 2: Strong Expansion (With Debt)

If the company issues debt, we must subtract the interest expense from EBIT: $\text{EBT} = 21,960 - 3,700 = 18,260$ Now, the tax payment will be: $18,260 \times 0.21 = 3,834.60$ $\text{Net Income (with debt)} = 18,260 - 3,834.60 = 14,425.40$

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4. Calculate EPS with and without Debt

• Current shares outstanding: 5,000 shares
• New shares after debt repurchase:
  The company will use the $50,000 debt to repurchase shares.
  $\text{Repurchase price per share} = \frac{168,000}{5,000} = 33.60$ The number of shares repurchased will be:
  $\frac{50,000}{33.60} \approx 1,488.10$ So, the new number of shares after the repurchase will be:
  $5,000 - 1,488.10 = 3,511.90$

EPS (without debt)

$\text{EPS (without debt)} = \frac{17,348.40}{5,000} = 3.47$

EPS (with debt)

$\text{EPS (with debt)} = \frac{14,425.40}{3,511.90} \approx 4.11$

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5. Percentage Change in EPS

The percentage change in EPS due to the debt issue under a strong expansion is: $\text{Percentage Change in EPS} = \frac{4.11 - 3.47}{3.47} \times 100 \approx 18.45\%$

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Final Answer

The percentage change in EPS under the new debt structure during a strong expansion will be approximately:

$\boxed{18.45\%}$

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Do you have any questions or need further details?

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Related Questions

1. What will be the EPS change if the economy experiences a recession?
2. How does the company's leverage affect the risk to shareholders?
3. What is the break-even EBIT where EPS is the same with and without debt?
4. What is the impact of different tax rates on EPS?
5. How many shares should the company repurchase to achieve a specific EPS target?

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Tip

When companies introduce debt, the financial leverage amplifies both gains and losses. This means that EPS increases more in good times, but can decline sharply in bad times.