Question

Gulf Shores Inn is comparing two separate capital structures. The first structure consists of 300,000 shares of stock and no debt. The second structure consists of 252,000 shares of stock and $1.78 million of debt. What is the price per share of equity?

Multiple choice

$42.38

$47.92

$38.85

$45.64

$37.08

Answer 1

Answer is $37.08

Plan I:

Number of shares = 300,000

Plan II:

Number of shares = 252,000
Debt = $1,780,000

Price per share = Debt under Plan II / (Number of shares under Plan I - Number of shares under Plan II)
Price per share = $1,780,000 / (300,000 - 252,000)
Price per share = $1,780,000 / 48,000
Price per share = $37.08

So, price per share of equity is $37.08

Answer 2

Calculation :-

1. Understand the Problem:

• Structure 1: 300,000 shares + $0 debt.

• Structure 2: 252,000 shares + $1.78 million debt.

• Gulf Shores Inn is comparing two capital structures:

• We need to find the price per share of equity.

• 
  

2. Key Insight:

• The value of the firm (total equity + debt) should be the same regardless of capital structure (assuming no taxes/bankruptcy costs).

• So, the equity value under Structure 1 = equity value under Structure 2 + debt.

• 
  

3. Set Up the Equation:
   Let $P$ = price per share.

   Since both represent the same firm:

   $$300,000P=252,000P+1,780,000$$

• Structure 1 Equity Value: $300,000\times P$.

• Structure 2 Equity Value + Debt: $252,000\times P+\mathrm{\$}1,780,000$.

• 
  

5. Solve for $P$:
   Subtract $252,000P$ from both sides:

   $$48,000P=1,780,000$$

   Divide both sides by 48,000:

   $$P=\frac{1,780,000}{48,000}=37.08$$

---

Conclusion:

The price per share is $37.08, matching the last option