Executive Cheese has issued debt with a market value of $100 million and has outstanding 15 million shares with a market price of $10 a share. It now announces that it intends to issue a further $60 million of debt and to use the proceeds to buy back common stock. Debtholders, seeing the extra risk, mark the value of the existing debt down to $70 million.

a-1. Calculate the market price of the stock following the announcement.

To calculate the market price of the stock following the announcement, we need to use the following steps:

1. **Calculate the total value of the firm before the announcement:**

   \[
   \text{Total value of the firm} = \text{Market value of debt} + \text{Market value of equity}
   \]
   \[
   \text{Total value of the firm} = 100\ \text{million (debt)} + (15 \times 10)\ \text{million (equity)} = 100 + 150 = 250\ \text{million}
   \]

2. **Adjust the firm's total value after the announcement:**

   After the announcement, the market value of the debt decreases to $70 million. The new total value of the firm is:

   \[
   \text{New total value of the firm} = \text{New value of debt} + \text{Value of equity}
   \]
   However, the **total firm value remains unchanged**, so it’s still $250 million.

   \[
   \text{Value of equity} = \text{New total value of the firm} - \text{New value of debt}
   \]
   \[
   \text{Value of equity} = 250 - 70 = 180\ \text{million}
   \]

3. **Calculate the number of shares repurchased with the new debt:**

   Executive Cheese raises $60 million in new debt and uses it to repurchase stock at the new market price. Let the new market price of the stock be $ P $. The number of shares repurchased is:

   \[
   \text{Number of shares repurchased} = \frac{60\ \text{million}}{P}
   \]

   After the repurchase, the remaining shares outstanding will be:

   \[
   \text{Remaining shares} = 15 - \frac{60}{P}
   \]

4. **Calculate the new price per share:**

   The total equity value of $180 million is distributed among the remaining shares. Therefore:

   \[
   P = \frac{\text{Total equity value}}{\text{Remaining shares}}
   \]
   \[
   P = \frac{180}{15 - \frac{60}{P}}
   \]

   Multiply through by $ (15 - \frac{60}{P}) $ to eliminate the fraction:

   \[
   P(15 - \frac{60}{P}) = 180
   \]
   \[
   15P - 60 = 180
   \]
   \[
   15P = 240
   \]
   \[
   P = 16
   \]

### Final Answer:

The market price of the stock following the announcement is **$16 per share**.

---

Would you like to see further steps or explanations? Here are five related questions:

1. What would happen to the stock price if debtholders reduced the debt value even further?
2. How is the market price of stock affected by changes in perceived risk?
3. What assumptions are made in this calculation about the efficiency of markets?
4. How would this calculation change if the firm issued equity instead of debt?
5. What is the effect on the firm's weighted average cost of capital (WACC) after the buyback?

**Tip:** Always remember to verify how new financial announcements impact both equity and debt markets simultaneously.

Discover how to calculate the stock price after a debt issuance and stock repurchase. This step-by-step example covers key finance concepts such as market valuation, equity adjustments, and the impact of debt on stock price. Suitable for finance and business students.

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