Let's break down the problem step by step and calculate the share price after the repurchase in both scenarios.

1. Initial Setup:

• Enterprise Value (EV): $380 million
• Excess Cash: $130 million
• Number of shares outstanding: 10 million
• No debt

AMC's enterprise value is the total value of the business, excluding cash and debt. The market capitalization of the company can be found by subtracting the excess cash from the enterprise value. This will give us the value of equity, which, divided by the number of shares, gives the share price.

2. Current Share Price:

The current market capitalization (before the repurchase) is:

$\text{Market Cap} = \text{EV} - \text{Excess Cash} = 380 \, \text{million} - 130 \, \text{million} = 250 \, \text{million}$

Now, to find the current share price, we divide the market capitalization by the number of shares outstanding:

$\text{Share Price} = \frac{\text{Market Cap}}{\text{Shares Outstanding}} = \frac{250 \, \text{million}}{10 \, \text{million}} = 25 \, \text{per share}$

3. Repurchase of Shares:

AMC is using its $130 million in excess cash to repurchase shares. The share price at the time of the repurchase is $25, so the number of shares they can buy back is:

$\text{Shares Repurchased} = \frac{130 \, \text{million}}{25} = 5.2 \, \text{million shares}$

So, after the repurchase, the remaining number of shares will be:

$\text{Remaining Shares} = 10 \, \text{million} - 5.2 \, \text{million} = 4.8 \, \text{million shares}$

4. After the Repurchase:

Now, we consider two scenarios for AMC's enterprise value after the repurchase: it could increase to $580 million or decrease to $180 million.

Scenario 1: EV increases to $580 million

The new market capitalization (after the repurchase and increase in EV) is:

$\text{Market Cap} = \text{EV} = 580 \, \text{million}$

Now, to find the new share price, we divide the market capitalization by the remaining number of shares:

$\text{New Share Price} = \frac{580 \, \text{million}}{4.8 \, \text{million shares}} = 120.83 \, \text{per share}$

Scenario 2: EV decreases to $180 million

The new market capitalization (after the repurchase and decrease in EV) is:

$\text{Market Cap} = \text{EV} = 180 \, \text{million}$

Now, to find the new share price, we divide the market capitalization by the remaining number of shares:

$\text{New Share Price} = \frac{180 \, \text{million}}{4.8 \, \text{million shares}} = 37.50 \, \text{per share}$

Final Answer:

1. If EV increases to $580 million: The share price will be $120.83.
2. If EV decreases to $180 million: The share price will be $37.50.

Would you like to explore any particular detail further?

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Follow-up Questions:

1. What is the relationship between enterprise value and market capitalization?
2. How does a share repurchase impact the share price?
3. Why does reducing the number of shares affect the share price post-repurchase?
4. What other factors could influence the post-repurchase share price aside from changes in enterprise value?
5. What are the advantages and disadvantages of a company using excess cash for a share repurchase?

Tip:

A share repurchase reduces the number of outstanding shares, which generally increases the earnings per share (EPS) and often leads to a higher share price if the company maintains or grows its value.