To determine the share price after the share repurchase, we need to go through the following steps.

1. Initial Calculation

We are given the following dataTo determine the share price after the share repurchase, we need to go through the following steps.

1. Initial Calculation

We are given the following

• Enterprise Value (EV): $390 million
• Excess Cash: $115 million
• Shares Outstanding: 15 million shares
• No Debt

Enterprise Value (EV) represents the market value of the firm’s operating assets and excludes excess cash. When the firm uses the excess cash to repurchase shares, the cash is no longer part of the company's value.

So, the current total firm value (including cash) is: $\text{Total Firm Value} = \text{EV} + \text{Excess Cash} = 390 + 115 = 505 \text{ million dollars}.$

The current share price before the repurchase can be calculated as: $\text{Current Share Price} = \frac{\text{Total Firm Value}}{\text{Shares Outstanding}} = \frac{505}{15} \approx 33.67 \text{ dollars per share}.$

2. Repurchase of Shares

The company will use its $115 million of excess cash to repurchase shares. The number of shares repurchased can be found by dividing the total cash available by the current share price:

$\text{Shares Repurchased} = \frac{115}{33.67} \approx 3.42 \text{ million shares}.$

After the repurchase, the remaining shares outstanding will be: $\text{Remaining Shares} = 15 - 3.42 = 11.58 \text{ million shares}.$

3. Share Price After the Enterprise Value Changes

Now, we need to calculate the share price after the repurchase based on two different enterprise values (EVs):

a. If the enterprise value goes up to $590 million:

After the share repurchase, the firm no longer holds excess cash, so the total firm value is just the enterprise value: $\text{New Total Firm Value} = 590 \text{ million dollars}.$ The new share price will be: $\text{New Share Price} = \frac{590}{11.58} \approx 50.95 \text{ dollars per share}.$

b. If the enterprise value declines to $190 million:

Similarly, the new total firm value is: $\text{New Total Firm Value} = 190 \text{ million dollars}.$ The new share price will be: $\text{New Share Price} = \frac{190}{11.58} \approx 16.41 \text{ dollars per share}.$

Final Answers:

• Part 1: If the enterprise value increases to $590 million, the new share price will be $50.95.
• Part 2: If the enterprise value declines to $190 million, the new share price will be $16.41.

Would you like more details on any step, or have any questions?

Here are 5 related questions to deepen your understanding:

1. How does enterprise value relate to share price in general?
2. Why is excess cash subtracted from the firm's EV in valuation?
3. What factors might cause AMCAMC's enterprise value to change so significantly?
4. How would the calculations change if the firm had debt?
5. What are the risks of a share repurchase in this context?

Tip: Always double-check if the EV includes or excludes cash before performing calculations related to share price.