Uptown Interior Designs is an all equity ﬁrm that has 40,000 shares outstanding.The company has decided to borrow €1 million to buy out the shares of a deceased equityholder who holds 2,500 shares.What is the total value of this ﬁrm
If you ignore taxes?
A)€15.5 million
B)€15.6 million
C)€16.0 million
D)€16.8 million
E)€17.2 million

Question

Quizplus · Accepted Answer

To find the total value of the firm, we need to add the value of the equity and the value of the debt. 
Number of shares outstanding = 40,000
Price per share = Total equity value / Number of shares outstanding
We don't know the price per share, but we can use the fact that the deceased equityholder holds 2,500 shares to find the price per share:
2,500 shares / 40,000 shares = 0.0625 or 6.25%
So the deceased equityholder owns 6.25% of the equity of the firm. If we assume that the value of the firm is the same before and after the buyout (ignoring the effects of the debt), then the deceased equityholder's share is worth:
6.25% x Total equity value = Value of 2,500 shares = €1 million
Solving for Total equity value:
Total equity value = €1 million / 6.25% = €16 million
The total value of the firm is then:
Total value = Total equity value + Debt amount = €16 million + €1 million = €17 million
So the closest answer choice is C, €16.0 million.

Uptown Interior Designs Is an All Equity ﬁRm That Has