An all-equity-financed firm is worth $500 million and raises another $100 million with new equity, paying $20 million in issuing fees. Calculate the percentage dilution, assuming that all
The dilution is due to the dilution of ownership interest of the existing shareholders. Round
Your answer to the nearest tenth of a percent.
A)17.2%
B)19.8%
C)20.0%
D)none of the above

Question

Quizplus · Accepted Answer

The post-money valuation of the company after the equity raise and fees is:

$500 million + $100 million - $20 million = $580 million

The percentage dilution can be calculated as:

($100 million / $580 million) x 100% = 17.2%

However, this only represents the dilution from the new equity raised. The total percentage dilution will be higher, as the existing shareholders' ownership will also be diluted. To calculate the total percentage dilution, we can use the formula:

Total percentage dilution = 1 - (pre-money valuation / post-money valuation)

Plugging in the numbers, we get:

Total percentage dilution = 1 - ($500 million / $580 million) = 19.8%

Therefore, the best choice is (B) with the explanation that the total percentage dilution after the equity raise and fees is 19.8%. The market value of the firm before issuing new equity is $500 million. After issuing new equity, the market value of the firm is $600 million ($500 million + $100 million). 
The issuing fees of $20 million reduces the net proceeds to $80 million ($100 million - $20 million). 
The percentage dilution can be calculated as (1 - Pre-money valuation/Post-money valuation) x 100%. 
So, the percentage dilution is (1 - $500 million/$600 million) x 100% = 16.67%. 
However, this calculation does not take into account the issuing fees. The actual amount of new equity issued is ($80 million / $600 million) x 100% = 13.33%. 
To calculate the percentage dilution including the issuing fees, we need to adjust the calculation as follows: 
Percentage dilution = ($100 million / $580 million) x 100% - 1 = 17.24% 
Rounding to the nearest tenth of a percent gives us 19.8%. Therefore, the best choice is B.

An All-Equity-Financed Firm Is Worth $500 Million and Raises Another