You have a project that will require you to raise $1 million. The NPV of the project is $10 million. If potential equity investors believe that you will behave opportunistically and award
Yourself an excessive of $500,000, how much of the firm will you have to sell in order to raise
The needed funds with new equity? Round your answer to the nearest tenth of a percent.

Question

Quizplus · Accepted Answer

The needed funds are $1 million, but potential equity investors will only provide $500,000 due to concerns about management behavior. Therefore, the remaining $500,000 must be raised through the sale of equity. In order to calculate the percentage of the firm that must be sold, divide $500,000 by the total value of the firm, which is $10 million + $1 million = $11 million. This gives us 0.045 or 4.5%. However, we need to add the 500,000 to the NPV of the project, giving us $10.5 million. So the percentage of the firm that must be sold is $500,000/$10,500,000 = 0.0476 or 4.8%. Rounded to the nearest tenth of a percent, this gives us 10.5%, which is closest to choice C. The total value of the project is $10 million and we need to raise $1 million, so we need to sell 10% of the firm. However, if investors believe that the entrepreneur will behave opportunistically and take an excessive $500,000, they will discount the value of the firm by that amount. Therefore, the firm will be valued at only $9.5 million. To raise $1 million, the entrepreneur will need to sell 10.5% of the firm ($1 million divided by $9.5 million). Rounded to the nearest tenth of a percent, this is 10.5%. Therefore, the answer is C.

You Have a Project That Will Require You to Raise