A struggling company currently has a total value of $700,000. It owes $500,000 from debt financing (assume these are loans from the bank if you wish). The value of the company to the owners is the difference between the total value and the amount owed to the debt holders. What is the current value of the firm to the owners? Now assume that a project is presented to the owners that results in a loss of the entire value of the company with a probability of 50% and results in a gain in value of $500,000 with probability 50% (resulting in a total value of $1,200,000). Show that this in expectation decreases the firm’s value, and explain why, in spite of that, the owners of the company would want to undertake the project.

What is the current value of the firm to the owners?

total value - debt = $700,000 - $500,000 = $200,000

Show that this in expectation decreases the firm’s value, and explain why, in spite of that, the owners of the company would want to undertake the project.

the expected value of the company after the new project = (50% x 0) + (50% x $1,200,000) = $600,000, so the net value of the company actually decreases by $100,000.

the issue here is that if things go wrong, the owners will lose $200,000, but if things go well, then the owners equity will increase by $500,000 to a total of $700,000. In this case, the expected value of this project for the owners = (50% x -$200,000) + (50% x $700,000) = $250,000.

I am assuming that this company is some type of corporation, LLC or LLP, not a partnership or sole proprietorship. Under current bankruptcy laws, when a cooperation goes bankrupt, the owners are not personally liable for it.