Consider the situation of a CEO of an all-equity company, which has a market value of $50 million. She is trying to decide whether to invest in a corporate jet. The retail cost of the jet is $4,000,000, and the company estimates that $2,500,000 of this cost can be recouped through savings on airfares for commercial flights, etc. In addition, the CEO will get personal utility from the jet (i.e., she thinks having a jet is cool), which she values at $1,000,000.

Suppose that the CEO owns 100% of the equity of the firm, and is interested only in maximizing her own utility. Will she choose to invest in the jet? What would happen to the company's worth if she did invest? What would happen to her own net worth? What would happen to her utility?