Your firm consists of $10 million in cash and a $40 million factory (thus, your firm value is $50 million). You owe $40 million (either in the form of cash or factory) to a debtholder at the end of the year whose contract specifies that you cannot pay dividends until after he is repaid. You have no other liabilities. Assume the discount rate is zero. The only project you are considering over the next year is a $10 million sprinkler system in your factory. Without the sprinkler system there is a 50% chance that the factory will burn down overthe next year (in which case the factorys value will drop from $40 million to $0). With the sprinkler system there is a 0% chance the factory will burn down.

Will equity holders decide to install the sprinkler system? Why? (Numerically explain)

In three sentences or less, explain intuitively why equity holders make this decision