You currently have $50,000 in cash. You have access to a project which requires an initial investment of $50,000. One year from now this project will pay either $40,000 with a probability 50% or $100,000 with probability 50%. After this, there are no further cash flows.
Assume risk neutrality and an annual discount rate of 10%. This is also the risk-free rate.
(a) What is the NPV of this project?
(b) Suppose you decide to finance this project with your own cash. How much money do you expect to have one year from now?
(c) You have found investors who will fund the full cost of the project through equity. You will invest your cash at a risk-free rate. What is the share of equity they will ask for? How much money do you expect to have one year from now?
(d) You have found investors who will give you a loan for the full cost of the project. You will invest your cash at a risk-free rate. Assume in case of default, these investors can claim all of the project's cash flows, but cannot claim the cash you have invested outside of the project. What is the face value of the loan and the interest rate? How much money do you expect to have one year from now?
(e) In light of your numerical answers above, discuss Modigliani and Miller's 1st proposition.