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You own a project which requires an initial investment of £1M. One year from now this project will pay either £0.8M with probability 40% or £1.5M with probability 60%. After this, there are no further cash flows. You have no money to finance this project on your own.
Assume risk neutrality and an annual discount rate of 15%.
a. What is the NPV of this project?
b. You have found investors who will give you a loan for the full cost of the project. What is the face value of the loan and the interest rate? What is the expected present value of your payoff?
c. You have found investors who will fund the full cost of the project through equity. What is the share of equity they will ask for? What is the expected present value of your payoff?
d. You have found investors who will give you a loan for half of the cost of the project. You will finance the rest with equity. What is the face value of the loan and the interest rate? What is the share of equity promised to the equity investors? What is the expected present value of your payoff?
e. In light of your numerical answers above, discuss Modigliani and Miller’s 1st proposition.
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