You own a project which requires an initial investment of £1M. One year from now
ID: 2725642 • Letter: Y
Question
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.
please provide clear explanations for your calculations
Explanation / Answer
Assume risk neutrality and an annual discount rate of 15%.
a. What is the NPV of this project?
NPV = –1 + (0.4 * 0.8 + 0.6 * 1.5)/1.15 = £0.061M
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?
Loan calculation:
1 = (0.4 * 0.8 + 0.6 * F)/1.15
F = 1.383
Interest is = .383 or 38.3%
Putting the value of face value of loan we will calculate the NPV
NPV =[0.4 * 0 + 0.6 * (1.5 – F)]/1.15
=[0.4 * 0 + 0.6 * (1.5 – 1.383)]/1.15
= 0+(0.6*0.117)/1.15
=0.0702 / 1.15
= £0.061M
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?
Let a be the fraction of equity promised to outsiders. It must be that:
1 =a* (0.4 * 0.8 + 0.6 * 1.5)/1.15
a= 1.061 /1.15
a= 92.26%
Putting the value of face value of equity we will calculate the NPV
NPV= (1 –a) * 1.061
= £0.061
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?
Loan calculation
0.5 = (0.4 * F + 0.6 * F)/1.15
Face value of loan = 0.575
Interest rate = 15
Leta be the fraction of equity promised to outsiders. It must be that:
0.5 = a* [0.4 * (0.8 – F) + 0.6 * (1.5 – F)]/1.15
= a* 0.561
a =0.5 / 0.561
a =89.13 %
NPV: (1–a) * 0.561 = £0.061
e. In light of your numerical answers above, discuss Modigliani and Miller’s 1st
proposition.
Note that in (b),(c) and (d) the payoff was always the same and equal to the NPV in (a). This is exactly the point of M&M; financing method (capital structure) is irrelevant. The payoff to the firm’s owner will be the same regardless of which capital structure is chosen, as long as the conditions stipulated by M&M hold
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