Question 4. (20 points) A risk-neutral entrepreneur contemplates an irre- versible investment of / = $510 min. The project will generate a constant...
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I don't get how the

find V0,1(C) in the last part: where does the -10C and -9C comes from? and where does the 0.5 comes from too? and shouldn't it be in the first part of the system too?

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Question 4. (20 points) A risk-neutral entrepreneur contemplates an irre-
versible investment of / = $510 min. The project will generate a constant
stream of revenues of $150 min. annually starting a year after the invest-
ment has been made. The current operating cost is SC min. per year. In
a year from now, the operating cost may go up or down by 10% and will
remain constant thereafter. Assume that risk-neutral probabilities of each
event are 0.5. There is no operating cost to be paid until the project starts
generating revenues. The annual risk free interest rate is r = 0.1.
(a) (5 points) What is the expected present value (EPV) of immediate in-
vestment as a function of C?
DO
Vo,o (C) = 0.5
150 - 1.10
+
150 - 0.90
1.1t
1.1t
- 510
= 0.5
150 - 1.10
150 - 0.90
0.1
0.1
- 510
=
990 - 100,
provided C < $99 min. Thus
990 - 100 if C < 99,
if C > 99.
(b) (5 points) What is the EPV of investment at t = 1 as a function of O?
Vi,I(110) =
150 - 1.10
- 510 =
990 - 110 if C < 90,
1.1t
if C > 90.
Vi,1 (0.90) =
150 - 0.90
990 - 90 if C < 110,
1.10
- 510 =
if C > 110.
Hence,
990-100
1.1
if C < 90,
Vo,1 (O) =
D.5(990-90)
1.1
if 90 < C < 110,
if C > 110.

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