PROBLEM A [CORPORATE FINANCE] A firm is considering an investment project, whose future state-contingent perpetual payoffs, starting in one year from now (t=1), are summarized in the below table: State Prob Perpetuity high 0.4 100 low 0.6 20 Le., there is a 40% probability that at the end of every year, the payoff from the investment is 100, while there is a 60% probability that the payoff will be only 20. The risk associated with the project is idiosyncratic, so that the discount rate is the risk-free interest rate of 5%. The initial investment required is 1,200. 1. What is the NPV of this project at t=0? Assume that after one year (t=1), having learned whether the high or low state is realized, the firm has the opportunity to repeat the investment again at the same terms, if the first investment was undertaken. If the investment is repeated, the second investment amount will be paid at the end of the first period (t-1), and the first cash flow of the second investment will be received at the end of the second period (t=2). 2. What is the NPv of the combined investment at t=0? How much of the NPV, in dollar terms, comes from the growth option? Should the combined investment be undertaken? In addition to the above real option, the firm also has the opportunity to scale down the initial investment after one year, in a similar fashion as the option to repeat the investment. If the firm chooses to scale down the investment, 50% of the investment amount will be recovered but only 40% of the cash flows will remain compared to the case of not scaling down the investment. 3. Conditional on being in the low state one year from now, what is the NPV at t=1 of scaling down the investment? 4. What is the new NPV of the project at t=0, with the option to scale down the investment?
PROBLEM A [CORPORATE FINANCE] A firm is considering an investment project, whose future state-contingent perpetual payoffs, starting in one year from now (t=1), are summarized in the below table: State Prob Perpetuity high 0.4 100 low 0.6 20 Le., there is a 40% probability that at the end of every year, the payoff from the investment is 100, while there is a 60% probability that the payoff will be only 20. The risk associated with the project is idiosyncratic, so that the discount rate is the risk-free interest rate of 5%. The initial investment required is 1,200. 1. What is the NPV of this project at t=0? Assume that after one year (t=1), having learned whether the high or low state is realized, the firm has the opportunity to repeat the investment again at the same terms, if the first investment was undertaken. If the investment is repeated, the second investment amount will be paid at the end of the first period (t-1), and the first cash flow of the second investment will be received at the end of the second period (t=2). 2. What is the NPv of the combined investment at t=0? How much of the NPV, in dollar terms, comes from the growth option? Should the combined investment be undertaken? In addition to the above real option, the firm also has the opportunity to scale down the initial investment after one year, in a similar fashion as the option to repeat the investment. If the firm chooses to scale down the investment, 50% of the investment amount will be recovered but only 40% of the cash flows will remain compared to the case of not scaling down the investment. 3. Conditional on being in the low state one year from now, what is the NPV at t=1 of scaling down the investment? 4. What is the new NPV of the project at t=0, with the option to scale down the investment?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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This is for the next part, can you help with question 3.
First picture is question, the second picture shows the solution that i cant figure out
Transcribed Image Text:State
Prob
Perpetuity
high
0.4
100
low
0.6
20
1)
Inv
1200
r
0.05
NPV
-160
2)
NPV high
800
NPV low
-800
PV go
304.7619
NPV
144.7619
4)
Frac recovered
0.5
Frac CF remain
0.4
PV CF if high
PV go if high 761.9048
2000
Check
PV CF if low
160
343.619
PV recovered if low 571.4286
240
331.4286
NPV
343.619
331.4286
3)
Recovered investment
600
PV of lost cash flows
252
NPV at t=1
348
![PROBLEM A [CORPORATE FINANCE]
A firm is considering an investment project, whose future state-contingent perpetual payoffs, starting
in one year from now (t=1), are summarized in the below table:
State
Prob
Perpetuity
high
0.4
100
low
0.6
20
L.e., there is a 40% probability that at the end of every year, the payoff from the investment is 100,
while there is a 60% probability that the payoff will be only 20. The risk associated with the project is
idiosyncratic, so that the discount rate is the risk-free interest rate of 5%. The initial investment
required is 1,200.
1. What is the NPV of this project at t=0?
Assume that after one year (t=1), having learned whether the high or low state is realized, the firm
has the opportunity to repeat the investment again at the same terms, if the first investment was
undertaken. If the investment is repeated, the second investment amount will be paid at the end of
the first period (t=1), and the first cash flow of the second investment will be received at the end of
the second period (t=2).
2. What is the NPV of the combined investment at t=0? How much of the NPV, in dollar terms,
comes from the growth option? Should the combined investment be undertaken?
In addition to the above real option, the firm also has the opportunity to scale down the initial
investment after one year, in a similar fashion as the option to repeat the investment. If the firm
chooses to scale down the investment, 50% of the investment amount will be recovered but only 40%
of the cash flows will remain compared to the case of not scaling down the investment.
3. Conditional on being in the low state one year from now, what is the NPV at t=1 of scaling
down the investment?
4. What is the new NPV of the project at t=0, with the option to scale down the investment?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad6d3522-58fe-4a42-a237-8062bf310251%2Fce0b9b32-9401-4364-8aef-581dc802701e%2Fb2otf7p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:PROBLEM A [CORPORATE FINANCE]
A firm is considering an investment project, whose future state-contingent perpetual payoffs, starting
in one year from now (t=1), are summarized in the below table:
State
Prob
Perpetuity
high
0.4
100
low
0.6
20
L.e., there is a 40% probability that at the end of every year, the payoff from the investment is 100,
while there is a 60% probability that the payoff will be only 20. The risk associated with the project is
idiosyncratic, so that the discount rate is the risk-free interest rate of 5%. The initial investment
required is 1,200.
1. What is the NPV of this project at t=0?
Assume that after one year (t=1), having learned whether the high or low state is realized, the firm
has the opportunity to repeat the investment again at the same terms, if the first investment was
undertaken. If the investment is repeated, the second investment amount will be paid at the end of
the first period (t=1), and the first cash flow of the second investment will be received at the end of
the second period (t=2).
2. What is the NPV of the combined investment at t=0? How much of the NPV, in dollar terms,
comes from the growth option? Should the combined investment be undertaken?
In addition to the above real option, the firm also has the opportunity to scale down the initial
investment after one year, in a similar fashion as the option to repeat the investment. If the firm
chooses to scale down the investment, 50% of the investment amount will be recovered but only 40%
of the cash flows will remain compared to the case of not scaling down the investment.
3. Conditional on being in the low state one year from now, what is the NPV at t=1 of scaling
down the investment?
4. What is the new NPV of the project at t=0, with the option to scale down the investment?
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