1. Investment Decision Under Uncertainty
Al Imam Mohammad Ibn Saud Islamic University
College of Economics and Administrative Sciences
Department of Finance and Investment
Level 4: All Divisions
EXERCISE 3
Investment Decision Under Uncertainty

2. Question 1
The financial characteristics of a risky project are as follows :
I0 = 100,000 $
E(CF1→12) : 18,000 $
Rf = 11%
Due to the risk of the project, the Chief Financial Officer (CFO) confuses to reduce 2 or 3 years of uncertain cash flows. Determine the adjusted net present value under these two scenarios. What conclusion can be deduced?

3. Answer 1: First scenario: reducing 2 years of project lifetime:
Decision: Accept the Project
Second scenario: reducing 3 years of project lifetime:
Decision: Reject the Project

4. Question 2:
Assume the following information's for the investment project: 1 2 3 4 5 CF
-50,000
30,000
20,000
15,000
17,000 αt
0.98
0.90
0.82
0.73
0.64
If the risk-free rate is equal to 10%, calculate the adjusted net present value with the Certainty Equivalent Method

5. Answer 2:
The adjusted net present value with the Certainty Equivalent Method

6. Question 3:
Assume the following information's for the investment project: 1 2 3 4 5 CF
-50,000
30,000
20,000
15,000
17,000
If the risk-free rate is equal to 10%, and the Ordinary Firm Risk Premium α1 = 0.5% and the Specific Project Risk Premium α2 = 0.7%, calculate the adjusted net present value with the Risk Adjusted Discounted Rate Method.

7. Answer 3:
The Risk Adjusted Discounted Rate k is equal to , as k = Rf + α1 + α2
NPV adjusted will be shown as follows:

8. Question 4
The following table presents for one period project, the NPV and probabilities of each alternative. Calculate the expected and the standard deviation of NPV?
NPV
400
500
600
700
1000 5 pi
0.2
0.3 ?
0.1
0.05
0.03
What is the probability that the NPV of the project is less than or equal to zero?

9. Answer 4: Pi NPV Pi x NPV Pi (NPV –ENPV)2 0.2 400 80 4041.3 0.3 500
150
532.98
0.32
600
192
0.1
700 70
0.05
1000 50
0.03 5
0.15
8655.9
Total
542.15 SD
165.15

10. Answer 4 :

11. Question 5
Suppose we have an investment project with initial expenditure equal to 9000 SAR and the distribution of cash flows are as follows:
Period 1
Period 2
Cash-flow Pi
4000
5000
6000
7000
8000
0.25
0.10
0.30
3000

12. Question 5 Period 1 Cash-flow Pi E(CF) V(CF) 4000 5000 6000 7000 8000
0.25
0.10
0.30
1000
500
1800
700
2000
100000

13. Question 5 Period 2 Cash-flow Pi E(CF) V(CF) 3000 4000 5000 6000 7000
0.10
0.25
0.30
300
1000
1500
700
400000
250000

14. Answer 5 Calculate the expected value of CF1 and CF2 ECF1 ECF2
Calculate the expected value of NPV if the risk-free rate equal to 8%.
ENPV

15. Q5 If cash flows are considered independent.
Calculate the variance and standard deviation of the NPV.
Vcf1 =
Vcf2=
VNPV=
SD= =

16. Answer 5
What is the probability that the NPV of the project is less than or equal to zero?

17. Answer 5 If cash flows are considered totally dependent.
Calculate the variance and standard deviation of the NPV.
SD =
VNPV= 5,526,668.48
What is the probability that the profitability index is greater than 2?

18. Question 6
Suppose we have an investment in Project "X" that cost 5000 SAR, can provide the following cash flows at the end of years 1 and 2 and the risk-free rate is fixed at 10%. 
Period1
Period2
Cash-flows Pi
3000
0.4
4000
0.3
5000
0.7
8000
0.6
7000
0.5
10000
What is the relation type between cash flows?
Partially dependent

19. Answer 6

20. Question 7
The Company "Gulf Corp" intends to establish a new Project named "A" beside its current project "E". The table below shows the net present value "NPV" of the company's current project "E", and the new project "A" according to economic states:
Economy Status
Probability pi
Company's project "E"
New Project "A"
Bust
0.25
70 000
2000
Normal Growth
0.35
80 000
4000
Boom
0.4
90 000
10 000

21. Question 7 After simple calculus we obtain:
E(NPVE) = 81, V(NPVE) = 62,750,000
σ(NPVE) = 7, CV E = 0.1
E(NPVA) = 5, V(NPVA) = 11,790,000
σ(NPVA) = 3, CV A = 0.58
You are asked to study the establishment of Project "A" within two scenarios:
First Scenario: the project "A" is considered independently of the Company current project "E".
What is your decision about the project A? !!! Note: Use the coefficient of variation decision rule to evaluate this opportunity.
Second Scenario: the proposed project "A" is considered with the actual projects of the company "E".
Calculate :
E NPVP
V (NPVP)
δ (NPVP)
ρ (E; A)

22. Question 7 Decision : Reject Project A
First Scenario: the project "A" is considered independently of the Company current project "E".
What is your decision about the project A? !!! Note: Use the coefficient of variation decision rule to evaluate this opportunity.
Decision : Reject Project A

23. Pi(NPVE - ENPVE) (NPVA - ENPVA)
Question 7
Second Scenario: the proposed project "A" is considered with the actual projects of the company "E".
Economy Status pi
Project "E"
Project "A"
Pi(NPVE - ENPVE) (NPVA - ENPVA)
Bust
0.25
70 000
2000
Normal
0.35
80 000
4000
997500
Boom
0.40
90 000
10 000
E(NPV)
81500
5900
Cov E;A

24. Answer 7 E(NPVp) = E(NPVA) + E(NPVE) = 5900 + 81500 = 87400
Cov (A;E) = P(NPVE – ENPVE) ( NPVA – ENPVA)=
V(NPVp) = V(NPVA) + V(NPVE) + 2 Cov(A;E)
= ( ) =
σ(NPVp) = 11262
CV p = 0.13
ρ (E;A) = Cov (E;A)/ σ(NPVA)* σ(NPVE ) = 0.96

25. وفقكم الله