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

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?

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

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

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

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.

Answer 3: The Risk Adjusted Discounted Rate k is equal to 0.112 , as k = Rf + α1 + α2 NPV adjusted will be shown as follows:

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?

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 1070.92 0.1 700 70 2491.66 0.05 1000 50 10481.33 0.03 5 0.15 8655.9 Total 542.15 27274.13 SD 165.15

Answer 4 :

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

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 1000000 100000 2200000

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 1300000

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

Q5 If cash flows are considered independent. Calculate the variance and standard deviation of the NPV. Vcf1 = Vcf2= VNPV= SD= = 1685.73

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

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?

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

Answer 6

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

Question 7 After simple calculus we obtain: E(NPVE) = 81,500 V(NPVE) = 62,750,000 σ(NPVE) = 7,921.49 CV E = 0.1 E(NPVA) = 5,900 V(NPVA) = 11,790,000 σ(NPVA) = 3,433.66 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)

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

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 11212500 Normal 0.35 80 000 4000 997500 Boom 0.40 90 000 10 000 13940000 E(NPV) 81500 5900 Cov E;A 26150000

Answer 7 E(NPVp) = E(NPVA) + E(NPVE) = 5900 + 81500 = 87400 Cov (A;E) = P(NPVE – ENPVE) ( NPVA – ENPVA)= 26150000 V(NPVp) = V(NPVA) + V(NPVE) + 2 Cov(A;E) = 11790000 + 62750000 + 2 (26150000) = 126840000 σ(NPVp) = 11262 CV p = 0.13 ρ (E;A) = Cov (E;A)/ σ(NPVA)* σ(NPVE ) = 0.96

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