1. Investment Decision Under Certainty
Al Imam Mohammad Ibn Saud Islamic University
College of Economics and Administrative Sciences
Department of Finance and Investment
Level 4: All branches
EXERCISE 2
Investment Decision Under Certainty

2. Problem 1
Assuming that your firm is considering investment in a new project with the cash flows shown below, that the required rate of return on this project is 10%, and that the maximum allowable payback and discounted payback statistics for your company are 3 and 3.5 years, respectively.
Time 1 2 3 4 5
C F
-70000
15000
20000
40000
45000
50000

3. Questions
Use the payback decision rule to evaluate this project; should it be accepted or rejected? Justify your answer.
Use the DPB decision rule to evaluate this project; should it be accepted or rejected? ? Justify your answer.
Use the Net Present Value (NPV) decision rule to evaluate this project; should it be accepted or rejected?
Use the Profitability Index (PI) decision rule to evaluate this project; should it be accepted or rejected?
Use the IRR decision rule to evaluate this project; should it be accepted or rejected?
Use the MIRR decision rule to evaluate this project; should it be accepted or rejected?

4. Answer 1: Cumulative PV Cash flows Periods -70000 -55000 15000 1
-55000
15000 1
-35000
20000 2
5000
40000 3
50000
45000 4
100000 5
35000/40000 =0.88
0.88*12=10.56 months 0.56*30=16.8 days
2 years , 10 month , 17days

5. Answer 2: Cumulative PV DCF Cash flows Period -70000 1 -56364 13636
-56364
13636
15000
-39835
16529
20000 2
-9782
30053
40000 3
20954
30736
45000 4
52000
31046
50000 5
9782/30736 =0.32
0.32*12 =3.84 months *30=25.2 days
3 years , 3 months , 26 days

6. Answers 3 & 4:
NPV :
NPV =
PI :
PI = 1.74

7. Answer 5: 1- IF K1 is 30%, guess IRR NPV = 802
2- then guess IRR at 31%:
NPV = -862
IRR

8. Answer 6:
MIRR
Given that reinvestment rate is 10%
MIRR =22.93%

9. Problem 2
Consider the following abbreviated financial statements for a proposed investment
Years  1 2 3
Sales 
400,000
600,000
800,000
Costs 
140,000
300,000
Depreciation 
Gross Profit
Taxes (20%) 
Net Income 

10. Questions:
If the total investment cost of this project is 600,000 Saudi Riyals, what is the average accounting return (ARR) for the proposed investment?
Calculate the (NPV), (IRR) and the (PI) for this investment?
(the required rate of return on projects of this risk class is 8%).

11. Answer 1: Average net profits = 48000+ 80000+ 160000 = 96000
Average Investment= 600, , ,
=1,200,000/4 = 300,000 Or
(600, )/2= 300,000

12. Answer 2: NPV & PI NPV NPV = 155464.11

13. Answer 2: IRR NPV if IRR 20% NPV = 9444.44 NPV if IRR 21%

14. Answer 2: MIRR
MIRR= 16.62

15. Problem 3
ALHILAL Inc. is considering two mutually exclusive projects with widely differing lives. The company's cost of capital is 14%. The project cash flows are summarized as follows:
Cash flows
Project A
Project B
CF0
-30,000
-28,000
CF1
17,500
8,200
CF2
CF3
CF4
CF5
CF6
CF7
CF8
CF9

16. Questions 1- Compare the two projects by using NPV.
2- Compare the projects by using the replacement chain approach.
3- Compare the projects by using the EAA method.
4- Chose a project and justify your choice.

17. Answer 1
NPV of Project A
NPV = 10629
NPV of Project B
NPV = 12560

18. Answer 2 Year Project 1st Renewal 2nd Renewal Total Annual Cash Flow
Discounted CF
-30000 1
17500
15351 2
13466 3
-12500
-8437 4
10361 5
9089 6
-5695 7
6994 8
9135 9
5381
22645

19. Answer 3
We choose Project A