Al Imam Mohammad Ibn Saud Islamic University (IMSU)
College of Economics and Administrative Sciences
Department of Finance and Investment
Fin101: Principles of Finance & Investments
Level 4: All branches
Investment Decisions under Certainty
Problem 1
Suppose your firm is considering investing in a project with the cash flows shown
below, that the required rate of return on projects of this risk class is 11%, and that the
maximum allowable payback and discounted payback statistics for your company are
3 and 3.5 years, respectively.
Time
Cash Flow
0
-$235,000
1
2
3
4
5
$65,800 $84,000 $141,000 $122,000 $81,200
1- Use the payback decision rule to evaluate this project; should it be accepted or rejected?
2- Use the discounted payback decision rule to evaluate this project; should it be accepted or
rejected?
3- Use the IRR decision rule to evaluate this project; should it be accepted or rejected?
4- Use the MIRR decision rule to evaluate this project; should it be accepted or rejected?
5- Use the Net Present Value (NPV) decision rule to evaluate this project; should it be
accepted or rejected?
6- Use the Profitability Index (PI) decision rule to evaluate this project; should it be accepted
or rejected?
Problem 2
Consider the following abbreviated financial statements for a proposed investment:
Year
Gross Book Value
Accumulated Dep.
Net Book Value
Sales
Costs
Depreciation
Taxes (50%)
Net Income
0
$160
$160
1
$160
40
$120
2
$160
80
$80
3
$160
120
$40
4
$160
160
$0
$95
33
40
$11
$11
$90
30
40
$10
$10
$97
25
40
$16
$16
$80
10
40
$15
$15
1- What is the average accounting return (AAR) for the proposed investment?
2- Calculate the Payback period (PB), Discounted Payback Period (DPB), Net
present value (NPV), the Internal Rate of Return (IRR) and the Profitability
Index (PI) for the investment (the required rate of return on projects of this
risk class is 10%).
Problem 3
ALHILAL Inc. is considering two mutually exclusive projects with widely differing
lives. The company's cost of capital is 12%. The project cash flows are summarized
as follows:
Cash flows
CF0
CF1
CF2
CF3
CF4
CF5
CF6
CF7
CF8
CF9
Project A
(25,000)
14,742
14,742
14,742
Project B
(23,000)
6,641
6,641
6,641
6,641
6,641
6,641
6,641
6,641
6,641
1- Compare the 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.
Problem 4
You are considering an investment in two projects, A and B. both projects have an
initial cash outlay of $50 000 and the projected cash flows are as follows:
Year
1
2
3
4
5
Project A
20 000
25 000
30 000
35 000
40 000
Project B
35 000
30 000
25 000
20 000
15 000
Assuming that the cost of capital is 15%, the NPV and the IRR are presented as
follows:
NPV
IRR
Project A
45918.82
44.65%
Project B
38449.71
50%
1- Create an NPV profile chart for projects A and B.
2- What is the exact crossover rate for these two projects?
Decision
Choice of project A
Choice of project B
Solutions (Problem1)
1- Cumulative cash flow will switch from negative and positive between years 2 and 3:
Year
Cash Flow
Cumulative
Cash Flow
0
-$235,000
-$235,000
1
$65,800
-$169,200
2
3
$84,000 $141,000
-$85,200 $55,800
4
$122,000
$177,800
5
$81,200
$259,000
$85, 200
 2.6043 years so this project should be accepted.
$141, 000
Specifically, PB  2 
2- Cumulative PV of cash flow will switch from negative and positive between years 3 and
4:
Year
Cash
Flow
0
-$235,000
Cash
Flow
PV
-$235,000
Cum.
Cash
Flow
PV
-$235,000
1
$65,800
2
$84,000
3
$141,000
4
5
$122,000 $81,200
$65,800
$84, 000
$141, 000
$122, 000
1.11
1.11
1.11
1.11
1
2
3
4
 $59, 279.28
 $68,176.28
 $103, 097.98
 $80, 365.18
-$175,721
-$107,544
-$4,446
$75,919
$4, 446
 3.05 years , which is less than the maximum
$80, 365.18
allowable discounted payback, so project should be accepted.
Specifically, DPB  3 
3- The IRR for this project will be the solution to:
$235, 000 $65,800
$84, 000
$141, 000 $122, 000
$81, 200
0





0
1
2
3
4
5
1  IRR  1  IRR  1  IRR  1  IRR  1  IRR  1  IRR 
IRR  .2879, or 28.79%
Since IRR > i, this project should be accepted.
4- Cash flows will be moved as shown below:
0
Year
Cash
$235,000
Flow
Future
Value (If
Positive)
Sum of
FV
Modified
$235,000
CFs
1
2
3
4
5
$65,800
$84,000
$141,000
$122,000
$81,200
$65,800  1.11
 $99,889.03
4
$84, 000  1.11
 $114,881
3
$141, 000  1.11
 $173, 726.10
2
$122, 000  1.11
1
 $135, 420
$81, 200
$605,116.14
$605,116.14
With this new set of modified cash flows, the MIRR is:
0
$235, 000
1  IRR 
0

$605,116.14
1  IRR 
5
IRR  .2082, or 20.82%
Since our MIRR decision statistic is greater than the 11 percent cost of capital,
we would accept the project under the MIRR method.
5-
NPV  $235, 000 
$65,800
1.11
1

$84, 000
1.11
2

$141, 000
1.11
3

$122, 000
1.11
4

$81, 200
1.11
5
 $124,106.98
Since NPV > 0, the project should be accepted.
6- PI =1. 5281
Since PI > 0, the project should be accepted.
Solutions (Problem 2)
1- The average net income is [($11 + $10 + $16 + $15)/4] = $13. The average
book value is $80, so the AAR is ($13/$80) = .1625 = 16.25%.
2- Cash flows are $51, $50, $56, and $55, respectively over the four-year period.
The initial investment is $160.
NPV=7.33
PB=3.05
DPB=3.81
IRR=12.06%
PI=1.046
Solutions (Problem 3)
1- NPV (A) = $10,407, NPV (B) = $12,385 Project B is preferred.
2- Chain project A to nine years: NPV (A) = $23,088, NPV(B)= $12,385
A chained to B's time horizon is the preferred option based on NPV.
3- Project A:
EAA = $4,333
Project B:
EAA = $2,324
Project A is preferred, because it has the larger EAA.
4- Project A is preferred on all counts except the original NPV calculation, and
that disparity is due to the time horizon problem. Hence A is the best choice.
Solutions (Problem 4)
1- NPV profile chart for projects A and B
NPV Trend
120000
Project A
100000
Project B
IRR Project A
Crossover rate
60000
40000
IRR Project B
20000
0
-20000
Discount Rate
2- Crossover rate= 29.32%
NPV SAR
80000