HW#7 ‫ خوله‬.‫د‬
April 2015
1. Consider two investments with the following sequences of cash flows:
n
0
1
2
3
Cash Flow
-$100,000
$10,500
$60,000
$80,000
Project B
-$100,000
$70,000
$50,000
$20,500
a) Compute the ROR for each investment.
b) At MARR = 10%, determine the acceptability of each project.
a)
Project (A):
0
 Solve using calculator:
Project (B):
0
 Solve using calculator:
b)
‫اإلحسان يَ ُحطُ من‬
.‫قدر من يتَلَّقونه‬
HW#7 ‫ خوله‬.‫د‬
April 2015
2. A plant engineer is considering two types of solar water-heating systems:
Item
Initial cost
Annual Savings
Annual Maintenance
Expected Life
Salvage Value
Model A
$5,000
$700
$100
20 years
$400
Project B
$7,000
$1,000
$50
20 years
$500
The firm’s MARR is 10%. On the basis of the ROR criterion, decide
which system is the better choice.
Model (A):
0
1
2
∫
∫
∫
∫
∫
∫
∫
∫
0
 Solve using calculator:
Model (B):
0
1
2
0
Solve using calculator:
Model (B) is the better choice, as it has the higher ( ).
‫ الخطوة‬،‫بُعد المسافة ال يهم‬
.‫األولى فقط هي األكثر صعوبة‬
HW#7 ‫ خوله‬.‫د‬
April 2015
3. Consider following two mutually exclusive alternatives:
Net Cash Flow
N
Project A1
0
-$10,000
1
$5,000
2
$5,000
3
$5,000
Project A2
-$12,000
$6,100
$6,100
$6,100
a. Determine the ROR on the incremental investment in the amount
of $2,000.
b. If the firm’s MARR is 10%, which alternative is the better choice?
a)
n
0
1
2
3
-$2,000
$1,100
$1,100
$1,100
0
 Solve using calculator:
b)
‫ال تكمننننن م انننناة الحدنننناة فنننني نننند‬
‫ لكننن فنني ال‬، ‫وصولنن إ ىلننى الهنن د‬
.‫يكون لإ هد تحاول ال وصول ىلده‬
HW#7 ‫ خوله‬.‫د‬
April 2015
4. Consider the following two mutually exclusive investment alternatives:
Net Cash Flow
N
Project A1
0
-$16,000
1
$7,500
2
$7,500
3
$7,500
ROR
19,19%
Project A2
-$20,000
$5,000
$15,000
$8,000
17,65%
a) Determine the ROR on the incremental investment in the amount of
$4,000. (Assume that MRR = 10%).
b) If the firm’s MARR is 10%, which alternative is the better choice?
a)
n
0
1
2
3
-$4,000
-$2,500
+$7,500
+$500
0
 Solve using calculator:
b)
‫تستح من ى طاء القلدل‬
‫ال‬
ِ
.‫فإن الحرمان قل منه‬
HW#7 ‫ خوله‬.‫د‬
April 2015
5. Consider the following two mutually exclusive investment projects:
Net Cash Flow
N
Project A
0
-$100
1
$600
2
$50
3
$50
ROR
28.89%
Project B
-$200
$120
$150
21.65%
Assume that MARR = 15%. Which project would be selected under an
infinite planning horizon with project repeatedly likely, according to the
ROR criterion?
 Solve using calculator:
‫يتم ىنجاز األ مال في مو دها‬
.‫الصحدح في المفكرة فقط‬
HW#7 ‫ خوله‬.‫د‬
April 2015
6. Apply Test 1 to determine the given cash flows have single or multiple
internal rates of return. Also find the values of these RORs. Show that this
ROR is a realistic (single) ROR.
End of Year
0
1
2
3
4
5
Project A ($)
-5,000 2,500
2,500
2,500
2,500
0
Project B ($)
-250
-125
-125
-125
375
500
Project C ($)
0
-600
200
380
-160
544
Project D ($)
-1,000 5,700
-12,140 11,448 -4,032 0
Project (A) & project (B) have a single ROR.
Project (A):
0
 Solve using calculator:
Project (B):
0
 Solve using calculator:
Project (c) & project (D) have multiple ROR, as condition 2.
Test 1 fails for looth, therefore, apply test 2.
Project (c): Test 2 succeeds, 80, project c has a single ROR
0
 Solve using calculator:
Project (D): Test 2 fails
Multiple ROR
‫ىما نختار ن نحدا حداتنا و نترك‬
.‫غدرنا يحداها ندابة نا‬
HW#7 ‫ خوله‬.‫د‬
April 2015
7. Apply Test 1 and Test 2 to the cash flows given below and determine the
internal rate of return for each cash flow.
End of Year
Project A ($)
Project B ($)
Project C ($)
0
-3,000
-10,000
-2000
1
7,500
50,000
0
2
4,620
-93,500
0
3
0
77,500
20,000
4
0
-24,024
-20,000
Project (A):
Test 1 succeeds, project (A) has a single ROR.
0
 Solve using calculator:
Project (B):
Condition 2, in test 1 fails.
Apply test 2
Condition 2, in test 2 fails
there are
0
10%
20%
30%
40%
50%
60%
-24
0
0
0
0
-4.74
-18.3
‫نسدان غاية المرء هو كثر‬
.‫شكال الغباء انتشارا‬
HW#7 ‫ خوله‬.‫د‬
April 2015
Project (c):
Condition 2& 3 in Test 1 fail.
Apply Test 2.
Condition 2 in Test 2 fails
there are 2
s.
0
10%
20%
30%
40%
50%
60%
-2,000
-634
-71
100.77 82.5
-24.7
-168.9
By interpolation:
‫ىن ي شكل من شكال التخطدط فضل‬
.‫من د التخطدط لى اإلطالق‬