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FIN622 Assignment 1 Fall 2012 Solution

Tuesday, November 20, 2012 Edit This
Net Present Value (NPV)
NPV = -Io + CF1 / (1+i)^1 + CF2 / (1+i)^2 + CF3 / (1+i)^3 + CF4 / (1+i)^4 +…….+ ∞
For Alpha:
Io= 20,000
i = initial investment for alpha = 14%
For Beta:
Io= 20,000
i = initial investment for Beta = 12%
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PV of Future Cash Flows of project ALPHA = 53428+ 63435 + 52956+ 37725
= 207547

PI= 207547/200000

ye calculation apni kr laina...main ny rounded kiya howa hy.... same isi tarah BETA ki b calculate krni hy.....just intial investment ki amount less nahi krni....balky intial investment ko divide krna hy
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Net Present Value (NPV)
NPV = -Io + CF1 / (1+i)^1 + CF2 / (1+i)^2 + CF3 / (1+i)^3 + CF4 / (1+i)^4 +…….+ ∞
For Alpha:
Io= 20,000
i = initial investment for alpha = 14%
For Beta:
Io= 20,000
i = initial investment for Beta = 12%
......................
Profitability Index (PI):
Profitability Index = PV of Future Net Cash Flows / Initial Investment Required

......................
Net Present Value (NPV)
NPV = -Io + CF1 / (1+i)^1 + CF2 / (1+i)^2 + CF3 / (1+i)^3 + CF4 / (1+i)^4 +…….+ ∞
For Alpha:
Io= 20,000
i = initial investment for alpha = 14%
For Beta:
Io= 20,000
i = initial investment for Beta = 12%

Profitability Index (PI):
Profitability Index = PV of Future Net Cash Flows / Initial Investment Required

Year Project Alpha
YearsEnd Rs.(000)FVIF 
12.3%=1/(1.123)^t
PVPI
-200,0001.000-200000
-0.85
160,0001.12367380
2.83
280,0001.261100890.32
2.12
375,0001.416106218.59
2.27
460,0001.59095426.78128
2.83
Total
75,000
169915.6913
Project Beta
YearsEnd Rs.(000)FVIF 
12.3%=1/(1.123)^t
PVPI
-200,0001.000-200000
-0.851
155,0001.12361765
3.093
265,0001.26181973.385
2.617
370,0001.41699137.35069
2.430
480,0001.590127235.7084
2.126
TotalNPV170111.4441
PV of Future Cash Flows of project ALPHA = 53428+ 63435 + 52956+ 37725
= 207547

PI= 207547/200000
......................

Answers are
1: Net present values (NPV):
Alpha: NPV = 7545.63
Beta: NPV = 243.8
Profitability index (PI):
Alpha: PI = 1.0377
Beta: PI = 1.0012
2) NPV of Alpha is higher, it is favorable
3) Profitability index of Alpha is higher
4) IRR of Alpha is higher so it is favorable project.
......................
Answer 4:
PROJECT ALPHA
Year EndProject AlphaIRRIRR+1(IRR+1)^TNPV of Cash Flow
0-20000014.00%1 + 14% = 1.14(1.14)^0=1.000(200,000.00)
16000014.00%1 + 14% = 1.14(1.14)^1=1.14052,631.58
28000014.00%1 + 14% = 1.14(1.14)^2=1.30061,557.40
37500014.00%1 + 14% = 1.14(1.14)^3=1.48250,622.86
46000014.00%1 + 14% = 1.14(1.14)^4=1.68935,524.82
TOTAL NPV336.66
PROJECT Beta
Year EndProject AlphaIRRIRR+1(IRR+1)^TNPV of Cash Flow
0-20000012.00%1 + 12% = 1.12(1.12)^0=1.000(200,000.00)
15500012.00%1 + 12% = 1.12(1.12)^1=1.12049,107.14
26500012.00%1 + 12% = 1.12(1.12)^2=1.25451,817.60
37000012.00%1 + 12% = 1.12(1.12)^3=1.40549,824.62
48000012.00%1 + 12% = 1.12(1.12)^4=1.57450,841.45
TOTAL NPV1,590.81

Using IRR criterion, project Beta IRR is higher than Project Alpha. So, Select Project Beta. Answer 4:
PROJECT ALPHA
Year EndProject AlphaIRRIRR+1(IRR+1)^TNPV of Cash Flow
0-20000014.00%1 + 14% = 1.14(1.14)^0=1.000(200,000.00)
16000014.00%1 + 14% = 1.14(1.14)^1=1.14052,631.58
28000014.00%1 + 14% = 1.14(1.14)^2=1.30061,557.40
37500014.00%1 + 14% = 1.14(1.14)^3=1.48250,622.86
46000014.00%1 + 14% = 1.14(1.14)^4=1.68935,524.82
TOTAL NPV336.66
PROJECT Beta
Year EndProject AlphaIRRIRR+1(IRR+1)^TNPV of Cash Flow
0-20000012.00%1 + 12% = 1.12(1.12)^0=1.000(200,000.00)
15500012.00%1 + 12% = 1.12(1.12)^1=1.12049,107.14
26500012.00%1 + 12% = 1.12(1.12)^2=1.25451,817.60
37000012.00%1 + 12% = 1.12(1.12)^3=1.40549,824.62
48000012.00%1 + 12% = 1.12(1.12)^4=1.57450,841.45
TOTAL NPV1,590.81

Using IRR criterion, project Beta IRR is higher than Project Alpha. So, Select Project Beta.
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