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% 
......................................
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
Years	End Rs.(000)	FVIF  12.3%=1/(1.123)^t	PV	PI
	-200,000	1.000	-200000	-0.85
1	60,000	1.123	67380	2.83
2	80,000	1.261	100890.32	2.12
3	75,000	1.416	106218.59	2.27
4	60,000	1.590	95426.78128	2.83
Total	75,000		169915.6913
Project Beta
Years	End Rs.(000)	FVIF  12.3%=1/(1.123)^t	PV	PI
	-200,000	1.000	-200000	-0.851
1	55,000	1.123	61765	3.093
2	65,000	1.261	81973.385	2.617
3	70,000	1.416	99137.35069	2.430
4	80,000	1.590	127235.7084	2.126
Total	NPV		170111.4441

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 End	Project Alpha	IRR	IRR+1	(IRR+1)^T			NPV of Cash Flow
0	-200000	14.00%	1 + 14% = 1.14	(1.14)^0	=	1.000	(200,000.00)
1	60000	14.00%	1 + 14% = 1.14	(1.14)^1	=	1.140	52,631.58
2	80000	14.00%	1 + 14% = 1.14	(1.14)^2	=	1.300	61,557.40
3	75000	14.00%	1 + 14% = 1.14	(1.14)^3	=	1.482	50,622.86
4	60000	14.00%	1 + 14% = 1.14	(1.14)^4	=	1.689	35,524.82
				TOTAL NPV			336.66
PROJECT Beta
Year End	Project Alpha	IRR	IRR+1	(IRR+1)^T			NPV of Cash Flow
0	-200000	12.00%	1 + 12% = 1.12	(1.12)^0	=	1.000	(200,000.00)
1	55000	12.00%	1 + 12% = 1.12	(1.12)^1	=	1.120	49,107.14
2	65000	12.00%	1 + 12% = 1.12	(1.12)^2	=	1.254	51,817.60
3	70000	12.00%	1 + 12% = 1.12	(1.12)^3	=	1.405	49,824.62
4	80000	12.00%	1 + 12% = 1.12	(1.12)^4	=	1.574	50,841.45
				TOTAL NPV			1,590.81

Using IRR criterion, project Beta IRR is higher than Project Alpha. So, Select Project Beta. Answer 4:

PROJECT ALPHA
Year End	Project Alpha	IRR	IRR+1	(IRR+1)^T			NPV of Cash Flow
0	-200000	14.00%	1 + 14% = 1.14	(1.14)^0	=	1.000	(200,000.00)
1	60000	14.00%	1 + 14% = 1.14	(1.14)^1	=	1.140	52,631.58
2	80000	14.00%	1 + 14% = 1.14	(1.14)^2	=	1.300	61,557.40
3	75000	14.00%	1 + 14% = 1.14	(1.14)^3	=	1.482	50,622.86
4	60000	14.00%	1 + 14% = 1.14	(1.14)^4	=	1.689	35,524.82
				TOTAL NPV			336.66
PROJECT Beta
Year End	Project Alpha	IRR	IRR+1	(IRR+1)^T			NPV of Cash Flow
0	-200000	12.00%	1 + 12% = 1.12	(1.12)^0	=	1.000	(200,000.00)
1	55000	12.00%	1 + 12% = 1.12	(1.12)^1	=	1.120	49,107.14
2	65000	12.00%	1 + 12% = 1.12	(1.12)^2	=	1.254	51,817.60
3	70000	12.00%	1 + 12% = 1.12	(1.12)^3	=	1.405	49,824.62
4	80000	12.00%	1 + 12% = 1.12	(1.12)^4	=	1.574	50,841.45
				TOTAL NPV			1,590.81

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

STA301 Assignment 2 Solution Fall 2012

Question no 02 part a

If coefficient of skewness is zero then distribution is symmetric or zero skewed.\
\

question no 2 part b
The least squares regression line

The least squares regression line is the line which produces the smallest value of the sum of the squares of the residuals. A residual is the vertical distance from a point on a scatter diagram to the line of best fit. Therefore the least squares regression line can be seen as the best line of best fit.
The equation of the least squares regression line of y on x is:


Where b is:


As you can see there are 3 different ways to calculate the value for b, based on what information you are given in the question
Example

Calculate the least squared regression line of y on x from the following data:

x	20	30	40	50	60	70
y	2.49	2.41	2.38	2.14	1.97	2.03

Firstly draw up a table of the values you need and fill it out. In this example we'll use the third equation for b so we need all the values of x²and x_iy_i:

	x	y	x2	xiyi
	20	2.49	400	49.9
	30	2.41	900	72.3
	40	2.38	1600	95.2
	50	2.14	2500	107
	60	1.97	3600	118.2
	70	2.03	4900	142.1
Sum:	270	13.42	13900	584.7

Next step is to calculate the means of the x and y values:




Now the value of b can be calculated:
Hence the equation is therefore:


Cleaning it up: