A company is considering two investment projects whose present values are descri

Question

A company is considering two investment projects whose present values are described as follows: NPW(8%)= 18 X+ 7.5 XY, where X and Y are statistically independent discrete random variables with the following distributions: Compute the mean and variance of the NPW for project 1 (NPW_1), Identify the joint outcome (s) by the pair of NPW values (NPW_1 = ? and NPW_2 = ?) such that Project 2 is considered better than Project 1. Note there is a total of 4 possible NPW_1 values and four given NPW_2 values. Therefore, you have a total of 16 different pairs of NPW values. Calculate the probability that Project 1 is better than Project 2?

Explanation / Answer

NPV(8%) represents net present value with getting 8% profit.

NPV = 18x+ 7.5 xy

Mean of NPV can be calculated by multiplying the probabilty of the event with its value and fitting it into the equation.

= [18*0.55*20+7.5*0.55*20*0.3*10]+1[8*0.55*20+7.5*0.55*20*0.7*20]+[18*0.45*40+7.5*0.45*40*0.3*10]+[18*0.45*40+7.5*0.45*40*0.7*20]

=445.5+1243+729+2214

= $4631.5

this is mean NPV for project 1

value for variable x event 1, variable y event 1

=18*20+7.5*20*10

1860

variance for this case = (4631.5 - 1860) = 7681212

value for variable x event 1, variable y event 2

=18*20+7.5*20*20

=3360

variance for this case = (4631.5 - 3360)2 =

value for variable x event 2, variable y event 1

=18*40+7.5*40*10

3720

variance for this case = (4631.5 -3720)2 =

value for variable x event 2, variable y event 2

=18*40+7.5*40*20

=6720

variance for this case = (4631.5 - 6720)2 = 4361832

total variance = sum of variances in all four cases =

14490589

830832.3

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