A4Q2)- The following question is based on the textbook: Engineering Economic Ana

Question

A4Q2)- The following question is based on the textbook: Engineering Economic Analysis, Third Canadian Edition. D. Newnan, J. Whittaker, T. Eschenbach, J. Lavelle. Oxford University Press. Please provide all the formulas used and an example of how to use them, in case of solving part of the problem with Excel.

A company is considering two investment projects whose present values are described as follows:

Project 1: NPW(10%) = 20 X + 8 XY,

where X and Y are statistically independent discrete random variables with the following distributions:

Variable X

Variable Y

Event

Probability

Event

Probability

$20

0.55

$11

0.3

$40

0.45

$22

0.7

Project 2:

NPW(10%)

Probability

[a] Compute the mean and variance of the NPW for project 1 (NPW1),
[b] Identify the joint outcome(s) by the pair of NPW values (NPW1 = ? and NPW2=?) such that Project 2 is considered better than Project 1. Note there are a total of 4 possible NPW1 values and four given NPW2 values. Therefore, you have a total of 16 different pairs of NPW values.
[c] Calculate the probability that Project 1 is better than Project 2?

Variable X

Variable Y

Event

Probability

Event

Probability

$20

0.55

$11

0.3

$40

0.45

$22

0.7

Explanation / Answer

PROJECT 1

e(n.p = 20e(x) + 8 .e (x).e(y)

e(x) =20 *0.55 + 40*0.45 = 29

e(y) = 11*0.3 + 22*0.7 = 19 (approx)

e(x2) = 400 * 0.55 + 1600 *0.45 = 940

e(y2) =121*0.3 + 484* 0.7 = 374

var (x) = e(x2  ) - e (x) 2 = 940 - 292 = 99

var(y) = e(y2  ) - (e (y) )2 = 374 - 361 = 13

e(n.p = 20e(x) + 8 .e (x).e(y) = 20* 29 + 8.19.29 = 4988

variance = v( 20 x + 8xy) = 400.va(x) + 64 .v(xy)

= 400.var(x) + 64 * v(x)*v(y)

= 400 *29 + 64 * 99*13

=16748

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