Question

$20 21. Assume that we can estimate a project's cash flows as follows: n Expected Flow E(A) Estimate of Standard Deviation on 0 -$300 $120 $10 $150 $15 $150 $110 $100 $30 $20 $25 In this case, each annual flow can be represented by a random variable with known mean and variance. Further assume complete independence among the cash flows.

a) What is the NPV of the project at a MARR of 10%?

b) What is the variance of the NPV?

c) If the cash flows are normally distributed, determine the probability that the NPV exceed $200. Please enter the probability as a decimal value using 2 decimal places.

Answer 1

Computation of NPV at a MARR of 10%

Year	Expected Cash Flow	Discounting Factor -10%	Discounted Cash Flow
0	-$300	1.00	-$300
1	$120	0.909	$109
2	$150	0.826	$124
3	$150	0.751	$113
4	$110	0.683	$75
5	$100	0.621	$62
NPV			$183

a) The NV of the project at a MARR of 10% is summation of Cash outflow and cash inflow i.e.$183.

b) Computation of variance of NPV

Variance = Square root of Standard Deviation (SD) i.e. (SD)2

Year	Standard Deviation	Discounting Factor -10%	Discounted Standard Deviation
0	-$20	1.00	-$20
1	$10	0.909	$9.09
2	$15	0.826	$12.39
3	$20	0.751	$15.02
4	$25	0.683	$17.08
5	$30	0.621	$18.63
NPV			$52.21

Variance of the NPV is $52.21 X $52.21$=$ $2725.88

c) determination of the probability that the NPV exceed $200.

If the cash flows are normally distributed, the probability will computed in the following steps:

1. Compute Z value by using the following formula i.e. Z$=$ (Desired Value - Expected Mean)/Standard Deviation

If the Z value is positive, it means that fallen in "Right Tail" and if value is negative that falls under "Left Tail'

2. Identify the table value corresponding to the computed Z value

3. The probability can be find with above Z value either deduct or add the Z value to 0.5

In the given question

The desired value is $200 , The expected mean is nothing but NPV i.e.arrived in a) - $183.

The standard deviation of the project is as follows:

Year	Standard Deviation	Discounting Factor -10%	Discounted Standard Deviation
1	$10	0.909	$9.09
2	$15	0.826	$12.39
3	$20	0.751	$15.02
4	$25	0.683	$17.08
5	$30	0.621	$18.63
		Standard Deviation	$72.21

Z= (200-183)/72.21

$=$0.235 which is a positive falls under Right Tail

The table value of 0.235 is 0.09095, thi value to be added to 0.5 i.e.(0.5+0.09095)*100 = 59.095

The probability that NPV exceed $200 is 59.095%