End of Year Mean Net Cash Flow Standard Deviation of Cash Flow -$32,000 $1,000 1 $4,000 $2,000 2 $8,000 $3,000 3 $12,000 $5,000 4 $12,000 $6,000 $12,000 $7,000
End of Year Mean Net Cash Flow Standard Deviation of Cash Flow -$32,000 $1,000 1 $4,000 $2,000 2 $8,000 $3,000 3 $12,000 $5,000 4 $12,000 $6,000 $12,000 $7,000
End of Year Mean Net Cash Flow Standard Deviation of Cash Flow -$32,000 $1,000 1 $4,000 $2,000 2 $8,000 $3,000 3 $12,000 $5,000 4 $12,000 $6,000 $12,000 $7,000
A proposed project has the following cash flow estimates. Assuming independent cash flows, a normally distributed net present value, and a minimum attractive rate of return of 18%, determine the following. For the following questions, employ an analytical solution: a. The mean and standard deviation of net present value. b. The probability that the net present value is positive. c. The probability that the net present value is greater than $5,000. Assume the initial investment and annual receipts are normally distributed. d. Using a Monte Carlo simulation with 10,000 iterations, estimate the probability that the present worth is positive and estimate the probability that the present worth is greater than $5,000.
Transcribed Image Text:End of Year Mean Net Cash Flow Standard Deviation of Cash Flow
-$32,000
$1,000
1
$4,000
$2,000
2
$8,000
$3,000
3
$12,000
$5,000
4
$12,000
$6,000
$12,000
$7,000
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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