The net present value of a project is normally distributed with an expected value of $52,000 and a standard deviation of $31,515. Determine the probability that the project will have a net present value of less than zero.
A) 1.65%
B) 95.1%
C) 4.95%
D) Cannot be determined

Question

Quizplus · Accepted Answer

To find the probability that the net present value will be less than zero, we need to standardize the distribution by converting it to a standard normal distribution. We can do this using the formula:

z = (X - μ) / σ

where X is the net present value, μ is the expected value, and σ is the standard deviation.

Plugging in the values, we get:

z = (0 - 52000) / 31515
z = -1.65

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than -1.65 is 0.0495 or 4.95%. Therefore, the probability that the project will have a net present value of less than zero is 4.95%, which corresponds to choice C.

The Net Present Value of a Project Is Normally Distributed