A project has an expected NPV of $50,000 with a standard deviation of the NPV of $20,000. Assume that NPV is normally distributed. What is the probability that the project will have a net present value greater than $60,000?
A) 1915%
B) 69.15%
C) 0.13%
D) 30.85%

Question

Quizplus · Accepted Answer

First, we need to standardize the NPV using the formula:

z = (X - μ) / σ

where X is the value we want to find the probability for (in this case, $60,000), μ is the expected value ($50,000), and σ is the standard deviation ($20,000).

z = (60,000 - 50,000) / 20,000
z = 0.5

Next, we need to find the probability of getting a z-score of 0.5 or greater using a standard normal distribution table or a calculator. This is equivalent to finding the area to the right of z = 0.5 on a standard normal distribution curve.

Using a calculator, we can find this probability by using the normalcdf function:

normalcdf(0.5, E99)
0.3085375387

Rounding to two decimal places, we get 0.31 or 31%.

Therefore, the probability that the project will have a net present value greater than $60,000 is 30.85%. The correct choice is D.

A Project Has an Expected NPV of $50,000 with a Standard