Question

1. A company calculates the expected net present value of a project as $350,000. The standard

deviation is $200,000.

a. What is the probability that the project will have a net present value between $350,000 and

$600,000?

b. What is the probability that the project will have a negative net present value?

Answer 1

Given,

Expected Net Present Value = µ = 350000

Standard Deviation = σ = 200000

(a) Let the probability that NPV is less than 350000 be P(z1) and probability that the NPV is less than 600000 be P(z2)

Hence, probability that NPV is between 350000 and 600000 is P(z2) - P(z1)

z = (x - µ)/σ

x1 = 350000

=> z1 = (350000 - 350000)/200000 = 0

from z table, P(z1) = 0.50

x2 = 600000

=> z2 = (600000 - 350000)/200000 = 1.25

from z table, P(z2) = 0.8944

Hence, Probability that the NPV is between 350000 and 600000 = 0.8944 - 0.50 = 0.3944 or 39.44%

(b) Probability that the NPV is less than 0 = P(z)

x = 0

z = (0 - 350000)/250000 = -1.75

from z table, P(z) = 0.0400 or 4%