# Calculating the NPV of an investment

Order Description

1. Two investments (A and B, below) have been proposed to the Capital Investment committee of your organization;
a. The required rate of return for your company is 6%. What is the NPV for each investment? Assume all costs and benefits occur at the beginning of the year indicated.
b. What is the payback period for each investment?
c. Which investment would you recommend and why?
Investment A Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Costs: \$125,000 \$10,000 \$10,000 \$10,000 \$10,000 \$10,000
Benefits: – \$90,000 \$55,000 \$35,000 \$20,000 \$20,000

Investment B Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Costs: \$70,000
Benefits: \$45,000 \$15,000 \$10,000 \$10,000 \$15,000
2. Unfortunately, the Capital Investment Committee refused to approve your recommendation (Problem 1) since you did not consider the uncertainty inherent in these types of investments. You pull out your very dog-eared text from PMAN 635 and repeat your analysis, this time using Crystal Ball and the following information:
a. Investment A:
i. Year 0 Investment cost: Triangular distribution (optimistic: \$100,000; most likely: \$125,000; pessimistic: \$200,000)
ii. Year 1-5 operating cost: Normal distribution (mean of \$10,000, standard deviation of \$2,000)
iii. Year 1 Benefits: Normal distribution (mean of \$90,000, standard deviation of \$20,000)
iv. Year 2 Benefits: Normal distribution (mean of \$55,000, standard deviation of \$15,000)
v. Year 3 Benefits: Normal distribution (mean of \$35,000, standard deviation of \$10,000)
vi. Year 4 Benefits: Normal distribution (mean of \$20,000, standard deviation of \$5000)
vii. Year 5 Benefits: Normal distribution (mean of \$20,000, standard deviation of \$5000)
b. Investment B:
i. Year 0 Investment cost: Uniform distribution (Minimum: \$65,000; Maximum: \$75,000)
ii. Year 1 Benefits: Normal distribution (mean of \$45,000, standard deviation of \$20,000)
iii. Year 2 Benefits: Normal distribution (mean of \$15,000, standard deviation of \$5,000)
iv. Year 3 Benefits: Normal distribution (mean of \$10,000, standard deviation of \$3,000)
v. Year 4 Benefits: Normal distribution (mean of \$10,000, standard deviation of \$3,000)
vi. Year 5 Benefits: Normal distribution (mean of \$15,000, standard deviation of \$5,000)
If the IRR is still 6%, what is the NPV for each investment?

3. Using the forward and backward pass method, identify the Critical Path and total duration for the following network. Show all work.

a 10
b 5 a
c 8 a
d 3 b, c
4. For the network below:
a. Calculate T-E and Variance for each activity.
b. Calculate the expected duration of the network. Do not use Crystal Ball.
c. What is the probability the network will take no more than 21 days? Use the Z-table or Excel’s NORMDIST function, not Crystal Ball. Be sure to show all work.

Task Optimistic Duration Most Likely duration Pessimistic Duration T-E Var Pred
a 8 10 14
b 4 5 7 a
c 8 8 9 a
d 3 3 3 b, c

5. The first unit produced by a manufacturer required 6 hours. If the industry uses a 90 percent learning curve rate, how long should the following units take?
a. Unit 2
b. Unit 3
c. Unit 4

7. Enter the tasks and resources in the attached file (Midterm Question 7.doc) into MS Project. Note that there are two tables in this file. What is the total duration and cost for your project? Include your MSP project file with your submission.

a. What is the expected time to complete a task with an optimistic (a), most likely (m), and pessimistic (b) times of 3, 4 and 7 days respectively?
b. What is the standard deviation of the same task, assuming that 99.7% of the outcomes fall between a and b?
c. What is the standard deviation of the same task, assuming that 90% of the outcomes fall between a and b?

9. There are three (and only three) paths through a network (project), each with a probability of completion in less than 24 months as indicated:
• S- a-b-F P1(<24) = .95
• S- d-e-F P2(<24) = .85
• S- g-h-F P3(<24) = .90
a. If the tasks are independent, what is the probability of the project being completed within 24 months? Note: S is the start node, F is the finish node
b. What is the probability the project being completed in 24 months or longer?

10. You are a project manager who is reviewing the estimates for the cost of materials. You therefore begin tracking the estimated cost estimates of two procurement specialists and comparing their estimates with the actual costs of the materials once ordered. You obtain the information reflected in the attached tracking table.
a. Does the data indicate that either of the two procurement specialists is biased? Which one? In which direction?
b. Regardless of bias, does one procurement specialist appear to be more accurate in their estimates than the other? Which one?
Be sure to explain your answers. Hint, review the material in Section 4.3 of Mantel.

11. Referring to the project in question 7:
a. Using the information contained in the attached file (Midterm Question 11), what is the new duration and cost for the project? You do not have to use MSP to answer this question. Note, since the tasks are laddered, there is only one path through the network. Therefore, TEproject = ƩTE activities and the VARproject = ƩVARactivities.
b. Using Table 5-7 in Mantel, what is the probability that you can finish the project in 115 days?

12. Referring back to Question 2, you have proudly submitted your analysis of investments A and B. You are called back in to the Capital Investment Committee for what you assume will be to receive their gracious thanks for a job well done. Unfortunately, you realize there is a new member on the committee and you recognize a former Professor of yours from UMUC. He is still wearing both a belt and suspenders, so you are not surprised at his first question: “And what is the 90% solution?” You realize he is really asking for the value that each investment will exceed 90% of the time? Fortunately, you still have access to crystal ball, so you whip out your laptop and…
a. Well, what is the answer for Investment A?
b. And, what is the answer for Investment B?