Oliver LEHMANN, question 2 (about Present Value)

I have been struggling for a while now with an exercise which requires the PV=FV/(1+r)^n formula.

Weblink is: http://www.oliverlehmann.com/pmp-self-test/75-free-questions.htm

Right answer is supposed to be D but I cannot figured out where comes from the 3%...  I would greatly appreciate that someone show me step by step how to solve this exercise which has been torturing me for 2 days now


A company has to make a choice between two projects, because the available resources in money and kind are not sufficient to run both at the same time. Each project would take 9 months and would cost $250,000.

The first project is a process optimization which would result in a cost reduction of $120,000 per year. This benefit would be achieved immediately after the end of the project.


The second project would be the development of a new product which could produce the following net profits after the end of the project:

1. year:  $  15,000

2. year:  $  125,000

3. year:  $  220,000


Assumed is a discount rate of 5% per year. Looking at the present values of the benefits of these projects in the first 3 years, what is true?


A) Both projects are equally attractive.

B) The first project is more attractive by app. 7%.

C) The second project is more attractive by app. 5%.

D) The first project is more attractive by app. 3%. 

Formula is:  PV = FV/(1+r)^n

First Project


PV for 1st year = 120000/(1+.05)^1 = 114285.71

PV for 2nd year = 120000/(1+.05)^2 = 108843.54

PV for 3rd year = 120000/(1+.05)^3 = 103662.75

PV for 1st project = 114285.71 + 108843.54 + 103662.75 = 326792


Second Project


PV for 1st year = 15000/(1+.05)^1  = 14285.71

PV for 2nd year = 125000/(1+.05)^2 = 113378.68

PV for 3rd year = 220000/(1+.05)^3 = 190048.38

PV for 2nd project = 14285.71 + 113378.68 + 190048.38 = 317712.77


To find which is attractive


= (326792-317712.77)/317712.77 = 9079.23/317712.77

= 0.0286


To find %


0.0286 * 100 = 2.86% = app. 3%


Hence answer is D) The first project is more attractive by app. 3%. 

 Thank You AP , 

Let me know if we are bothering you too much , but can you explain how Mr . Oliver lehmann got the 2nd answer.


Thanks in advance. 

27. A project manager made 3-point estimates on a critical path and found the following results:

Assuming ±3 sigma precision level for each estimate, what is the standard deviation of the allover path?

  App. 4.2 days
  App. 5.2 days
  App. 6.2 days
  You can not derive the path standard deviation from the information given.

It wuld be impossible to get to this result without a calculator, do they allow ? Also, will there be questions of this complexity in th exam ?

Thanks.. this forum is really helpful.

Dear Amar,

Calculators will be in-built in the system. These problems are not at all complex. It may look complex because of the way I have explaned in detail.

If you know the formulae to be applied and if you practice well, then you can easily crack these type of questions under 1 minute.



 Thanks AP !!

Sounds like only the smartest person would be a PMP

Thank you so much! I understand now why I could not get the 3% of difference between A and B... I actually wrongly used the PV = FV/(1+r)^n formula because I used the "n" variable with 3 as period value for Year1, 2 and 3...

SD for allover path = Square root of (allover Variance)

Variance for allover path = Sum of (square of SD) of individual activities

Calculate SD

SD = (P-O)/6

Act. A = (24-12)/6 = 2
Act. B = (14-8)/6  = 1
Act. C = (27-15)/6 = 2
Act. D = (28-10)/6 = 3
Act. E = (35-17)/6 = 3

variance = Sum of square of all SDs
= 4+1+4+9+9 = 27

Now, SD for all over path = Square root of allover Varaince
= square root of 27 = 5.196

= App. 5.2 days

 Thanks AP , a good lesson learnt.

Much appreciated , thanks again.

The answer & explanations are on Oliver's site. For 1st & 2nd time scores, you can check https://www.pmbypm.com/oliver-lehmann-pmp-questions/