# NCEES Morning Sample Question 102



## seysan

Problem 102 asks for the PW of the investment and maintenance cost. In the solution, I understand the first equation is a "single payment PW" equation for one system, and the second and third equation of the solution is a "uniform sreies PW" equation.

Please help me understand where the "20,000" in the second equation and the "10,000" in the third equation comes from.

Please help me understand why the first and third equation is calculated for "2 years", and why the second equation is calculated for "4 years".

Thank you in advanced for any help provided.


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## benbo

seysan said:


> Problem 102 asks for the PW of the investment and maintenance cost. In the solution, I understand the first equation is a "single payment PW" equation for one system, and the second and third equation of the solution is a "uniform sreies PW" equation.
> Please help me understand where the "20,000" in the second equation and the "10,000" in the third equation comes from.
> 
> Please help me understand why the first and third equation is calculated for "2 years", and why the second equation is calculated for "4 years".
> 
> Thank you in advanced for any help provided.


I don't have the book with me, but there is an errata for this problem -

http://www.ncees.org/exams/study_materials...ical_errata.pdf

If this doesn't solve it for you, and nobody else answers, I'll try to answer when I get home.


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## chicago

seysan,

In the problem statement, it states, "Each unit requires a maintenance cost of $10,000/year of operation." Hence, that is where the $20,000 comes from in the 2nd equation--&gt; 2*$10,000 for both units.

The second equation, n=4 due to the 2nd computer being installed 2 years later. This, in turn, leads to why they subtracted with n=2 years in the third equation for the offset. Draw the equivalence cash flow diagram and it will be more clear. I know it helped me a lot in solving this question.

Hope that helps.


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## seysan

benbo and chicago,

Thanks for the replies. I am still having a hard time understanding why n=2 for the first eqn, n=4 for the second eqn, and why n=2 for the third eqn. My apologies, I have been out of college too long.


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## grownupsara

seysan said:


> benbo and chicago,Thanks for the replies. I am still having a hard time understanding why n=2 for the first eqn, n=4 for the second eqn, and why n=2 for the third eqn. My apologies, I have been out of college too long.


my best understanding of these problems is that all the time periods have to be taken from the same "base year", t=0. so, while you have a $10,000 cost from t=0 to t=4, it's impossible to separately add the second $10,000 cost from t=2 to t=4. instead, their solution shows that you have to just pretend that you have both costs, $20k, from year t=0 to t=4. then, you subtract off $10k from years t=0 to t=2 since you only have one unit for those first 2 years. that method is basically a way to just get around not being able to add that second expense in at year 2.

p.s. this is my first post on this forum, but i've been lurking around here for a while now. i'm getting ready to post a few questions about the NCEES prac exam, so i thought i'd help out with this question for good karma.


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## benbo

Good explanation! Welcome aboard. If history repeats, you are probably a "power" ranger - so I may be of limited help. But there are a lot of power experts around here.


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## jdd18vm

Okay at the risk of showing what a dunce i am two days prior to the exam.

I dont understand what fundamental rule I am missing I took the approach Shell did.

I sent a pm to shell but in case they dont get it.

can anyone explain how the cash flow diagram would look. Ive tried it every way i could think of. year 0-4 50K at 0, 10K year one ...60 at 0, ...ugh0

And the initial year 0 is taken at the year 1 rate in the table.

Simple stuff, or so its been said...LOL

John


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## shellbell500

jdd18vm said:


> Okay at the risk of showing what a dunce i am two days prior to the exam.
> I dont understand what fundamental rule I am missing I took the approach Shell did.
> 
> I sent a pm to shell but in case they dont get it.
> 
> can anyone explain how the cash flow diagram would look. Ive tried it every way i could think of. year 0-4 50K at 0, 10K year one ...60 at 0, ...ugh0
> 
> And the initial year 0 is taken at the year 1 rate in the table.
> 
> Simple stuff, or so its been said...LOL
> 
> John


try this (i'm basing this on the book problem which is what i have in front of me):

cash flow diagram should have:

@ n=1, $50K. @ n=2, $10K. @ n=3, $50K plus $10K. @ n=4, $20K. @ n=5, $20K. Now, the way I have been doing these is to convert all of those "future worths" (F) into "present worths," P, by using the F/P factors. You can simplify the calc by using the uniform series factors, but i'm trying to KISS (keep it simple stupid) and just use a slower but more clear approach (to me that is).

Does that help?


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## benbo

The econ problems on my actual exam were easier than this. They were gimees. Not to say that is always the case, but it's possible.


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## jdd18vm

shellbell500 said:


> try this (i'm basing this on the book problem which is what i have in front of me):
> cash flow diagram should have:
> 
> @ n=1, $50K. @ n=2, $10K. @ n=3, $50K plus $10K. @ n=4, $20K. @ n=5, $20K. Now, the way I have been doing these is to convert all of those "future worths" (F) into "present worths," P, by using the F/P factors. You can simplify the calc by using the uniform series factors, but i'm trying to KISS (keep it simple stupid) and just use a slower but more clear approach (to me that is).
> 
> Does that help?


Shell

Yes, it partially helps in that, this is exactly what I had so at least THAT was right.

But now for the DUH :blink: . Will post my misunderstanding in hopes that in the very unlikely event someone thinks as assbackwards as me, they can benefit.

As I looked at initial cost 50K n=1 (I actually used 0-4) I applied the 4 year P/W value to this, the 3 year to the 10K etc. On the way home from work a light went off!

I don't know if you got my second pm, nothing shows in my sent. But that was what I was asking.

Also, do we do nothing with the ROR? and Why?

I am ALL about KISS

John


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## chicago

shellbell500 said:


> @ n=1, $50K. @ n=2, $10K. @ n=3, $50K plus $10K. @ n=4, $20K. @ n=5, $20K. Now, the way I have been doing these is to convert all of those "future worths" (F) into "present worths," P, by using the F/P factors.


shellbell500,

If you're treating all those future costs from t=1 to 5 as future worths and you want to convert everything to present worth, shouldn't you be using the P/F factors instead?

Just want to make sure John and you and anyone else reading this are on the same page...

And John, the rate of return doesn't play a factor. I think it's just extra information.


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## shellbell500

chicago said:


> shellbell500,
> If you're treating all those future costs from t=1 to 5 as future worths and you want to convert everything to present worth, shouldn't you be using the P/F factors instead?
> 
> Just want to make sure John and you and anyone else reading this are on the same page...
> 
> And John, the rate of return doesn't play a factor. I think it's just extra information.


Yes - sorry, I should be using the P/F factors, not the F/P!  THanks!!!


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