economics problem

[alejo12]

hi everyone,

Not sure if I'm posting this particular problem in the right forum , but its worth a try.

The problem wants us to find the present value of a reconstruction alternative for a pavement.

Given:

$7,000,000 Reconstruction Cost

Anual Maitenance 1st 10 years ....... $40,000

2nd 10 years........$85,000

Major Maintenance ( every 10 yrs ) $350,000

Residual Value................................$400,000

So,

$7,000,000 + ($40,000)(P/A,i=5,n=10) + $(85,000)(P/A,i=5,n=10)(P/F,i=5,n=10) + ($350,000)(P/F,i=5,n=10) - ($400,000)(P/F,i=5,n=20)

Why is the 2nd anual cost multiplied by (P/F) ??

will appreciate any help.

 

[Chucktown PE]

Because you are starting those payments 10 years from now. So the P/A brings all future payments back to the value 10 years from now, and the P/F brings that value back to present value.

 

[HokieGirl]

Chuck's right. You start paying it on year 10. So, when you bring it back to "present" with the first part of the equation (P/A,i=5,n=10), you're really only bringing it right before you started paying it, which is year 10. Then, you have to bring that number back to present.

Personally, I like to draw it out and write down subscripts when dealing with this kind of a problem. I would call it (P10/A,i,10) just to keep it in my mind that it's the value at year 10. Then, treat it just like you treat the maintenance at year 10.

If this isn't clear, let me know and I'll draw it up and send it to you. Sometimes it's easier to see it in graph form.

 

[alejo12]

Yes , this helps a lot.

Thanks everyone.

 

[Samuel]

Chuck's right. You start paying it on year 10. So, when you bring it back to "present" with the first part of the equation (P/A,i=5,n=10), you're really only bringing it right before you started paying it, which is year 10. Then, you have to bring that number back to present.
Personally, I like to draw it out and write down subscripts when dealing with this kind of a problem. I would call it (P10/A,i,10) just to keep it in my mind that it's the value at year 10. Then, treat it just like you treat the maintenance at year 10.

If this isn't clear, let me know and I'll draw it up and send it to you. Sometimes it's easier to see it in graph form.

Hey if we treat the first 10years of maintenance as P/A, why are we multiplying the 2nd yeras of maintenance by P/F. It is confusing. Can somebody really explain this?

 

[Chucktown PE]

Because P/A is only applicable if the A starts in the current year.

 

[HokieGirl]

DELETING THIS POST AND WILL RESPOND BETTER LATER.

It didn't show up as I wanted it to. Sorry.

 

[HokieGirl]

Okay, so what I was trying to say, I've put in an Excel file. Hopefully that will clear things up a bit.

Looking only at the section of annual maintentance in years 11-20, you do P/A to bring back to year 10, which is right before you started paying your maintenance. Then you have this big lump at year 10 that has to be brought to current using P/F.

To bring back to the beginning of when you started paying this group of annual maintenance, you use the following equation:

X = $(85,000)(P/A,i=5,n=10)

To bring that back to the present value, you use the following equation:

Y = (X)(P/F,i=5,n=10)

Where X is what you calculated in the equation above.

You can only slide the annual payments left to the point of where you start making the payments.

See the Excel file to see it drawn out in graph form.

econ_prob.xls

 

[civilized_naah]

Or, you can also think of it as an annuity of $85k for 20 years MINUS an annuity of $45 k for the first 10 years. Both of these have their 'origin' at year zero and therefore can be used directly. Both approaches give you the same anwser.

Method 1: 40k x (P/A,10 years) + 85k x (P/A,10years) x (P/F, 10 years)

Method 2: 85k x (P/A,20years) - 45k x (P/A,10years)

 

[Samuel]

Or, you can also think of it as an annuity of $85k for 20 years MINUS an annuity of $45 k for the first 10 years. Both of these have their 'origin' at year zero and therefore can be used directly. Both approaches give you the same anwser.
Method 1: 40k x (P/A,10 years) + 85k x (P/A,10years) x (P/F, 10 years)

Method 2: 85k x (P/A,20years) - 45k x (P/A,10years)

It's now very clear, Thanks everyone for your contribution

 

[winner9459]

Thanks groupies, this does help. I was stuck at one such kind of problem and I come here, and baam....I landed right on it. Keep up the good work.