# Economics and uniform series formula problems

1. Sep 12, 2010

### MHrtz

1. The problem statement, all variables and given/known data

A Machine at a cost of $5,000 was purchased 3 years ago. It can be sold now for$3,000. If the machine is kept, the annual operating and maintenance costs will be $1,500. If it is kept and operated for next five years, determine the amount at time 0 (now) equivalent to the cost of owning and operating the machine can be sold for$1,000 at the end of the five year period. Use an interest rate of 10%.

A. 8065
B. 6550
C. 9522
D. 5002

2. Relevant equations

Not exactly sure which to use but here are the ones from the chapter we are studying:

F = P(1 + i)^n

F = A [((1 + i)^n - 1))/i]

P = A [((1 + i)^n - 1))/((i(1 + i)^n))]

3. The attempt at a solution

1500 * 5 = 7500
7500 - 1000 = 6500
6500 is not one of the choices

What now?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 14, 2010

### Redbelly98

Staff Emeritus
As nobody else has replied, I'll try to offer a hint or two ...

It looks like you have to consider two situations...

(A) The machine is sold today for $3000 (B) The machine is kept, operated for 5 years, and then sold for$1000.

... and then take the difference between the $3000 you could make, versus the money (a negative number) which must be set aside today to cover 5 years of operating costs. So, how much money must be set aside to cover operating costs over the next 5 years? Hint, it is not simply$1500*5, you must take into account the 10% interest.

As a final twist, the $1000 earned in the future must be taken into account as well. 3. Sep 14, 2010 ### MHrtz That's what i thought also so I used the 3rd equation. A = 1500 n = 5 i = .1 but I get 5686.18 as an answer for P. Then I realized that didn't make any sense because 1500 dollars is not an annuity. In other words, the 1500 dollars doesn't collect interest because it's merely a recurring cost. 4. Sep 15, 2010 ### Redbelly98 Staff Emeritus You should have to set aside less than$1500 for each year of operating cost in the future. That money then accrues interest at 10%, until it is worth the necessary $1500 to cover operating costs at the appropriate time. It's not clear to me if operating costs are paid annually, monthly, continuously, or what -- hopefully that has been explained to you in the textbook or your course lectures. 5. Sep 26, 2010 ### MHrtz The solutions were finally posted. Here is what you were supposed to do: P =$3,000
Operating and maintenance costs / year = $1,500 n = 5 years Salvage value =$1,000
Interest rate = 10%
PW of costs = 3,000 + 1,500 (P/A, 10%, 5) - 1,000(P/F, 10%, 5)
= 3,000 + 1,500 (3.791) -1,000(0.6209)
= \$8,065.60