Economics and uniform series formula problems

[MHrtz]

Homework Statement

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

Homework 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))]

The Attempt at a Solution

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

What now?

 

[Redbelly98]

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.

 

[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.

 

[Redbelly98]

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.

 

[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
The answer is, “A”.

What I didn't understand was that everything must be taken to the present including the salvage value which is also affected by the interest rate. Money is not worth the same in the future as it is in the present.