math
posted by Anna on .
I cant figure this thing out fully, I feel so clueless. Does anyone have any pointers or tips for me?
Company needs a new copy machine. Rent costs are = 17.5 cents / each.
Number of copies = atleast 200 000. (The company agrees to buy at least that number)
Buying the unit costs 150 000 SEK. The bank wants a 6.5% interest rate and
after 5 years, the unit needs to be fully paid for.
Maintenance and operation is estimated to cost 6 cents / copy.
In both cases, the actual paper costs will be the same for both options.

What is the total cost after 5 years, which is cheapest?
How many copies / year, before it pays to buy the machine instead of renting?
Which maximum price / copy, can you pay to the leasing company in case you want to have equal cost to lease / purchase if you copy 200,000 copies / year. (Other values are equal)

Option #1.
Cost = (0.175+0.06)cents/copy * 200,000copies/yr * 5yrs = $235,000 = cost of renting for 5 yrs.
Option # 2.
Cost = $150,000 + $150,000*0.065*5 =
150,000 + 48,750 = $198,750 = cost of
buying for 5 yrs.
Buying is cheapest after 5 years.
N = the # of copies /yr.
C = (0.175+0.06)cts/copy * N copies *
5yrs = 198,750,
C = 1.175N = 198,750,
N = 169,149 copies/yr. before it pays to buy.
Max. price per copy = $P.
Cost=$P/copy *200,000copies/yr * 5yrs =
198,750,
1,000,000P = 198,750,
P = $0.198750 = 19.8750 Cents/copy
. 
Thank you Henry! I really appreciate your help! :) Great!