A new optical reader for scanning documents is being considered by a retail bank. The new

system has a fixed cost of $30,000$ per year and a variable cost of $2\mathrm{.}5$ per batch. The cost of

the new scanner is $100,000.$ The bank charges $10$ per batch for scanning documents and

it believes that the demand for its scanning services will be $2,000$ batches in year $1,5,000$

batches in year $2,10,000$ batches in year $3,$ and then $12,000$ batches per year from year

$4$ onwards. If the realistic discount rate for the bank is $6$ per cent, calculate the net present

value of the investment over a five$-$year period.