In five years, Kent Duncan will retire. He is exploring the possibility of opening a self$-$service car wash. The car wash could be managed in the free time he has available from his regular occupation, and it could be closed easily when he retires. After careful study, Mr$.$ Duncan has determined the following:

A building in which a car wash could be installed is available under a five$-$year lease at a cost of $$5,900$ per month.

Purchase and installation costs of equipment would total $$245,000.$ In five years the equipment could be sold for about $9\%$ of its original cost.

An investment of an additional $$9,000$ would be required to cover working capital needs for cleaning supplies, change funds, and so forth. After five years, this working capital would be released for investment elsewhere.

Both a wash and a vacuum service would be offered with a wash costing $$1\mathrm{.}12$ and the vacuum costing $$0\mathrm{.}70$ per use.

The only variable costs associated with the operation would be $7\mathrm{.}5$ cents per wash for water and $10$ cents per use of the vacuum for electricity.

In addition to rent, monthly costs of operation would be: cleaning, $$1,400$; insurance, $$75$; and maintenance, $$1,895.$

Gross receipts from the wash would be about $$3,024$ per week. According to the experience of other car washes, $60\%$ of the customers using the wash would also use the vacuum.

Mr$.$ Duncan will not open the car wash unless it provides at least a $13\%$ return.

Required:

$1.$ Assuming that the car wash will be open $52$ weeks a year, compute the expected annual net cash receipts from its operation.

$2-$a$.$ Determine the net present value using the net present value method of investment analysis. $($Any cash outflows should be indicated by a minus sign. Round the final answers to the nearest whole dollar.$)$

$2-$b$.$ Would you advise Mr$.$ Duncan to open the car wash?