Kent Duncan is exploring the possibility of opening a self$-$service car wash and operating it for the next five years until he retires. He has gathered the following information:

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 $$230,000.$ In five years the equipment could be sold for about $8\%$ of its original cost.

An investment of an additional $$4,000$ 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. Each customer would pay $$1\mathrm{.}12$ for a wash and $$0\mathrm{.}65$ for access to a vacuum cleaner.

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, $$4,500$; insurance, $$75$; and maintenance, $$1,935.$

Gross receipts from the wash would be about $$3,248$ 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 $11\%$ return.

Click here to view Exhibit $12$B$-1$ and Exhibit $12$B$-2,$ to determine the appropriate discount factor$($s$)$ using tables.

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$.$ What is the net present value of the investment in the car wash?

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