It was recently reported in the financial press that a major retailer spent $$29$ million an hour on cashier wages. Concerned about future increasing labor costs, assume that this retailer installs self$-$checkouts for the customers to use in their purchases. The initial cost of these machines is $$82,000$ and these machines have a life of seven years. The yearly savings in cashier labor cost is $$125,000,$ the additional annual surveillance cost is $$15,000$ per machine, and the additional theft cost is $$16,000$ per machine. Using an $8\mathrm{.}4\%$ cost of capital and ignoring depreciation and taxes $($until covered in chapter $8),$ the net present value of these self$-$checkout machines is