Question

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 determined the following: A building in which a car wash could be installed is available under a five-year lease at a cost of $4,300 per month. Purchase and installation costs of equipment would total $315,000. In five years the equipment could be sold for about 10% of its original cost. An investment of an additional $7,000 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 $1.36 for a wash and $.65 for access to a vacuum cleaner. The only variable costs associated with the operation would be 7.5 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, $2,800; insurance, $75; and maintenance, $1,745. Gross receipts from the wash would be about $2,992 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.

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.

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

Answer 1

Please hit like if this helps, comment in case of any doubts.

Computation of expected annual cash receipt from operation
Particulars		Amount
Autowash cash receipt ($2992*52)		$1,55,584.00
Vacuum cash receipt ($2992/1.36*0.65*60%*52)		$44,616.00
Total cash receipt		$2,00,200.00
Less: Cash disbursements:
Water ($2992 / 1.36 * 0.075*52)	$8,580.00
Electricity ($2992/1.36*60%*0.10*52)	$6,864.00
Rent ( $4,300 * 12)	$51,600.00
Cleaning ( $2,800 * 12)	$33,600.00
Insurance ( $75 * 12)	$900.00
Maintenance ( $1,745 * 12)	$20,940.00
Total cash disbursements		$1,22,484.00
Annual net cash flow from operations		$77,716.00

Solution 2-a:

Computation of NPV
Particulars	Period	Amount	PV Factor	Present Value
Cash outflows:
Cost of equipment	0	$3,15,000	1	$3,15,000
Working capital	0	$7,000	1	$7,000
Present value of cash outflows (A)				$3,22,000
Cash Inflows:
Annual cash inflows	1-5	$77,716	3.696	$2,87,238
Salvage value	5	$31,500	0.593	$18,680
Release of working capital	5	$7,000	0.593	$4,151
Present value of cash inflow (B)				$3,10,069
NPV (B-A)				-$11,931

Solution 2-b:

No, Mr. Duncan should not open the car wash because the NPV is negative which implies that the IRR is less than 11% required rate of return.