Question

n 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 $3,800 per month.

Purchase and installation costs of equipment would total $210,000. In five years the equipment could be sold for about 9% of its original cost.

An investment of an additional $3,000 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 $1.35 for a wash and $.90 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, $2,300; insurance, $75; and maintenance, $1,795.

Gross receipts from the wash would be about $2,295 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 15% return.

Click here to view Exhibit 13B-1 and Exhibit 13B-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. 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

1.

No. of washes per week = $ 2,295/$ 1.35 = 1,700 washes

No. of washes per year = 1,700 x 52 = 88,400 washes

Cash receipt from washes = 88,400 x $ 1.35 = $ 119,340

No. of vacuum per week = 1,700 x 60% = 1,020

No. of vacuum per year = 1,020 x 52 = 53,040

Cash receipt from vacuum = 53,040 x $ 0.9 = $ 47,736

Total cash receipt in a year = $ 119,340 + $ 47,736 = $ 167,076

Auto wash cash receipt	$        119,340
Vacuum cash receipt	$          47,736
Total cash receipt		$    167,076
Cash disbursement
Fixed cost
Rent ( $ 3,800 x 12)	$          45,600
Cleaning ( $ 2,300 x 12)	$          27,600
Insurance ( $ 75 x 12)	$                900
Maintenance ( $ 1,795 x 12)	$          21,540
Total fixed cost	$          95,640
Variable cost
Water ($0.075 x 88,400)	$            6,630
Electricity ($ 0.1 x 53,040)	$            5,304
Total variable cost	$          11,934
Total cash disbursement in a year		$ 107,574
Net annual cash receipt		$     59,502

2.

PV of annual cash flow for 5 years = Cash flow x PVoA (i, n)

PVoA = Present value of an annuity

PV of annual cash flow for 5 years = $ 59,502 x PVoA (15 %, 5)

                             = $ 59,502 x 3.35216 = $ 199,460.22

Additional cash inflow in year 5 = Salvage value + working capital

                                                         = ($ 210,000 x 0.09) + $ 3,000

                                                         = $ 18,900 + $ 3,000 = $ 21,900

PV of additional cash inflow = FV x Future value factor (i, n)

                                                    = $ 21,900 x Future value factor (15 %, 5)

                                                    = $ 21,900 x 0.4972 = $ 10,888.68

PV of cash inflow = $ 199,460.22 + $ 10,888.68 = $ 210,348.90

Initial investment = Cost of equipment + working capital =

                                            = $ 210,000 + $ 3,000 = $ 213,000

Net present value = PV of cash inflow – initial investment

                                 = $ 210,348.90 - $ 213,000 = - $ 2,651.10

3.

As NPV is negative Mr. Duncan should not open the car wash.