Question

Problem 13-27 (Modified) – determine Simple Rate of Return, Payback Method, Net Present Value, Internal Rate of Return, and Decision Making (25 points).

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 an auto wash could be installed is available under a five-year lease at a cost of $1,700 per month.

Purchase and installation costs of equipment would total $200,000. In five years, the equipment could be sold for about 10% of its original cost. Depreciation in done using the straight-line method over its useful life.

An investment of an additional $2,000 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 car wash and a vacuum service would be offered with a wash costing $2.00 and a vacuum costing $1.00 per use.

The only variable costs associated with the operation would be $0.20 per wash for water and $0.10 per use of the vacuum for electricity.

In addition to rent, monthly costs of operation would be: cleaning, $450; insurance, $75; and maintenance, $500.

Gross receipts from the car wash would be about $1,350 per week. This would be 675 car washes per week. According to the experience of other car washes, 60% of the customers using the wash would also use the vacuum. There would be 405 vacuum uses (675 * 60%) per week

Mr. Duncan will not open the car wash unless it provides at least a 10% return, since this is the amount that could be easily be earned by placing the $200,000 in high-grade securities.

Required:

Assuming that the car wash will be open 52 weeks a year, compute the expected net annual cash receipts (gross cash receipts less cash disbursement) from its operation. Do not include the cost of the equipment, the working capital, or the salvage value in these computations. Use the template below!

The expected net annual cash receipts will be:

Car wash cash receipts
Vacuum cash receipts
Total cash receipts
Less cash disbursements:
Washer
Electricity
Rent
Cleaning
Insurance
Maintenance
Total cash disbursements
Net annual cash receipts

a.     Calculate the simple rate of return using the following formula:

Annual rate of return = Cash Receipts - Depreciation/ Initial Investment

Would the car wash be purchased using the 10% required rate of return?

b.     Calculate the payback period using the following formula:

Payback period = Investment / Cash Receipts

Kent Duncan hopes to recover his initial investment within three years. Would he accept this investment using these criteria?

c.     Compute the net present value using the required rate of return of 10% and set your problem up using the following template and use the NPV formula below!

Item	Now (0)	Year 1	Year 2	Year 3	Year 4	Year 5
Initial Investment
Working capital
Cash inflows
Salvage value
WC released
Net annual cash flows

Net Present Value = Cash flow yr. 0 + NPV(R of R, cash flow yr. 1: cash flow yr.5)

d.     Approximate the internal rate of return using the following formula:

Internal Rate of Return = Investment / cash flows = IRR(cash flow yr. 0: cash flow yr.5)

2.     Would you advise Kent Duncan to open the car wash using all of the above capital budgeting evaluations methods at the 10% required rate of return?

Answer 1