Question

Laundromat is trying to enhance the services it provides to? customers, mostly college students. It is looking into the purchase of new? high-efficiency washing machines that will allow for the? laundry's status to be checked via smartphone.

FulmarFulmar

estimates the cost of the new equipment at

$178,000.

The equipment has a useful life of 9 years.

FulmarFulmar

expects cash fixed costs of

$80,000

per year to operate the new? machines, as well as cash variable costs in the amount of

15%

of revenues.

FulmarFulmar

evaluates investments using a cost of capital of

6?%.

Requirement 1. Calculate the payback period and the discounted payback period for this? investment, assuming

FulmarFulmar

expects to generate

$ 190 comma 000$190,000

in incremental revenues every year from the new machines.? (Round your answer to two decimal? places.)

The payback period for the investment assuming uniform net cash inflows is

years.

Requirements:

1.	Calculate the payback period and the discounted payback period for this? investment, assuming FulmarFulmar expects to generate $ 190 comma 000$190,000 in incremental revenues every year from the new machines.
2.	Assume instead that FulmarFulmar expects an uneven stream of incremental cash revenues from installing the new washing machines. Based on this estimated revenue? stream, what are the payback and discounted payback periods for the? investment?

                                                                                              

Year	1	2	3	4	5	6	7	8	9
Projected Revenue	$85,000	$130,000	$140,000	$170,000	$180,000	$170,000	$140,000	$150,000	$185,000

Answer 1

Cost of Equipment = 178,000

Life: 9 years

Fixed Cash Cost per year = 80,000

Variable Cost = 15% of Revenues

Cost of Capital = 6%

Requirement 1:

Payback period when revenue per year = 190,000

Net Cash Flow per year:

Revenue = 190,000

Less: Variable Cost 28500

Less: Fixed Cost 80,000

Incremental Cash Flows per year = 81500

Payback period = Initial Investment/Annual Cash Inflow

=178,000/81500 = 2.184 Years

Discounted payback period: Discounted Cash inflows are considered under discounted payback period method

Year	Cash Flow	PVF@6%	PV of Cash Flows	Cumulative Cash Flows
1	81500	0.943	76855	76855
2	81500	0.890	72535	149390
3	81500	0.840	68460	217850
4	81500	0.792	64548	282398
5	81500
6	81500
7	81500

Initial Investment of 178,000 will be recovered between year 2 and 3

Payback period = 2 + (217850-178000)/(217850-149390)

=2+0.582 = 2.582 years

2. Uneven Cash Flows:

Year	Revenue	Variable cost	Fixed Cost	CF	Cum. Cash Flows
1	85000	12750	80,000	-7750	-7750
2	130,000	19500	80,000	30500	22750
3	140000	21000	80,000	39000	61750
4	170,000	25500	80,000	64500	126250
5	180000	27000	80,000	73000	199250
6	170,000	25500	80,000	64500	263750
7	140,000	21000	80,000	39000	302750
8	150,000	22500	80,000	47500	350250
9	185000	27750	80,000	77250	427500

Initial Investment of 178,000 will be recovered between year 4 and 5

Payback period = 4 + (199250-178000)/(199250-126250)

=4+0.291 = 4.291 years

On the basis of Discounted Cash Flows:

Year	Cash Flows	PV@6%	PV Cash Flows	Cum. Cash Flows
1	-7750	0.943	-7308	-7308
2	30500	0.890	27145	19837
3	39000	0.840	32760	52597
4	64500	0.792	51084	103681
5	73000	0.747	54531	158212
6	64500	0.705	45473	203685
7	39000	0.665	25935
8	47500	0.627	29783
9	77250	0.592	45732

Discounted Payback period = 5 + 0.565

=5.565 years