Question

7x P21-38 (book/static) Assigned Media Question Help Sage 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. Sage estimates the cost of the new equipment at $159,000. The equipment has a useful life of 9 years. Sage expects cash fixed costs of $80,000 per year to operate the new machines, as well as cash variable costs in the amount of 5% of revenues. Sage evaluates investments using a cost of capital of 10%. Present Value of $1 table Present Value of Annuity of $1 table Future Value of $1 table Future Value of Annuity of $1 table Read the requirements. Requirement 1. Calculate the payback period and the discounted payback period for this investment, assuming Sage expects to generate $140,000 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 3.00 years. The discounted payback period for the investment assuming uniform net cash inflows is years.

Answer 1

Payback period is the time period in which the initial investment is recovered
i.e. Cost of Equipment/Annual cash flow
Annual cash inflow = Incremental Revenues - Variable costs - Fixed costs
=140000-140,000*5% - 80000
53000
Payback period = 159000/53000
3	Years
Calculation of discounted payback period
Year	Cash flows	Discount rate	Discounted cash flows	Cumulative discounted cash flows
0	-159000	1	-159000	-159000
1	53000	0.909	48177	-110823
2	53000	0.826	43778	-67045
3	53000	0.751	39803	-27242
4	53000	0.683	36199	8957
5	53000	0.621	32913	41870
6	53000	0.564	29892	71762
7	53000	0.513	27189	98951
8	53000	0.467	24751	123702
9	53000	0.424	22472	146174
Discounted payback period = 3 + 27242/36199 = 3.75 years