P21-38 (similar to) Question Help Sparrow Laundromat is trying to enhance the se
ID: 2791144 • Letter: P
Question
P21-38 (similar to) Question Help Sparrow 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. Sparrow estimates the cost of the new equipment at $191,000. The equipment has a useful life of 9 years. Sparrow 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. Sparrow evaluates investments using a cost of capital of 10% (Click the icon to view the Future Value of $1 factors.) Click the icon to view the Future Value of Annuity of $1 factors. (Click the icon to view the Present Value of $1 factors.) Click the icon to view the Present Value of Annuity of $1 factors. Read the requirements Requirement 1. Calculate the payback period and the discounted payback period for this investment, assuming Sparrow expects to generate $150,000 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 3.06 years The discounted payback period for the investment assuming uniform net cash inflows is 3.83 years Requirement 2. Assume instead that Sparrow 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? Start by determining the net initial investment unrecovered amounts at the end of each year by first entering the net cash inflow(outflow) amounts and then calculating the cumulative net cash flows for each year. (Use a minus sign or parentheses for net cash outflows and to show negative cumulative net cash flows Once the net initial investment is fully recovered enter a zero for that year's line and for each subsequent year's line in the "net initial investment unrecovered at end of year" column.) Net Cash Cumulative Net Net initial investment Year Inflowl(Outflow) Cash Flows unrecovered at end of yean 191,000 10,250 20,500 83,000 117,000 217,500 308,500 371,000 405,000 510,250 10,250 S 10,250 62,500 34,000 100,500 91,000 62,500 34,000 105,250 6Explanation / Answer
Payback period is the period in which the initial investment is recovered by the cash inflows of the project. In simple payback period, we will use non-discounted cash flows and in discounted payback period we use discounted cash flows.
From the above, we can see that the initial investment gets recovered in year 5. For the exact payback period, we need to interpolate -
Cash flow required in year 5 = $74000
Total cash flow in year 5 = $100500
Payback period = 4 years + 1 year x $74000 / $100500 = 4.74 years
Discounted payback period
From the above, we observe that the initial investment gets recovered in year 6. Again, to arrive at the payback period we need to interpolate -
Discounted Cash Inflow required in Year 6 = 40646.25
Total discounted cash inflows in Year 6 = 51324
Payback period = 5 years + 1 year x 40646.25 / 51324 = 5.79 years
Year Net cash inflow ($) Cumulative net cash inflow($) Initial investment unrecovered at the end of the year ($) 0 - - 191000 1 10250 10250 191000 - 10250 = 180750 2 10250 10250 + 10250 = 20500 180750 - 10250 = 170500 3 62500 83000 108000 4 34000 117000 74000 5 100500 217500 0 6 91000 308500 0 7 62500 371000 0 8 34000 405000 0 9 105250 510250 0Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.