Chapter $12$: Payback Period

XYZ Inc. is considering two different investment plans, Plan A and Plan B$.$ Both plans require an initial investment, but they offer different cash inflow structures. XYZ Inc. wants to determine which plan has a shorter payback period.

Plan A involves an initial outlay of $$150,000.$ It is expected to generate annual cash inflows of $$40,000$ for the first three years and then $$50,000$ for the next two years.

Plan B requires an initial investment of $$150,000$ as well. This plan will generate $$30,000$ in the first year, and the annual cash inflow will increase by $$20,000$ each subsequent year. For example, the cash inflow in the second year would be $$50,000,$ in the third year $$70,000,$ and so on$.$

Calculate the payback period for each plan and determine which plan offers the quicker recovery of the initial investment.