A company wants to replace a machine with a better version. The replacement machine will require a net investment of $$200,000$ and is expected to generate free cash flow of $$100,000$ per year for the next $5$ years. The company requires $10\%$ return on capital investments of this sort and desires a $48$month pay back period. The existing machine would continue to function for the next five years if it is not replaced, but gradually become less useful. Free cash flows for the existing machine are forecasted to be $$80,000$ in year $1,$$$60,000$ in year $2,$$$40,000$ in year $3,$$$20,000$ in year $4$ and $$10,000$ in year $5.$

What is the incremental cash flow for year $1?$ Answer: $$20,000$

What is the incremental cash flow for year $2?$ Answer: $$40,000$

What is the incremental cash flow for year $3?$ Answer: $$60,000$

What is the incremental cash flow for year $4?$ Answer: $$80,000$

What is the incremental cash flow for year $5?$ Answer: $$90,000$

What is the net present value of this scenario? Answer: $$6,842\mathrm{.}5530$

What is the internal rate of return for this scenario? Answer: $11\mathrm{.}07\%$

How many months is the pay back period for this scenario? Answer: $48$ months $(4\mathrm{.}0$ years$)$

Can you please explain the answers math $?$