A new furnace for your small factory is being installed right now, will cost $$38,000,$ and will be completed in one year. At that point, it will require ongoing maintenance expenditures of $$1,200$ a year. But it is far more fuel$-$efficient than your old furnace and will reduce your consumption of heating oil by $3,500$ gallons per year. Heating oil this year costs $$2$ a gallon; the price per gallon is expected to increase by $$0\mathrm{.}50$ a year for the next $3$ years and then to stabilize for the foreseeable future. The furnace will last for $20$ years from initial use, at which point it will need to be replaced and will have no salvage value. $($Specifically$,$ the firm pays for the furnace at time $0$ and then reaps higher net cash flows from that investment at the end of years $120.)$ The discount rate is $8\%.$

What is the net present value of the investment in the furnace?

Note: Do not round intermediate calculations. Round your answer to the nearest whole dollar.

What is the IRR?

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to $2$ decimal places.

What is the payback period?

What is the equivalent annual cost of the furnace?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

What is the equivalent annual savings derived from the furnace?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Compare the PV of the difference between the equivalent annual cost and savings to your answer to part $($a$).$ Are the two measures the same or is one larger?