A new furnace for your small factory is being installed right now, will cost $$46,000,$ and will be completed in one year. At that point, it will require ongoing maintenance expenditures of $$4,000$ a year. But it is far more fuel$-$efficient than your old furnace and will reduce your consumption of heating oil by $4,300$ gallons per year. Heating oil this year costs $$3$ a gallon; the price per gallon is expected to increase by $$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 $10\%.$

a$.$ 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.

b$.$ What is the IRR?

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

c$.$ What is the payback period?

d$.$ What is the equivalent annual cost of the furnace?

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

e$.$ What is the equivalent annual savings derived from the furnace?

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

f$.$ 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?

please give me real answers of the question with the numbers. For example, what is the NPV in the first question. You only gave me the way of solution but i do not want to this. I want clear answers.