Question

A new furnace for your small factory will cost $39,000 and a year to install, will require ongoing maintenance expenditures of $1,100 a year. But it is far more fuel-efficient than your old furnace and will reduce your consumption of heating oil by 3,600 gallons per year. Heating oil this year will cost $2 a gallon; the price per gallon is expected to increase by $0.50 a year for the next 3 years and then to stabilize for the foreseeable future. The furnace will last for 20 years, at which point it will need to be replaced and will have no salvage value. The discount rate is 10%. or 20 years, ateuchto increase by $0. Of heating oil by a. What is the net present value of the investment in the furnace? (Do not round intermediate calculations. Round your answer to the nearest whole dollar.) b. What is the IRR? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) c. What is the payback period? (Do not round intermediate calculations. Round your answer to 2 decimal places.) d. What is the equivalent annual cost of the furnace? (Do not round intermediate calculations. Round your answer to 2 decimal places.) e. What is the equivalent annual savings derived from the furnace? (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? a. b. C. NPV IRR Cumulative cash flows are positive in: Equivalent annual cost Equivalent annual savings Are the two measures the same or is one larger? d. e. f.

Answer 1

Please find below answer for the first four sub parts
Part A: Cost of the furnac Amount ($) Dis. factor Present Value Instalation Price -39,000.00 1.00 (39,000.00) Maintenance -1,100.00 8.514 (9,364.92) Total (48,364.92) Year Amount ($) Dis. factor Present Value 7,200.00 0.909 6,545.45 9,000.00 0.826 7,438.02 10,800.00 0.751 8,114.20 12,600.00 6.027 75,936.57 98,034.24 Total Net Present Value 49,669.32

Part B: At IRR, NPV should be zero, let assue discounting factor o 24.36% Cost of the furnac Amount ($) Dis. factor Present Value Instalation Price -39,000.00 1.00 (39,000.00) Maintenance -1,100.00 4.053 (4,457.91) Total (43,457.91) Year 2 Amount ($) Dis. factor Present Value 7,200.00 0.804 5,789.64 9,000.00 0.647 5,819.44 10,800.00 0.520 5,615.41 12,600.00 2.082 26, 232.92 43,457.41 3 Total Net Present Value (0) So the IRR is 24.36%

Part C: Saving from Maintenan Total Year 1 Cash Flow 7200 -1100 Year 2 Cash Flow 9000 -1100 Year 3 Cash Flow 10800 -1100 Year 4 to 20 Cash F 12600 -1100 6100 7900 9700 11500 Initial Cost is 39000 Saving upto 3 year is $ 23,700. Remainning is $39,000 - $ 23,700 = $ 15, 300 then we use general formula=investment/cash flow per year = 15300/11500 = 1.33 The payback period will be 4.33 years (i.e. 3 years + 1.33 years)

Part D: Equivalent annual cost is NPV of the Cost devide by the present value of the annuity factor Cost of the furnac Amount ($) Dis. factor Present Value Instalation Price -39,000.00 1.00 (39,000.00) Maintenance -1,100.00 8.514 (9,364.92) NPV of the Cost (48,364.92) Equivalent Annual Cost = NPV Xr/{1-(1+r)^-n =-48364.92 X.10/{1-(1+.10)^-20} -5,680.93 So the EAC is - 5680.93