Question

A new furnace for your small factory will cost $29,000 and a year to install, 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 2,800 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 6%.

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?

Answer 1

You have asked a question with some 6 sub parts. I have addressed the first four sub parts. Please post the balance sub parts as a separate question.

Please see the table below. Please be guided by the second row to understand the mathematics. The last two rows highlighted in yellow contain your answers for part (a) and part (b). Subsequent parts have been answered after the table. Figures in parenthesis, if any, mean negative values. All financials are in $. Adjacent cells in blue contain the formula in excel I have used to get the final output.

E н Purchase cash flows Maintenance Price per gallon c Cumulative cash flows Net cash flows Savings Year 84 cash flows D Cx 2800 E = A + B + D (29,000) A B (29,000) Cumulative of E (29,000) 85 86 (1,200) 5,800 (23,200) 1 2.50 7,000 87 (16,000) (7,400) 2. (1,200) 8,400 3.00 7,200 88 (1,200) 9,800 8,600 3.50 89 (1,200) 3.50 9,800 4 8,600 1,200 90 (1,200 9,800 8,600 9,800 3.50 91 (1,200) 3.50 8,600 6 9,800 18,400 92 (1,200) 3.50 7 9,800 8,600 27,000 93 (1,200) 3.50 35,600 8 9,800 8,600 94 (1,200) 3.50 44,200 9 9,800 8,600 95 (1,200) 3.50 9,800 52,800 10 8,600 96 (1,200) 3.50 61,400 11 9,800 8,600 97 (1,200) 3.50 9,800 70,000 12 8,600 98 (1,200) 3.50 9,800 8,600 78,600 13 99 (1,200) 9,800 8,600 87,200 14 3.50 100 (1,200) 9,800 8,600 15 3.50 95,800 101 (1,200) 8,600 16 3.50 9,800 104,400 102 (1,200) 3.50 8,600 113,000 17 9,800 103 (1,200) 3.50 18 9,800 8,600 121,600 104 (1,200) 3.50 8,600 19 9,800 130,200 105 20 (1,200) 3.50 8,600 138,800 9,800 106 107 65,754NPV(6%,187:1106)+J86 108 Part (a) NPV 26.56% IRR(J86:J 106) IRR 109 Part (b) m n LO

Part (c) Look at the last column. Cumulative cash flows turn positive between year 3 and 4. Hence, payback period = 3 + 7,400 / 8,600 = 3.86 years

Part (d)

EAC = Annual maintenance cost + equivalent annual cost of the initial investment = 1,200 + PMT (Rate, Nper, PV) = 1,200 + PMT (6%, 20, -29000) = 1,200 + $2,528.35 = $  3,728.35