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A new furnace for your small factory will cost $45,000 and a year to install, will require ongoing maintenance expenditures of $1,400 a year. But it is far more fuel-efficient than your old furnace and will reduce your consumption of heating oil by 4,200 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 12%.a. What is the net present value of the investment in the furnace?b. What is the IRR? (Do not round intermediate calculations.c. What is the payback period? (Do not round intermediate calculations.d. What is the equivalent annual cost of the furnace? (Do not round intermediate calculations.e. What is the equivalent annual savings derived from the furnace?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?

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Answer:

a) NPV = $43,874.65

b) IRR = 24.37%

c) payback period = 5.33 years

d) equivalent annual cost = $6,024.55

e) equivalent annual savings = $13,298.61

f) since the NPV is positive, the equivalent annual savings must be higher than the equivalent annual costs

Explanation:

initial outlay year 0 = -$45,000

net savings year 1 = -$1,400 + (4,200 x $2) = $7,000

net savings year 2 = -$1,400 + (4,200 x $2.50) = $9,100

net savings year 3 = -$1,400 + (4,200 x $3) = $11,200

net savings years 4 - 20 = -$1,400 + (4,200 x $3.50) = $13,300

discount rate = 12%

using a financial calculator:

NPV = $43,874.65

IRR = 24.37%

payback period = 5.33 years

equivalent annual cost = (present value of costs x 12%) / / [1 - (1 + 12%)⁻ⁿ] =[($45,000 + $10,457.22) x 12%] / [1 - (1 + 12%)⁻ⁿ] = $6,654.87 / 0.89633 = $7,424.57

equivalent annual savings = (present value of savings x 12%) / / [1 - (1 + 12%)⁻ⁿ] = ($99,332.87 x 12%) / / [1 - (1 + 12%)⁻ⁿ] = $11,919.94 / 0.89633 = $13,298.61

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