A new furnace for your small factory will cost $40,000 to install and will require ongoing...

A new furnace for your small factory will cost $40,000 to install and will require ongoing maintenance expenditures of $2,800 a year. But it is far more fuel efficient than your old furnace and will reduce your consumption of heating oil by 3,700 gallons per year. Heating oil this year will cost $3 a gallon; the price per gallon is expected to increase by $.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 8%.

d. What is the equivalent annual savings derived from the furnace?

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Expert Solution

Saving of heating oil in gallons 3700

Annual cost per year given as $2800

Heating oil this year costs 3, assuming the machine is fully operational from next year (year 1), the cost will increase by 0.50 till year 3 and then stabilize

To calculate equivalent annual savings, we need the present value of savings from year 1 to year 20.

((-2800+(3700*3.5)) / 1.08) + ((-2800+(3700*4)) / ((1.08)^2)+ ((-2800+(3700*4.5)) / ((1.08)^3)

9398.15 + 10288.07 + 10994.58

30680.79

as on year 4, cash flow will stabilize as the rate per gallon stabilizes

Even cash flow * (1-((1+i)^-n))/i

13850 * (9.1216)

126334.69

to bring it back to present value TODAY

126334.69 * ((1+0.08)^-3) = 100288.55

Formula for Annuity Factor calculation

(1- ((1+r)^-n))) / r

((1-((1+0.08)^-20))/0.08)

9.8181

Formula for equivalent annual savings = (Present value of savings from year 1 to year 20)/ Annuity factor

30680.79 +100288.55

130969.34/9.8181

13339.52

jeff jeffy answered 1 year ago

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