In: Finance
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?
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
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