A building owner is considering installing solar roof panels on a building. The

Question

A building owner is considering installing solar roof panels on a building. The cost of installing solar panels is $22,000 + $19.90*S where S is the square footage of the solar panels. There is an annual maintenance cost of $5.50 per square foot of installed solar panel. The solar panels will last 19 years, and there is no salvage value or disposal cost. The electricity usage for a single hour for the building with operating solar solar panels is
E = 1000/S
where E is the electricity usage in kWh (kilowatt-hour) and S is the square footage of the solar panels. The cost of electricity is $0.12 per kWh, and the solar panels will operate for 16 hours per day, 365 days per year. The building owner's MARR is 10%. Assuming the building owner wants to minimize the annual equivalent cost, how many square feet of solar panels should be installed?
HINT: You should convert the cost of installing the solar panel to an annual cost."

Explanation / Answer

Ans. Annual equivelant cost is calculated by NPV of the cost/Annuuity factor

Here we will see with different square foot how much it costs, and what is the best size. One thing is for sure, that the electricity usage for a single hour will be less as the pannel is more.

To calculate the annual cost, firstly the cost for one year has to be calcuated . The annuity factor is calculated as (1-(1/1+r)/r)^t)/r. R= 10%

Took the size of the pannel for a 1600 sq feet building as 900. There will be a point after which the cost will not reduct but increase with respect to the amount invested

If the square foot is taken as 800, the total cost will shoot to $20,142.39. The biggest factor playing here is the total unit generated, if it is 800 sq feet in size then the electricity consumed will be more, as the size will not be apt for the entire building, this will increase the cost per kWh, and total cost in an year.  

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Cost of installing the pannel -39910 Maintenance Cost 4950 4950 4950 4950 4950 4950 4950 4950 4950 4950 4950 4950 4950 4950 4950 4950 4950 4950 4950 Electricity Usage for an hour 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 1.111111111 Total Electricity usage in a day 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 17.77777778 Electricity usage in an year 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 6488.888889 Cost of electricity in an year 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 778.6666667 PV Of the cost ($11,124.04) ($10,112.76) ($9,193.42) ($8,357.66) ($7,597.87) ($6,907.15) ($6,279.23) ($5,708.39) ($5,189.45) ($4,717.68) ($4,288.80) ($3,898.91) ($3,544.46) ($3,222.24) ($2,929.31) ($2,663.01) ($2,420.92) ($2,200.83) ($2,000.76) Total of the PV ($126,829.77) Total cost ($166,739.77) Annuity Factor 8.364920092 Equivalent Annual Cost ($19,933.22) Rate 10% Instal 39910 Square foot 900

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