Question

A city has identified two options for developing solar power capacity. The investment basis for comparison is 8 years, with interest fixed at 12% per year.

Option A is to build a photovoltaic array at 50% capacity now, at a cost of $1 million, with an operating cost of $200,000 at the end of each year for 4 years. At the end of year 4, the array will be expanded to 100% capacity, at a cost of $900,000. After the expansion, operating costs will become $350,000 per year.

Option B is to build a full-scale solar thermal electric generation plant now at a cost of $1.5 million, with end-of-year operating costs of $250,000.

Which option should be chosen?

Answer 1

To decide the option, we need to calculate the Present Value (PV) of all costs for each option.

Option A: Operating cost (1st 4 years) = 200,000

PV of Op.cost: PMT = 200,000; N = 4; rate = 12%, CPT. PV = 607,469.87

Operating cost (2nd 4 years) = 350,000

PV of Op.cost at the end of 4 years: PMT = 350,000; N = 4; rate = 12%, CPT PV.

PV = 1,063,072.27

PV of this cost today = 1,063,072.27/(1+12%)^4 = 675,601.65

Total PV of operating costs over 8 years = 607,469.87 + 675,601.65 = 1,283,071.52

PV of expansion cost in 4 years = 900,000/(1+12%)^4 = 324,549.02

Total PV of costs = initial cost + PV of operating costs + PV of expansion cost

= 1,000,000 + 1,283,071.52 + 324,549.02 = 2,607,620.54

Option B: PV of operating costs over 8 years is

PMT = 250,000; N = 8; rate = 12%, CPT PV.

PV = 1,241,909.94

Total PV of costs = initial cost + PV of operating costs = 1,500,000 + 1,241,909.94 = 2,741,909,94

Option A should be chosen as PV of total costs is lower than for Option B.