Question

As an engineer, you are asked to choose between a PV panel system and a wind turbine for your site. PV panel system costs 900,000 USD to implement while the cost of the wind turbine system is 500,000 USD. PV panels have a lifetime of 25 years, and wind turbine lifetime is 15 years. The annual operation and maintenance cost of PV is 30,000 USD, and wind turbines are 50,000 USD. From the annual electricity generation, PV panels are making 250,000 USD every year, while this amount is 180,000 USD for the wind turbine. The salvage value of the PV is 80,000 USD, and the salvage value of the wind turbine is 30,000 USD. The interest rate is 10%.

a) Compare the annual worth of PV and wind turbines.

b) Compare the payback period of PV and wind turbines.
c) Compare the Benefit/Cost ratio of PV and wind turbines.
d) Select one option (PV or turbine) for your site. Include an explanation of why you select that option.

Answer 1

Question (a): Compare the annual worth of PV and Wind turbines

Solution:

[ All amounts are in US Dollar]

Given:

PV Panel

Cost, F= $ 900,000

Lifetime, n =25 years

Annual Operation and maintenance cost: $30,000

Annual electricity generation: $250,000

Salvage Value: $80,000

Wind Turbine

Cost, F= $ 500,000

Lifetime, n =15 years

Annual Operation and maintenance cost: $50,000

Annual electricity generation: $180,000

Salvage Value: $30,000

Calculation of Annual Worth of PV Panel

In order to calculate the annual worth, we have to calculate the Net Present Value (NPV) of the equipment, the formula for calculating the

PV inflow = Recurring Payments + Salvage Price

PV outflow = Initial Cost

Initial Cost of PV Panel

F = Initial amount / Cost of equipment

i = Discount rate or interest rate in %

n = Number of years

Therefore

Recurring payments of PV Panel

Where A is the cash inflow

i = Discount rate or interest rate in %

n = Number of years

A = Annual electricity generation – Annual Operation and maintenance cost

A = $250,000 – $30,000

A = $220,000

Salvage price of PV Panel

Where S is the salvage price

S = Cash inflow – Salvage cost

S = 220,000 – 80,000

S = 140,000

i = Discount rate or interest rate in %

n = Number of years

Therefore

Therefore

NPV = (Recurring Payments + Salvage Price) - Initial Cost

NPV = ($1996948.804 + $12921.43) - $900,000

NPV = $1109870.23

Annual Worth is given by

The Annual worth of PV Panel is $122,272.26

Calculation of Annual Worth of Wind Turbine

Initial Cost of Wind Turbine

F = Initial amount / Cost of equipment

i = Discount rate or interest rate in %

n = Number of years

Therefore

Recurring payments of Wind Turbine

Where A is the cash inflow

i = Discount rate or interest rate in %

n = Number of years

A = Annual electricity generation – Annual Operation and maintenance cost

A = $180,000 – $50,000

A = $130,000

Salvage price of Wind Turbine

Where S is the salvage price

S = Cash inflow – Salvage cost

S = 130,000 – 30,000

S = 100,000

i = Discount rate or interest rate in %

n = Number of years

Therefore

Therefore

NPV = (Recurring Payments + Salvage Price) - Initial Cost

NPV = ($988790.33+ $23939.20) - $500,000

NPV = $512729.50

Annual Worth is given by

The Annual worth of Wind Turbine is $67410.487

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(b) Payback Period

• Payback Period of PV Panel

• Payback Period of Wind Turbine

Therefore

• Payback Period of PV Panel is 4 years 2 months
• Payback Period of Wind Turbine is 3 years 11 months

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Question (c): Benefit/Cost ratio of PV Panel and Wind Turbines

The Benefit-Cost ratio is defined as the ratio of PV of Benefit expected from the project to the PV of the cost of the project

Therefore

► The Benefit-Cost ratio of PV panel system is

► The Benefit-Cost ratio of Wind Turbine is

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Question (d): Benefit-Cost ratio of PV Panel and Wind Turbines

It has been found that the Benefit-cost ratio of PV Panel system (1.233) is 20.29% higher than the Benefit-cost ratio of Wind Turbine (1.025)

Since the Benefit-Cost ratio is higher for the PV Panel, The option selected for the site is PV Panel.

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