Using the same subsidy of 15% as the previous question, how many years does system B need to be operational to earn the own investment back (assume that the electricity price of €0.23/kWh does not change)?
To calculate the number of years it takes for System B to earn back its own investment, we need to consider the initial investment and the annual savings.
1. Determine the initial investment:
Let's assume the initial investment for System B is €100,000.
2. Calculate the annual savings:
System B generates 100,000 kWh per year and the electricity price is €0.23/kWh.
Annual savings = 100,000 kWh/year × €0.23/kWh = €23,000/year
3. Calculate the subsidy:
The subsidy for System B is 15% of the initial investment.
Subsidy = 15% of €100,000 = €15,000
4. Calculate the net annual savings after subtracting the subsidy:
Net annual savings = Annual savings - Subsidy = €23,000/year - €15,000 = €8,000/year
5. Calculate the payback period:
Payback period = Initial investment / Net annual savings
= €100,000 / €8,000/year
To find the answer, we need to calculate the division:
Payback period = €100,000 / €8,000/year
= 12.5 years
Therefore, System B needs to be operational for approximately 12.5 years to earn back its own investment, assuming the electricity price remains constant and a subsidy of 15% is applied.
To determine how many years System B needs to be operational to earn back its own investment, we need to calculate the payback period. The payback period is the length of time it takes for an investment to generate enough cash flows to recover the initial investment.
First, let's calculate the annual cash flow generated by System B with the 15% subsidy.
1. Determine the annual electricity production: If we know the capacity of System B and the expected capacity factor, we can calculate the annual electricity production. Let's assume System B has a capacity of 100 kW and a capacity factor of 20%. The annual electricity production would be:
Annual Electricity Production = Capacity * Capacity Factor = 100 kW * 20% = 20,000 kWh
2. Calculate the annual revenue: The annual revenue can be calculated by multiplying the annual electricity production by the electricity price. Given the electricity price of €0.23/kWh, the annual revenue would be:
Annual Revenue = Annual Electricity Production * Electricity Price = 20,000 kWh * €0.23/kWh = €4,600
3. Calculate the annual subsidy: The annual subsidy is 15% of the annual revenue. Using the calculated annual revenue of €4,600, the annual subsidy would be:
Annual Subsidy = Annual Revenue * Subsidy Percentage = €4,600 * 15% = €690
4. Calculate the annual cash flow: The annual cash flow is the difference between the annual revenue and the annual subsidy. Therefore, the annual cash flow would be:
Annual Cash Flow = Annual Revenue - Annual Subsidy = €4,600 - €690 = €3,910
Now that we have the annual cash flow, we can calculate the payback period by dividing the initial investment by the annual cash flow.
Let's assume that the initial investment for System B is €30,000.
Payback Period = Initial Investment / Annual Cash Flow = €30,000 / €3,910 ≈ 7.67 years
Therefore, System B would need to be operational for approximately 7.67 years to earn back its own investment.
Subsidized Price: (0.85)(€0.14379 / kWh) = €0.1222 / kWh
Savings Per kWh: (€0.23 / kWh) - (€0.1222 / kWh) = €0.10778 / kWh
Savings Per Year: (€0.10778 / kWh)(765 kWh / yr) = €82.45 / yr
Years To Regain Investment: (€2200) / (€82.45 / yr) = 26.7 yrs