Question

Gas Heating Option: The initial equipment and installment of the natural gas system would cost $225,000 right now. The maintenance costs of the equipment are expected to be $2,000 per year, starting next year, for each of the next 20 years. The energy cost is expected to be $5,000 starting next year and is expected to rise by 5% per year for each of the next 20 years due to the price of natural gas increasing. Geothermal Heating Option: Because of green energy incentives provided by the government, the geothermal equipment and installation are expected to cost only $200,000 right now, which is cheaper than the gas lines. There would be no energy cost with geothermal, but because this is a relatively newer technology the maintenance is expected to be $10,000 per ear, staring next year, for each of the next 20 years. Which is the lower cost option for the company?

Answer 1

To determine the lower cost option for the company, we need to compare the total costs of the gas heating option and the geothermal heating option over a period of 20 years.

Step-by-step explanation:

To determine the lower cost option for the company, we need to compare the total costs of the gas heating option and the geothermal heating option over a period of 20 years.

For the gas heating option, the initial equipment and installation cost is $225,000. The annual maintenance cost is $2,000, and the energy cost starts at $5,000 and increases by 5% each year.

For the geothermal heating option, the equipment and installation cost is $200,000. There is no energy cost, but the annual maintenance cost is $10,000.

By calculating the total costs for both options over 20 years, we can determine which option is more cost-effective.

Answer 2

The geothermal heating option has a lower total cost over 20 years at $400,000 compared to the gas heating's total of $425,833.33. Therefore, the geothermal option is the more cost-effective choice for the company.

Step-by-step explanation:

To determine which heating option is more cost-effective for the company, we need to calculate the total costs of each option over a 20-year period and compare them.

Gas Heating Option:
Initial equipment and installation: $225,000
Maintenance: $2,000/year for 20 years = $40,000
Energy costs start at $5,000 and increase by 5% each year. To find the total energy cost, we must calculate the sum of a geometric series: Total energy cost = $5,000 * [(1 - 1.05^20) / (1 - 1.05)] = $5,000 * [1 - 2.6533] / [-0.05] = $160,833.33.

Geothermal Heating Option:
Initial equipment and installation: $200,000
Maintenance: $10,000/year for 20 years = $200,000
There is no energy cost with geothermal.

Now, we add up the costs for each system over the 20-year period:
Gas Heating: $225,000 + $40,000 + $160,833.33 = $425,833.33
Geothermal Heating: $200,000 + $200,000 = $400,000

Comparing the two totals, we see that the geothermal option is cheaper by $25,833.33 over the 20-year period.