Full Answer Section

Data Needed:

• Cost of Hybrid Car (CH):$[To be filled by you – Based on research]
• Cost of Gasoline Car (CG):$[To be filled by you – Based on research]
• Annual Fuel Cost for Gasoline Car (FGe):$[To be filled by you – Based on research on average fuel efficiency and gas prices]
• Annual Fuel Cost for Hybrid Car (FHy):$[To be filled by you – Based on research on average fuel efficiency and gas prices]
• Discount Rate (DR):[Your chosen discount rate – Assume a value between 5% and 10%]

Analysis Framework:

We will use the Net Present Value (NPV) method to determine which car is the more economical choice. NPV considers the initial investment (car purchase price), future fuel costs (discounted to their present value), and the discount rate.

Calculations:

1. Calculate the Present Value of Annual Fuel Costs (PV of F):

• For Gasoline Car:
  • PV(FGe) = FGe / (1 + DR)^1 + FGe / (1 + DR)^2 + … + FGe / (1 + DR)^10
• For Hybrid Car:
  • PV(FHy) = FHy / (1 + DR)^1 + FHy / (1 + DR)^2 + … + FHy / (1 + DR)^10

Formula:

• “FGe/FHy” represents the annual fuel cost for the respective car.
• “DR” represents the discount rate.
• The exponent “n” represents the number of years (10 in this case).

2. Calculate the Net Present Value (NPV):

• For Gasoline Car:
  • NPV(Gasoline) = CG – PV(FGe)
• For Hybrid Car:
  • NPV(Hybrid) = CH – PV(FHy)

Formula:

• “CG/CH” represents the cost of the respective car.
• “PV(FGe/FHy)” represents the present value of annual fuel costs for the respective car.

Decision Rule:

• Choose the car with the higher NPV. A positive NPV indicates a profitable investment over the 10-year period.

Example:

Let’s assume the following values (replace with your actual research):

• CH = $30,000 (Cost of Hybrid Car)
• CG = $25,000 (Cost of Gasoline Car)
• FGe = $2,000 (Annual Fuel Cost for Gasoline Car)
• FHy = $1,000 (Annual Fuel Cost for Hybrid Car)
• DR = 7% (Discount Rate)

Calculations:

PV(FGe):

• (2,000 / 1.07) + (2,000 / 1.07^2) + … + (2,000 / 1.07^10) = $14,067.22 (Approx.)

PV(FHy):

• (1,000 / 1.07) + (1,000 / 1.07^2) + … + (1,000 / 1.07^10) = $7,033.61 (Approx.)

NPV(Gasoline):

• $25,000 – $14,067.22 = $10,932.78

NPV(Hybrid):

• $30,000 – $7,033.61 = $22,966.39

Decision:

Based on this example, the Hybrid car has a higher NPV ($22,966.39) compared to the Gasoline car ($10,932.78). Therefore, in this scenario, considering the fuel savings over 10 years and the discount rate, the Hybrid car appears to be the more economical choice.