Question

Hybrid cars are touted as a "green" alternative; however, the financial aspects of hybrid ownership are not as clear. Consider the 2018 Edsel 550h, which had a list price of $5,800 (including tax consequences) more than the comparable Edsel 550. Additionally, the annual ownership costs (other than fuel) for the hybrid were expected to be $390 more than the traditional sedan. The EPA mileage estimate was 24 mpg for the hybrid and 16 mpg for the traditional sedan.

a. Assume that gasoline costs $3.40 per gallon and you plan to keep either car for six years. How many miles per year would you need to drive to make the decision to buy the hybrid worthwhile, ignoring the time value of money? (Do not round intermediate calculations and round your answer to nearest whole number, e.g., 32.)

b. If you drive 18,000 miles per year and keep either car for six years, what price per gallon would make the decision to buy the hybrid worthwhile, ignoring the time value of money? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

c. Gasoline costs $3.40 per gallon and you plan to keep either car for six years. How many miles per year would you need to drive to make the decision to buy the hybrid worthwhile? Assume the appropriate interest rate is 10 percent and all cash flows occur at the end of the year. (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

d. If you drive 18,000 miles per year and keep either car for six years, what price per gallon would make the decision to buy the hybrid worthwhile? Assume the appropriate interest rate is 10 percent and all cash flows occur at the end of the year. (Do not round intermediate calculations and round your answer to 2 decimal

Answer 1

Difference in Ownership Cost Annually = $ 390

Total Ownership Cost for 6 years = $390 x 6 = $ 2,340  
Difference in list price = $ 5,800

Total Costs = $ 8,140       
Mileage of Hybrid Model 24   MPG
Mileage of Traditional Model   16   MPG

Difference in mileage = 24-16 = 8 MPG

a. Calculation of Miles per year (with Time value of Money)

Cost of Gasoline   $3.40    per gallon
Let Miles required to justify the higher costs associated with Hybrid cars be M   
      
Cost saving because of better mileage will help justify the higher costs associated with the hybrid models

= Rate per gallon of gasoline x M / Difference in mileage = Total Additional Costs

= $ 3.40 x M / 8 MPG = $8,140

= M = 8,140 * 8 / 3.4 = 19152.94 Miles

b. Cost of Gasoline = C per gallon
Miles = 18,000
= Rate per gallon of gasoline x Miles / Difference in mileage = Total Additional Costs

= C x 18000 / 8 MPG = $8,140

= M = 8,140 * 8 / 18,000 = $ 3.6178 per gallon

c. Calculation of Miles per year (with Time value of Money)

Cost saving because of better mileage will help justify the higher costs associated with the hybrid models

= Rate per gallon of gasoline x M / Difference in mileage = Total Additional Costs x Present Value Annuity Factor ( r % , n years)

= $ 3.40 x M / 8 MPG = $5,800 + 390 x PVAF (10%, 6 years)

= 3.40 x M / 8 MPG = $ 5,800 + 390 * 4.3553

= 3.40 x M / 8 = $ 7498.57

= M = 7,498.57 * 8 / 3.40 = 17,643.69 Miles

d. Calculation of Cost of Gasoline (with Time value of Money)

Cost of Gasoline = C per gallon
Miles = 18,000
= Rate per gallon of gasoline x Miles / Difference in mileage = Total Additional Costs x Present Value Annuity Factor ( r % , n years)

= C x 18000 / 8 MPG = $5,800 + 390 x PVAF (10%, 6 years)

= C x 18000 / 8 MPG = $ 5,800 + 390 * 4.3553

= C x 18000 / 8 = $ 7498.57

= C = 7498.57 * 8 / 18,000 = $ 3.3327 per gallon

Note - PVF = (1 / (1 + r)^n)

PVAF = (1 / (1 + r)^1) + (1 / (1 + r)^2) + (1 / (1 + r)^3) + ...............+ (1 / (1 + r)^n)