You have been hired as a consultant to determine how cost effective hybrid cars

Question

You have been hired as a consultant to determine how cost effective hybrid cars are in the light of increasing gas prices. Assume:

the hybrid car costs $30,000, and goes 50 miles/gallon

its regular (non-hybrid) counterpart costs $20,000, and goes 20 miles/gallon

you drive 15,000 miles/year on the average.

Build a mathematical model (formula) showing the number of years it will take a hybrid car to pay for itself (PAYBACK) as a function of the price of the hybrid car (H-PRICE), the MPG of the hybrid car (H-MPG), the price of its regular (non-hybrid) counterpart (R-PRICE), the MPG of its regular counterpart (R-MPG), the average distance driven per year (DISTANCE), and the price of gas (GAS). Show this formula explicitly in the work you turn in.

Put this formula, as well as all the facts given above, into a spreadsheet. Use the spreadsheet to answer the following questions.

How long will the hybrid car take to pay for itself if the price of gas were $10/gallon?

At what current gas price will the hybrid car pay for itself in 5 years?

How sensitive is the payback period to the changes in the (average) distance driven per year?

The document you turn in should show the formula (easily built in MS-Word using the Equation capability under Insert) as well as the answers to questions 3/4/5 above. As usual, convert the Word document into pdf format before turning it in.

Note: By "a hybrid car paying for itself" we mean a hybrid car generating enough savings in fuel expenses to recoup the extra price the customer has to pay over its non-hybrid counterpart.

Explanation / Answer

Answer;-

Costs associated with the hybrid car are:

Intial Cost = H-PRICE = $30,000

Running Costs = (DISTANCE/ H-MPG) * GAS Per year

Costs associated with the regular car are:

Intial Cost = R-PRICE = $20,000

Running Costs = (DISTANCE/ R-MPG) * GAS Per year

For the Breakeven (PAYBACK), Costs would be equal.

H-PRICE + (DISTANCE/ H-MPG) * GAS*PAYBACK = R-PRICE + (DISTANCE/ R-MPG) * GAS*PAYBACK

This is the required formula.

GAS = $10/gallon

Thus,

30,000 + (15000/50)*10*PAYBACK = 20,000 + (15000/20)*10*PAYBACK

PAYBACK = 2.22 years

PAYBACK = 5 years

Thus,

30,000 + (15000/50)*5*GAS = 20,000 + (15000/20)*5*GAS

Thus, GAS = 4.44/ gallon

We revert back to the original cost of GAS = $10/gallon

30,000 + (DISTANCE/50)*10*PAYBACK = 20,000 + (DISTANCE/20)*10*PAYBACK

PAYBACK = 33333.33/ DISTANCE

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