Hybrid Car Problem (Interesting One)

What remaining value do the cars have at the end of the five-year period? Are you assuming that the selling prices would be the same?

resale remain the same
resale remain the same

thanx

I get $2395.63 and $4791.25. Assuming I did the math right....

I assumed compounded annually, and that you did not get the benefit of investing your gas savings during the year in which the money was saved.

I get $1214.91 and $2429.81 with the same assumptions.

delta_price = delta_gas / (1.08^5 + 1)

delta_gas = $3000 and $6000

You plan to drive 1250 miles per month, so the gas only is going to run you (1250 miles / 25 mpg)*(G $/gal) or $50G/month where G is the price of a gallon of gas. The hybrid will be $25G/month, so there is a $25G/month savings. From here, it is a standard future value of money problem. The future value of the money you can spend extra is:

PMT * (1+.08/12)^60 where PMT is the extra amount you spend on the hybrid. Note the annual interest rate is converted in a monthly rate.

The future value of the monthly cash stream is $25G is

25G * [(1+.08/12)^60 - 1]/(.08/12)

Crunching numbers and setting them equal,

PMT * 1.49 = 73.5 * 25G
PMT = $1,233 * G

My numbers differ from the other postings in that I assume you can take advantage of the monthly savings, if only to pay down your car payment early.

Here is another way to do this that may be more intuitive. Figure out the entire monthly payment for car and gas if you finance the car at 8%.

Payment for gas car = $20K / [(1 - (1+.08/12)^-60 ) / (.08/12)] = $405.53

Since you can pay $25*G more each month on the car by using your gas savings, at $2/gal, you can afford a payment of $455.53. Using the above equation in reverse, you can finance $22,465.92. At $4/gal, you can afford a payment of $505.53. That will support a car price of $24,931.84.

OK, I'll include my math this time.

Fuel savings is 300 gallons per year.

Case 1: Gasoline @ $2/gal. This means a savings of $600/year.

End of Year 1: Savings: $600, Invested savings: $0, Total savings to invest for the next year: $600
End of Year 2: Savings: $600, Invested savings: $648, Total savings to invest for the next year: $1248
End of Year 3: Savings: $600, Invested savings: $1347.84, Total savings to invest for the next year: $1947.84
End of Year 4: Savings: $600, Invested savings: $2103.67, Total savings to invest for the next year: $2703.67
End of Year 5: Savings: $600, Invested savings: $2919.96, Total savings: $3519.96

Amount to invest at 8% annual return to equal $3519.96 after 5 years: $2395.63


Repeat calculations for $4/gallon.


Engineer: I took the problem to mean that one is paying cash for the vehicle.

It comes out the same way cash or credit. I just thought the payment approach might be easier to see. Your approach is fine by me, you just did stuff yearly and I did it monthly. If I change the formulas I posted to a yearly basis, I would get your answer to the penny.

Thx. Good to know, as one contradicts Mark at one's peril....

Variations on a theme
Since this post is generating some responses, maybe we should expand it. What if gas is $2/gal today, but is going up 1% per month? How about if your investment returns are taxed at 15% annually?

And maintenance. Those batteries in a hybrid aren't cheap and they will require some maintenance that isn't required for a conventional automobile.

Remember---When the outflow exceeds in income the upkeep will be the downfall.

Rap

According to Toyota, the batteries are supposed to last as long as the vehicle does. Or so they claim. I drive one now, and so far, so good...

Perhaps I oversimplified the problem. I solved:

-CarC-GasC+(CarH-CarC)*1.08^5 = -CarH-GasH

Where:
CarC is the cost of the conventional car
CarH is the cost of the hybrid car
GasC is the 5-year cost of gas for the conventional car
GasH is the 5-year cost of gas for the hybrid car