B,C and D Please. B: 21.47 / 17.17 => WRONG C. 48575.97 / 2611.43 => WRONG Hybri

Question

B,C and D Please.

B: 21.47 / 17.17 => WRONG

C. 48575.97 / 2611.43 => WRONG

Hybrid cars are touted as a "green" alternative: however, the financial aspects of hybrid ownership are not as clear. Consider the 2010 easel 550h. which had a list price of $5, 800 (including tax consequences) more than the comparable easel 550. Additionally, the annual ownership costs (other than fuel) for the hybrid were expected to be $500 more than the traditional sedan. The EPA mileage estimate was 29 mpg for the hybrid and 21 mpg for the traditional sedan. Assume that gasoline costs $3.95 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 final answer to nearest whole number, (e.g.. 32)), If you drive 16.500 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 final answer to 2 decimal places, (e.g.. 32.16)) Gasoline costs $3.95 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 final answer to the nearest whole number, (e.g., 32)) If you drive 16.500 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 final answer to 2 decimal places, (e.g.. 32.16))

Explanation / Answer

First we need to determine the total additional cost of the hybrid. The hybrid costs more to purchase and more each year, so the total additional cost is:

Total additional cost = $5,800 + 6($500)
Total additional cost = $8,800

Next, we need to determine the cost per mile for each vehicle. The cost per mile is the cost per gallon of gasoline divided by the miles per gallon, or:

Cost per mile for traditional = $3.95/21
Cost per mile for traditional = $0.1975

Cost per mile for hybrid = $3.95/29
Cost per mile for hybrid = $0.136207

So, the savings per mile driven for the hybrid will be:

Savings per mile = $0.1975 – 0.136207
Savings per mile = $0.061293

a.

We can now determine the break-even point by dividing the total additional cost by the savings per mile, which is:

Total break-even miles = $8,800 / $0.061293
Total break-even miles = 143,573

So, the miles you would need to drive per year is the total break-even miles divided by the number of years of ownership, or:

Miles per year = 143,573 miles / 6 years
Miles per year = 23,928 miles/year

b.
First, we need to determine the total miles driven over the life of either vehicle, which will be:

Total miles driven = 6(16,500)
Total miles driven = 99,000

Since we know the total additional cost of the hybrid from part a, we can determine the necessary savings per mile to make the hybrid financially attractive. The necessary cost savings per mile will be:

Cost savings needed per mile = $8,800 / 99,000
Cost savings needed per mile = $0.088888

Now we can find the price per gallon for the miles driven. If we let P be the price per gallon, the necessary price per gallon will be:

P/21 – P/29 = $0.088888
P(1/21 – 1/29) = $0.088888
P = $6.76

c.
To find the number of miles it is necessary to drive, we need the present value of the costs and savings to be equal to zero. If we let MDPY equal the miles driven per year, the break-even equation for the hybrid car is:

Cost = 0 = –$5,800 – $500(PVIFA10%,6) + $0.061293(MDPY)(PVIFA10%,6)

The savings per mile driven, $0.061293, is the same as we calculated in part a. Solving this equation for the number of miles driven per year, we find:

$0.061293(MDPY)(PVIFA10%,6) = $6,972.76
MDPY(PVIFA10%,6) = 135,581.44
Miles driven per year = 31,131

d.

To find the cost per gallon of gasoline necessary to make the hybrid break even in a financial sense, if we let CSPG equal the cost savings per gallon of gas, the cost equation is:

Cost = 0 = –$5,800 – $500(PVIFA10%,6) + CSPG(16,500)(PVIFA10%,6)

Solving this equation for the cost savings per gallon of gas necessary for the hybrid to break even from a financial sense, we find:

CSPG(16,500)(PVIFA10%,6) = $6,973
CSPG(PVIFA10%,6) = $0.44986
Cost savings per gallon of gas = $0.103291

Now we can find the price per gallon for the miles driven. If we let P be the price per gallon, the necessary price per gallon will be:

P/21 – P/29 = $0.103291
P(1/21 – 1/29) = $0.103291
P = $7.23

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