Stan Moneymaker has been informed of a major automobile manufacturer\'s plan to

Question

Stan Moneymaker has been informed of a major automobile manufacturer's plan to conserve on gasoline consumption through improved engine design. The idea is called "engine displacement," and it works by switching from 8-cylinder operation to 4-cylinder operation at approximately 40 miles per hour. Engine displacement allows enough power to accelerate from a standstill and to climb hls while also permitting the automobile to cruise at speeds over 40 miles per hour with little loss in driving performance. The trade literature studied by Stan makes the claim that the engine displacement option will cost the customer an extra $1,000 on the automobile's sticker price. This option is expected to save 3 miles per gallon (an average of in-town and highway driving). A regular 8-cylinder engine in the car that Stan is interested in buying gets an average of 24 miles per gallon of gasoline. If Stan drives approximately 1,512 miles per month how many months of ownership will be required to make this $1,000 investment pay for itser Stan's opportunity cost of capital is 0.5% per month and gasoline costs $2.50 per gallon

Explanation / Answer

Number of gallon of gasoline required for regular engine per month = 1512/24 = 63 gallon

Number of gallon of gasoline required for improved engine per month = 1512/27 = 56 gallon

Savings of oil per month = 63-56 = 7 gallon

Dollar savings per month = 7*2.5 = $17.5

Now,

Investment = $1000

Monthly interested rate R = .5%

Let, time = n months

Then

1000 = 17.5*(1-1/1.005^n)/.005

1000*.005/17.5 = 1-1/1.005^n

1-.2857 = 1/1.005^n

1.005^n = 1.4

Taking long to the both sides,

n = log1.4/log1.005

n = 67.46 months

Hence, it will be 67.46 month to recover the investment of $1000.

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