A student is trying to decide which of two cars to purchase; an old V-8, or an e

Question

A student is trying to decide which of two cars to purchase; an old V-8, or an equally old V-4 Data are provided in the table. Each will serve the student's needs, and it is estimated that repair costs and lifetimes for the two cars will be about the same. The car will be kept 5 years and then sold for salvage value. The primary difference comes down to the gas mileage that the two cars get. The average price of gasoline is assumed to be $1.20 per gallon. Using the data in the table, determine how many miles per year the student would have to drive to cause the cost of the two options to be the same. If the student typically drives 8.000 miles per year, which car should be purchased? Sketch the breakeven chart. The student's MARR is 796.

Explanation / Answer

Let x miles per year be driven
Present Value of costs incurred in V-8=2000+500/1.07^5+(x/12*1.2)/0.07*(1-1/1.07^5)
Present Value of costs incurred in V-4=5000+1250/1.07^5+(x/30*1.2)/0.07*(1-1/1.07^5)

For the cost to be the same:
2000+500/1.07^5+(x/12*1.2)/0.07*(1-1/1.07^5)=5000+1250/1.07^5+(x/30*1.2)/0.07*(1-1/1.07^5)
=>x=14368.1684025859

SO, 14368.1684025859 miles per year should be driven to cause the cost of the two options to be the same

At x=8000: Total Present Cost of V-8 comes out to be 5636.651
Total Present Cost of V-4 comes out to be 7203.296
Hence, at x=8000 miles, V-8 is preferrable

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