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 hills 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 $1,500 on the automobile?s sticker price. This option is expected to save 5 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 20 miles per gallon of gasoline. If Stan drives approximately 1,000 miles per month, how many months of ownership will be required to make this $1,500 investment pay for itself? Stan?s opportunity cost of capital (i) is 0.25% per month, and gasoline costs $3.25 per gallon. Click the icon to view the interest and annuity table for discrete compounding when the MARR is 0.25% per month. Using the table given above and the interpolation method, months of ownership will be required to make this $1,500 investment pay for itself. (Round to one decimal place.)

Answer 1

First step: Compute Monthly fuel cost on 8 cylinder model Monthly fuel cost on 8 cylinder model -miles / (mileage x price per gallon) Monthly fuel cost on 8 cylinder model (1,000 / 20) x $3.25) Monthly fuel cost on 8 cylinder model 162.50 Second step: Monthly fuel cost on 4 cylinder model Monthly fuel cost on 4 cylinder model-miles / (mileage x price per gallon) Monthly fuel cost on 4 cylinder model = (1,000 /25) x $3.25) Monthly fuel cost on 4 cylinder model- 130 Third step: Comput e monthly savings Monthly saving - Cost on 8 cylinder model - Cost on 8 cylinder model Monthly saving 162.50 130 Monthly saving- 32.50 Compute the number of months using the "NPER" function of spreadsheet. Enter given values and formula in the spreadsheet as shown in the image below A B 4 1500 Initial cash flow, PV Future value, FV Mo Monthly interest rate, Rate 0.0025 savings, PMT 32.5 ut Number of months, Nper NPERD7,D6,-D4 D5,0) 10 NPER(rate, pmt, pv, [fvl, [type])

Obtained result is provided below. A B D E Input 4 Initial cash flow, PVS1.500.00 Future value, FV Monthly savings, PMT Monthly interest rate. Rate | 0.25% S0.00 S32.50 Output Number of months, Nper49.10 10 Thus, the required number of months is 49.10.