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 to4-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

$1,200

on the automobile's sticker price. This option is expected to save

3

miles per gallon (an average ofin-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

1296

miles per month, how many months of ownership will be required to make this

$1,200

investment pay for itself? Stan's opportunity cost of capital

(i)

is

0.25%

per month, and gasoline costs

$3.00

per gallon.

Explanation / Answer

Regular New 8 cylinder 4 cylinder Additional cost - 1200 Miles per gallon 24 27* * Saving in 3 miles per gallon means additional 3 miles with 1 gallon = 24 +3 =27 Usage per month (in gallons) = 1296/24 54 = 1296/27 48 Savings per month in gallons (54-48) 6 savings per month in $ (6 x 3) 18 Let t months be the time to recover 1200; Pv of tax savings @ 0.25% p.m. for t months = 1200 18 x PVAF(0.25%, t ) = 1200 Pvaf (0.25%, t ) = 1200/18 = 66.667 t PVAF 50 46.94617 t 66.66667 100 88.38248 Using linear interpolation t-50/100-50 = =66.667-46.9461/88.38248 - 46.9461 t-50 = 19.72049/41.43638 x 50 t= 23.79615 + 50 = 73.79615 months Please provide feedback…. Thanks in advance… :-)

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