Question

Jeffrey has been successful with his small business that he is planning to expand his shop. He is going to start enlarging the shop by purchasing a larger equipment. For the following data:

Original size: 25 gal

New size: 50 gal

Power sizing exponent: 0.2

Cost of the 25 gal equipment 10 years ago: $1500

Cost Index 10 years ago 150

Cost Index today: 200

A- if the Cost of the new 50 gal equipment 10 years ago is $1700 the Cost of the new 50 gal equipment today is closest to:

$2,267

$2,324

$2,258

$2,291

B-Cost of the new 50 gal equipment 10 years ago is closest to:

$1,723

$1,715

$1,717

$1,742

Answer 1

A- Cost of the product in the current year= Cost of the product in base year/(Cost index in Base year/Cost index in current year)

Here given cost of new 50 gal equipment 10 years ago = $1700

Cost index 10 years ago= 150

Cost index in current year = 200

Cost of new 50 gal equipment in current year = 1700/(150/200) = $2266.666 which is nearest to the value $2,267.

B- Using power sizing exponent value, cost of 50 gal equipment 10 years ago or in base year = Cost of 25 gal equipment 10 years ago/(Size of equipment 10 years ago/size of equipment in current year)ⁿ   Here n= power sizing exponent value = 0.2

Cost of 25 gal equipment 10 years ago = $1500

Size of equipment 10 years ago = 25 & size of equipment in current year = 50

Therefore cost of 50 gal equipment 10 years ago = 1500/(25/50)^0.2 = $1723.04 which is nearest to $1723.