Problem 545 bookstatic Question Help You are considering two

Problem 5-45 (book/static) Question Help You are considering two types of machines for a manufacturing process Machine A has a first cost of $75,200, and its salvage value at the end of six years of estimated service life is $21,000. The operating costs of this machine are estimated to be $6,800 per year. Extra income taxes are estimated at 52,400 per year. Machine B has a first cost of $44,000, and its salvage value at the end of six years\' service is estimated to be negligible. The annual operating costs will be $11,500 Compare these two mutually exclusive alternatives by the present-worth method at 13% Click the icon to view the interest factors for discrete compounding when : 13% per year. The present worth for machine A is S thousand (Round to the nearest whole number.) -

Solution

MACHINE A

The formula used to calculate present worth:

PW = -initial cost - (operating cost + extra income tax) ((1 + interest rate)ⁿ -1) / (interest rate( 1 + interest rate)) + salvage value ( 1 + interest rate)^{time period})

PW = -75,200(-6,800 + 2400) ((1 + 0.13)⁶) -1 / 0.13(1 + 0.13)⁶ + 21000( 1 +0.13)⁶

= -75,200 - 36,777 + 10,087

= - 101,890

HENCE THE VALUE OF MACHINE A IS $-101,890.

MACHINE B

Present worth for machine B can be calculated as:

PW = initial cost - operating cost -((1 + interest rate)ⁿ) - 1) / (intrest rate (1 + interest rate))

= -44,000 - 11,500 ((1 + 0.16)⁶ ) - 1 / 0.13(1 + 0.13( 1 + 0.13)⁶)

= -44,000 - 45,972

= - 89,972

Hence, the value of MACHINE B is $ - 89,972. or -$89,971.25

BY COMPARING BOTH MACHINE (A and B)

MACHINE B is the best alternative than the machine A.