Question

can you please solve by hand

Eddie is a production engineer for a major supplier of component parts for cars. He has determined that a robot can be installed at the production line to replace one employee. The employee earns $20 per hour and benefits worth $8 per hour for a total annual cost of $58,240 this year. Eddie estimates that this cost will increase 6% each year. The robot will cost $16,500 to operate for the first year with costs increasing by $1,500 each year. The firm uses an interest rate of 15% and a 10-year planning horizon. The robot costs $75,000 installed and will have a salvage value of $5,000 after 10 years. Should Eddie recommend that purchase of the robot?

Answer 1

The present worth of geometric series = A * [1 - (1+g)^n / (1+i)^n] / (i - g)

Present cost of an employee =  58240 * [1 - (1+0.06)^10 / (1+0.15)^10] / (0.15 - 0.06)

=  58240 * [1 - (1.06)^10 / (1.15)^10] / (0.09)

=  58240 * 6.19255376

= 360654.33

NPW of Robot = -75000 + 5000 * (P/F, 15%,10) - 16500 * (P/A, 15%,10) - 1500 * (P/G, 15%,10)

= -75000 + 5000 * 0.247185 - 16500 * 5.018769 - 1500 * 16.979477

= -182042.98

Net present cost of robot is 182042.98 and is less than the present cost of employee, so robot should be installed