Eddie is a production engineer for a major supplier of component parts for cars. He has determined that a robot can be installed on 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 this cost will increase 6% each year. The robot will cost $16,500 to operate for the first year with costs increasing by $1500 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 $5000 after 10 years. Should Eddie recommend that purchase of the robot

Eddie should recommend the purchase of the robot.

Explanation:

This can be determined using the following 3 steps:

Step 1: Calculation of the present worth (PW) of the cost of one employee

This can be calculated using the formula for calculating the the present value (PV) of a growing annuity as follows:

PWE = (P / (r - g)) * (1 - ((1 + g) / (1 + r))^n) (1)

Where;

PWE = Present worth of the cost of one employee = ?

P = first or this year annual cost = $58,240

r = interest rate = 15%, or 0.15

g = annual growth rate of cost of the one employee = 6%, or 0.06

n = number of years = 10

Substituting the values into equation (1), we have:

PWE = ($58,240 / (0.15 - 0.06)) * (1 - ((1 + 0.06) / (1 + 0.15))^10) = $360,654.33

Step 2: Calculation of the present worth (PW) of the cost of the robot

This can be calculated using the following formula:

PWR = C + ((P / (r - g)) * (1 - ((1 + g) / (1 + r))^n)) - (SV / (1 + r)^n) (2)

Where;

PWR = Present worth of the cost of the robot = ?

C = cost of installing the robot = $75,000

P = first year cost of operating the robot = $16,500

r = interest rate = 15%, or 0.15

g = annual growth rate of cost of operating the robot = Annual increase in cost / P =  $1500 / $16,500 = 0.0909090909090909

n = number of years = 10

SV = Salvage value = $5,000

Substituting the values into equation (2), we have:

PWR = $75,000 + (($16,500 / (0.15 - 0.0909090909090909)) * (1 - ((1 + 0.0909090909090909) / (1 + 0.15))^10)) - (SV / (1 + 0.15)^10) = $188,227.75

Step 3: Recommendation

PWE = Present worth of the cost of one employee = $360,654.33

PWR = Present worth of the cost of the robot = $188,227.75

Since present worth of the cost of the robot of $188,227.75 is lower than the present worth of the cost of one employee of $360,654.33, Eddie should recommend the purchase of the robot.

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