Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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

Sagot :

Answer:

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.

We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.