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.
