Question

Question 1 Based on the following data, calculate the single-factor productivity ratio using hours of labor for a housekeeping department.

•   Number of employees = 100

•   Average hourly rate = $5.50

•   Total hours worked in September = 15,570

•   Total square feet maintained = 190,000

ANSWER

Productivity = Output / Input Here, Output = total square feet maintained = 190,000 And, Input = total hours worked = 15,570 So, productivity will be 190,000 / 15,570 = 12.2 square feet maintained per hour ---------------------------------------------- One could have also used the input using the $ unit. In that case, the input will be Input = total hours worked x per hour rate = 15,570 x $5.50 = $85,635 Productivity = Output / Input = 190,000 / 85,635 = 2.22 square feet maintained per $

Question 3. Assume that a new piece of equipment could allow 25% of the labor force in Question 1 to be eliminated. Using a 173-hour working month for each employee, a total equipment cost of $60,000 (which has a useful life of 3 years), and ignoring the effect of cash flow and time value of money, would this be a good use of capital?

I am having a hard time understanding how the book came up with these answers. need it worked out so I understand the process

Yes, this would be a good use of capital. The total annual cost would be $20,000 ($60,000 ÷ 3) and total annual savings would be $285,450 ($23,787.50 per month × 12 months). Therefore, the total monthly benefit is $22,120.83.

Answer 1

Earlier, the entire Input was through labor hours.

The total cost of labor hours (monthly) was (173 labor hours x 100 employees x $5.50 per hour per employee) = $95,150 ----(1)

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Now, the 75% of the earlier cost of labor hours still exists i.e. $95,150 x 75% = $71,362.5 still exists

25% has been replaced by the machine which costs $60,000 for the 3 years i.e. $20,000 for a single year or $20,000/12 = $1,666.67 per month

Therefore the total cost (monthly) is $71,362.5 + $1,666.67 = $73,029.17 ----(2)

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So, the reduction is monthy total cost = difference of (1) and (2) = $95,150 - $73,029.17 = $22,120.83.

Since there is a positive reduction in monthly total expense, it is a good idea to go for the machine.