II. The Worker\'s Friend Mortgage Company has two branches, one in D.C, the othe
ID: 435251 • Letter: I
Question
II. The Worker's Friend Mortgage Company has two branches, one in D.C, the other in Montgomery County, Maryland. The company is licensed to issue mortgages in DC and Montgomery County, with both offices able to issue a mortgage in either jurisdiction. The DC branch has a staff of 5, each working 6 hours per day. Every staff member earns an hourly wage of $33. For each mortgage processed, there is a cost of $500 for legal documents. The firm has a daily overhead rate of 165%. Typically, this branch processes 5 mortgages per day, and charges customers $2400 for each mortgage processed. The Montgomery County branch currently has a staff of 6, each working seven hours per day, and earning an hourly wage of $27. For each mortgage processed, there is a cost of $500 for legal documents. The overhead rate for that branch to 135%. Typically, this branch processes 6 mortgages per day, and charges customers $2100 for each mortgage processed. a. Calculate both labor productivity and multifactor productivity for each office. b. Explain in a few sentences whether the higher productivity of one office implies that that office should be expanded and the other closed.Explanation / Answer
Generally productivity is calculated by output divided by input. In case of
Labor productivity = output/labor input
Multifactor productivity = output/total input
In most cases, if the data is available (as in this question), we convert the output and input into monetary form so that we get a pure ratio. We shall solve the questions based on these understanding (mentioned above). Please note that since the overhead is mentioned as percentage we need to identify the direct cost and indirect cost. Legal documents are usually considered as indirect cost (administrative cost) and we will follow that. This means that the percentage overhead will be applied only on the labor cost.
a.
DC branch
Output = 5*2400 = $12000
Labor input = 5*6*33 = $990
Total input = direct input (labor cost) + indirect input (legal cost) + overhead (percentage cost on direct cost) = 990 + 5*500 + 990*1.65 = $5123.5
Now let’s calculate the labor and multifactor productivity.
Labor productivity = 12000/990 = 12.12
Multifactor productivity = 12000/5123.5 = 2.34
Montgomery County branch
Output = 6*2100 = $12600
Labor input = 6*7*27 = $1134
Total input = 1134 + 6*500 + 1134*1.35 = $5664.9
This makes the productivity for this branch as
Labor productivity = 12600/1134 = 11.11
Multifactor productivity = 2.22
b.
Higher productivity indicates better conversion ratio and efficiency. In this example, since we have considered the input and output in terms of $, the productivity ratios provide the ROI of the operations. If it is necessary to shut down on of the office and expand the other office, then the one with the higher productivity should be chosen. Even though the overall revenue of the Montgomery branch is higher than DC, if we expand DC to the size of Montgomery branch, it will yield a better revenue.