Problem $6-45$

Interpreting Regression

Analysis in Cost Estimation

$($L$06-1,6-2,6-5)$

$3.$ Minimum bid for $200-$person

cocktail party: $$4,400$

Dana Rand owns a catering company that prepares banquets and parties for both individual and business functions throughout the year. Rand's business is seasonal, with a heavy schedule during the summer months and the year$-$end holidays and a light schedule at other times. During peak periods, there are extra costs; however, even during nonpeak periods Rand must work more to cover her expenses.

One of the major events Rand's customers request is a cocktail party. She offers a standard cocktail party and has developed the following cost structure on a per$-$person basis.

Food and beverages

$$15$

Labor $(.5$ hr$.$ @ $$10$ per hour$)$

$5$

Overhead $(5$ hr$.$ @ $$14$ per hour$)$

Total cost per person

$\frac{7}{\text{\$}27}$

When bidding on cocktail parties, Rand adds a $15$ percent markup to this cost structure as a profit margin. Rand is quite certain about her estimates of the prime costs but is not as comfortable with the overhead estimate. This estimate was based on the actual data for the past $12$ months presented in the following table. These data indicate that overhead expenses vary with the direct$-$labor hours expended. The $$14$ estimate was determined by dividing total overhead expended for the $12$ months $($$$805,000)$ by total labor hours $(57,600)$ and rounding to the nearest dollar.

$\backslash$table$[[$Month$,$Labor Hours,Overhead Expenses$],[$January$,2500,$$$55,000$

Rand recently attended a meeting of the local chamber of commerce and heard a business consultant discuss regression analysis and its business applications. After the meeting, Rand decided to do a regression analysis of the overhead data she had collected. The following results were obtained.

Intercept $($a$)$

Coefficient $(b)$

$48,000$

$4$

Required:

Explain the difference between the overhead rate originally estimated by Dana Rand and the overhead rate developed from the regression method.

Using data from the regression analysis, develop the following cost estimates per person for a cocktail party.

a$.$ Variable cost per person

b$.$ Absorption cost per person

Assume that the level of activity remains within the relevant range.

Dana Rand has been asked to prepare a bid for a $200-$person cocktail party to be given next month. Determine the minimum bid price that Rand should be willing to submit.

What other factors should Dana Rand consider in developing the bid price for the cocktail party?

$($CMA$,$ adapted$)$