Question

Maria Chavez owns a catering company that serves food and beverages at parties and business functions. Chavez’s business is seasonal, with a heavy schedule during the summer months and holidays and a lighter schedule at other times. One of the major events Chavez’s customers request is a cocktail party. She offers a standard cocktail party and has estimated the cost per guest as follows:

Food and beverages	$	17.00
Labor (0.5 hour @ $9.80 /hr.)		4.90
Overhead (0.5 hour @ $18.58/hr.)		9.29
Total cost per guest	$	31.19

The standard cocktail party lasts three hours and Chavez hires one worker for every six guests, so that works out to one-half hour of labor per guest. These workers are hired only as needed and are paid only for the hours they actually work.

When bidding on cocktail parties, Chavez adds a 13% markup to yield a price of about $35 per guest. She is confident about her estimates of the costs of food and beverages and labor but is not as comfortable with the estimate of overhead cost. The $18.58 overhead cost per labor-hour was determined by dividing total overhead expenses for the last 12 months by total labor-hours for the same period. Monthly data concerning overhead costs and labor-hours follow:

Month	Labor-Hours			Overhead Expenses
January	2,500			$	45,000
February	2,500				49,000
March	2,700				50,000
April	3,900				54,000
May	4,200				57,000
June	5,200				61,000
July	6,200				64,000
August	7,200				67,000
September	6,700				65,000
October	4,200				58,000
November	3,800				54,000
December	6,200				62,000
Total	55,300			$	686,000

Chavez has received a request to bid on a 175-guest fundraising cocktail party to be given next month by an important local charity. (The party would last the usual three hours.) She would like to win this contract because the guest list for this charity event includes many prominent individuals that she would like to secure as future clients. Maria is confident that these potential customers would be favorably impressed by her company’s services at the charity event.

A. Use the least-squares regression method to estimate the fixed and variable components of overhead expenses. (Round the Variable cost to 2 decimal places and Fixed Cost to the nearest whole dollar amount.)

	Fixed cost per month Variable cost per hour

B. Express these estimates in the form Y = a + bX. (Round the Variable cost to 2 decimal places and Fixed Cost to the nearest whole dollar amount.)

	Y= + X

C. If Chavez charges her usual price of $35 per guest for the 175-guest cocktail party, how much contribution margin will she earn by serving this event? (Round your intermediate calculations and final answers to 2 decimal places.)

D. How low could Chavez bid for the charity event in terms of a price per guest and still break even on the event itself?

E. The individual who is organizing the charity’s fundraising event has indicated that he has already received a bid under $34 from another catering company. Do you think Chavez should bid below her normal $35 per guest price for the charity event?

Answer 1

A.
Fixed cost per month	$38,503
Variable cost per hour	$4.05
Working:
Month	Labor	Overhead
	Hours	Expenses
	x	y	x^2	x*y
January	2500	45000	6250000	112500000
February	2500	49000	6250000	122500000
March	2700	50000	7290000	135000000
April	3900	54000	15210000	210600000
May	4200	57000	17640000	239400000
June	5200	61000	27040000	317200000
July	6200	64000	38440000	396800000
August	7200	67000	51840000	482400000
September	6700	65000	44890000	435500000
October	4200	58000	17640000	243600000
November	3800	54000	14440000	205200000
December	6200	62000	38440000	384400000
	55300	686000	285370000	3285100000
	Σx	Σy	Σx2	Σxy
Formulas
Unit Variable Cost=b=(nΣxy-Σx.Σy) / ((nΣx^2-(Σx)^2)
Total Fixed Cost=a=(Σy-bΣx) / n
Where,
n is number of pairs of units—total-cost used in the calculation;
Σy is the sum of total costs of all data pairs;
Σx is the sum of units of all data pairs;
Σxy is the sum of the products of cost and units of all data pairs; and
Σx2 is the sum of squares of units of all data pairs.
Unit variable cost = b =	(12*3285100000-55300*686000) / (12*285370000 - (55300)^2)
=	(39421200000 - 37935800000) / (3424440000 - 3058090000)
=	1485400000 / 366350000
=	$4.05
Total fixed costs = a    =	(686000 - 4.05*55300) / 12
=	462035 / 12
=	$38,503

B.

B.
The linear regression model is represented by
Total cost Y = 38,503 +4.05 x
Where x is the number of labor hours.

C.
Price per guest		$35.00
Variable cost:
Food and beverages	$17.00
Labor	$4.90
Variable overhead *	$2.03
Total variable cost		$23.93
Contribution margin per guest		$11.08
Variable overhead cost per hour		4.05
Hours per guest		0.5
Variable cost per guest *		2.03
Number of guests		175
Contribution margin for the event		$1,938
(175 x 11.08)