Question

aria 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

$ 18.00 Labor

(0.5 hour @ $10.00 /hr.) 5.00 Overhead

(0.5 hour @ $18.66/hr.) 9.33

Total cost per guest $ 32.33

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 11% markup to yield a price of about $32 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 $18.66 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 3,300 $ 53,000

February 2,100 57,000

March 2,300 58,000

April 3,500 62,000

May 3,800 65,000

June 4,800 69,000

July 5,800 72,000

August 6,800 75,000

September 6,300 73,000

October 3,800 66,000

November 3,400 62,000

December 5,800 70,000

Total 51,700 $ 782,000

Chavez has received a request to bid on a 160-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.

2a. Use the least-squares regression method to estimate the fixed and variable components of overhead expenses.

3. If Chavez charges her usual price of $32 per guest for the 160-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.)

4. How low could Chavez bid for the charity event in terms of a price per guest and still break even on the event itself? (Round your answer to the nearest whole dollar amount.)

2b. Express these estimates in the form Y = a + bX.

Answer 1

2a.	As per least squares regression method, Y=a+b.X
	Where,
	a=Total fixed cost
	b=Unit variable cost
	b=(n*∑xy- ∑x*∑y)/[n∑x^2-(∑x)^2]
	a=(∑y-b.∑x)/n
	x=Labor hours
	y=Overhead expenses
	n=Number of months used in the calculation
	x	Y	x^2	xy
	3300	53000	10890000	174900000
	2100	57000	4410000	119700000
	2300	58000	5290000	133400000
	3500	62000	12250000	217000000
	3800	65000	14440000	247000000
	4800	69000	23040000	331200000
	5800	72000	33640000	417600000
	6800	75000	46240000	510000000
	6300	73000	39690000	459900000
	3800	66000	14440000	250800000
	3400	62000	11560000	210800000
	5800	70000	33640000	406000000
	51700	782000	249530000	3478300000	2994360000	2672890000	321470000
	n=12
	∑x=51700
	∑y=782000
	∑x^2=428603572
	∑xy=37173339704
	b=[(12*3478300000)-(51700*782000)]/[(12*249530000)-(51700)^2]=1310200000/321470000=$ 4.08 per hour
	a=[782000-(4.08*51700)]/12=$ 47589
	Variable cost per hour=$ 4.08 per hour
	Fixed cost per month=$ 47589
2b.	As per least squares regression method, Y=a+b.X
	Where,
	a=Total fixed cost
	b=Unit variable cost
	Y=47589+4.08*X
3	Contribution per guest=price per guest-Variable cost per guest
	Variable cost per guest:
				$
	Food and beverages			18
	Labor	(0.5*10)		5
	Overhead	(0.5*4.08)		2.04
	Total			25.04
	Contribution per guest=32-25.04=$ 6.96 per guest
	Total contribution=Number of guests*Contribution per guest=160*6.96=$ 1113.6
4	The Lowest bid=Variable cost per guest=$ 25.04