Question

1. Taking into account the data in Exhibit 1, prepare a table that calculates when a hen is “spent” under normal conditions such as the CCF Brands contract, or that could be used to decide when it is no longer profitable to continue egg production. That is, create a model with formulas for which you can easily vary inputs, such as price, profit, or variable costs (such as in question 2 below). Use the output template provided below. (Hint: Distinguish between relevant and non-relevant costs. Determine the estimated revenue per dozen and weekly production costs first.)

Week(s)	# Eggs per Hen/Week	# Weeks	Dozen Eggs Laid	Marginal Costs	Marginal Revenue	Contribution to Profit
1-23	n/a	23	0	$(10.64)	$0	$(10.64)
24	3	1	0.25
25	4	1	0.33
26	5	1	0.42
27-28	6	2	1.00
29-39	7	11	6.42
40-64	6	25	12.50
65-76	5	12	5.00
77	4	1	0.33
78	3	1	0.25

2. Based on the model that you developed in question 1, and assuming that hens are already laying, how sensitive is the model to changes in expected contract profit? In variable costs? What course of action does the model indicate should be taken when contribution margin is negative?
   Exhibit 1. Arkansas Egg Company Cost and Production Information Arkansas Egg aimed to collect 26.6 dozen eggs from each hen over its productive laying cycle of 55 weeks. If that happened, based on the contract price, then AEC recovered the costs of bringing the bird to its productive cycle about 40 cents/dozen) as well as fixed overhead about 16 cents/dozen). The approximate contribution margin during this time was 7%. After the breakeven point, the only costs incurred were the variable production costs. Information on hen life cycle Approximate life of hen 78 weeks Pre-productive period of hen life cycle First 23 weeks of life Productive period or laying cycle Last 55 weeks of life Average age of laying hens at Summers' barns 43 weeks Average age of laying hens at Thomas' barns 48 weeks Minimum production target (PT) over which to allocate costs 26.6 dozen Approximate costs based on 26.6 dozen production target Total pre-production cost through week 23 Fixed overhead cost (facilities, debt service, depopulation, etc.) Variable production costs (feed, transportation, labor, etc.) Total cost for producing organic cage-free eggs Expected profit at 26.6 dozen (7%) $0.40 per dozen or $10.64 per bird $0.16 per dozen or $4.26 per bird $1.14 per dozen or $30.32 per bird $1.70 per dozen or $45.22 per bird $0.12 per dozen or $3.17 per bird Note: Arkansas Egg Company, as a family business with less than $25 million in revenue, used cash basis accounting for book and tax purposes. For purposes of this case, assume that revenue was produced after eggs are laid. Fixed and variable production costs were incurred evenly across the hen production cycle.
   

Answer 1

DETERMINATION OF REVENUE PER DOZEN
PARTCULARS	AMUNT IN $
TOTAL PRE PRODUCTION COST FOR FIRST 23 WEEKS	0.4
FIXED OVER HEAD COST	0.16
VARIABLE COT PER DOZEN	1.14
TOTAL COST	1.7
PROFIT ESTIMATED	0.12
REVENUE PER DOZEN	1.82
DETERMINATION OF WEEKLY PRODUCTION COSTS PER WEEK
WEEKS	DOZEN EGGS LAID	WEEKS	FIXED COST	VARIABLE COST	TOTAL COST
A	B	C	D=(4.26/55*C)	E=(1.14*B)
1--23	0	23		10.64	10.64
24	0.25	1	0.077454545	0.285	0.362454545
25	0.33	1	0.077454545	0.3762	0.453654545
26	0.42	1	0.077454545	0.4788	0.556254545
27-28	1	2	0.154909091	1.14	1.294909091
29-39	6.42	11	0.852	7.3188	8.1708
40-64	12.5	25	1.936363636	14.25	16.18636364
65-76	5	12	0.929454545	5.7	6.629454545
77	0.33	1	0.077454545	0.3762	0.453654545
78	0.25	1	0.077454545	0.285	0.362454545
	26.5	78	4.26	40.85	45.11
WEEKLY PROFIT ANALYSIS
WEEKS	DOZEN EGGS LAID	REVENUE	VARIABLE COST	CONTRIBUTION	FIXED COST	PROFIT
1--23	0	0	10.64	-10.64	0	-10.64
24	0.25	0.455	0.285	0.17	0.013167273	0.156833
25	0.33	0.6006	0.3762	0.2244	0.0173808	0.207019
26	0.42	0.7644	0.4788	0.2856	0.022121018	0.263479
27-28	1	1.82	1.14	0.68	0.052669091	0.627331
29-39	6.42	11.6844	7.3188	4.3656	0.338135564	4.027464
40-64	12.5	22.75	14.25	8.5	0.658363636	7.841636
65-76	5	9.1	5.7	3.4	0.263345455	3.136655
77	0.33	0.6006	0.3762	0.2244	0.0173808	0.207019
78	0.25	0.455	0.285	0.17	0.013167273	0.156833
TOTAL	26.5	48.23	40.85	7.38	1.395730909	5.984269
THE GIVEN MODEL IS SAFE IN EVERY WEEK, THE NEGATIVE CONTRIBUTION WAS SEEN ONLY IN THE FIRST 23 WEEKS
BESIDES THAT THE GIVEN MODL TAES THE COMPANY IN TO BREAK EVEN IN 48 WEEKS
WHILE CONSIDERING THE AVEAGE AGE OF THOMAS BARNS, THE COMPANY JUST TAKES BREAKEVEN
AND IN CASE OF SUMMER BARNS THE COMPANY HAS TO FACE LOSSES
HENCE THE SELLING PRICE MUS BE INCREASED TO GET PROFITS WITH IN THEIR AVERAGE AGE

HOWEVER WHEN THE HENS AVERAGE IS 78 WEEKS, THE COMPANY NEED NOT TO CHANGE ITS SELLING PRICE PER DOZEN