Question

Luke Corporation produces a variety of products, each within their own division. Last year, the managers at Luke developed and began marketing a new chewing gum, Bubbs, to sell in vending machines. The product, which sells for $5.25 per case, has not had the market success that managers expected, and the company is considering dropping Bubs.

The product-line income statement for the past 12 months follows:

Table 1

Revenue		$14,682,150
Costs
Manufacturing costs	$14,440,395
Allocated corporate costs	734,108	15,174,503
Product-line margin		$ (492,353)
Allowance for tax (@20%)		98,470
Product-line profit (loss)		$ (393,883)

All products at Luke receive an allocation of corporate overhead costs, which is computed as 5 percent of product revenue. The 5 percent rate is computed based on the most recent year's corporate cost as a percentage of revenue. Data on corporate costs and revenues for the past two years follow:

Table 2

	Corporate Revenue	Corporate Overhead Costs
Most recent year	$106,750,000	$5,337,500
Previous year	$76,200,000	$4,221,000

  Assume the fixed corporate overhead is $1,454,000 in each year. None of these fixed costs are specifically traceable to Bubbs.

Roy O. Andre, the product manager for Bubbs, is concerned about whether the product will be dropped by the company and has employed you as a financial consultant to help with some analysis. In addition to the information given above, Mr. Andre provides you with the following data on product costs for Bubs:

Table 3

Monthly Production and Production Costs
Month	Cases	Prod. Costs
1	207,000	1,139,828
2	217,200	1,161,328
3	214,800	1,169,981
4	228,000	1,185,523
5	224,400	1,187,827
6	237,000	1,208,673
7	220,200	1,183,699
8	247,200	1,226,774
9	238,800	1,225,226
10	252,600	1,287,325
11	250,200	1,241,760
12	259,200	1,272,451

  

Table 4 - Regression Analysis of Table 3 Data

Adjusted R-squared               0.957

Variable	Coefficient	t	p>|t|	Significance	Std Err
Units	2.236	15.71	< .001	***	0.1423
Constant	682,300	20.53	<.001	***	33,246

QUESTION: Assume the variable allocated corporate costs are $0.192 per case of Bubbs. Given methods used to compile Table 1, what would the price per case of Bubbs have to be for the product line margin to break-even. Assume no change in the number of units sold. You should apply allocated corporate overhead at the rate used by Lukes. Round to the nearest 0.001 per case.

Answer 1

SUMMARY OUTPUT

REGRESSION STATISTICS

MULTIPLE R 0.980345319

R SQUARE 0.961076945

ADJUSTED R SQUARE 0.957184639

STANDARD ERROR 7969.964262

OBSERVATIONS 12

ANNOVA

df ss MS F Significance F

Regression 1 15684258323 1.5684E+10 246.9171 2.23512E-08

Residual    10 635203303.4 63520330.3

Total 11 16319461626

Coefficients Standard Error t Stat P-value lower 95% upper 95%

intercept 682293.6573 33240.33583 20.5260759 1.66E-09 608229.5739 756357.7406

cases 2.235883256 0.142289713 15.7135973 2.24E-08 1.918842019 2.552924493

a. $ 2.24 per case

Relevant cost = variable cost production cost (X varaible coefficient in regresion summary output)

The estimated variable production cost is $ 2.24.this is the minimum that can be charged without reducing profit.

b.

To break even on the product ,Luke has to sell a sufficient number of cases to show or to cover fixed production costs on the product. The contribution margin, is lowered by the variable portion of the corporate costs. To determine these, we use high low method,only have two observations.

corporate costs are supposed to variable with respect to revenue, so using information on corporate costs varaible cost are 3.65% of revenue.

varaiable cost= cost at highest activity-cost at lowest activity/highest activity-lowest activity

= $ 5337500-4221000/$ 106750000-76200000

= 3.65 % of revenue

let q be the number of cases sold. Then, profit for q cases is -

Profit= Revenue -varaible corporate costs-fixed production cost

=(5.25*q)-(2.24*q)-(3.65%*5.25*q)- $ 682294

= $ 2.818*q

= $ 682294

q= 242120 cases

c.

This problem different from requirements (c) ,becuase the requirements that the revenue from the product covers th e production costs and the full 5% corporate cost allocation make the corporate cost allocation properly variable.

so, cases provide a profit equal to 5% of revenue

=5%*5.25*q

profit= revenue-varaible production costs-varaible corporate costs-fixed prouction costs

= 5.25*q-2.24*q-5%*5.25*q-682294

(5% *5.25*q)= 5.25 *q -2.24*q-5%*2.25*q-682294

q=274565 cases

d.

fixed manufacturing costs can be avoided. Luke will protect all the production cost plus the varaible corporate overhead.

lost revenue $(14682150)

production cost avoided 14440395

loss before corporate overhead savings (241755)

corporate costs avoided 3.65*14682150 535898

incraese profits before tax 294143

tax 20% 58829

incraesed profits $ 235314

d. $ 235314 increase

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