Question

Your company provides a variety of delivery services. Management wants to know the volume of a particular delivery that would generate $10,000 per month in operating profits before taxes. The company charges $20 per delivery.

The controller’s office has estimated overhead costs at $9,000 per month for fixed costs and $12 per delivery for variable costs. You believe that the company should use regression analysis. Your analysis shows the results to be:

Monthly overhead
=
$
26
,
501
+
$
10.70
 
per delivery
Monthly overhead=$26,501+$10.70 per delivery
Your estimate was based on the following data:

Month Overhead Costs Number of Deliveries
  1 $142,860.                  11,430
  2   151,890                     12,180
  3   192,600.                  15,660
  4   141,030                     11,250
  5   203,490.                   12,780
  6   180,630.                  14,730
  7   159,630                     12,510
  8   183,990                     15,060
  9   194,430.                   15,450
10   150,120                     11,970
11   154,080.                   12,630
12   184,800.                  15,300
13   183,120.                   14,580
The company controller is somewhat surprised that the cost estimates are so different. You have been asked to recheck your work and see if you can figure out the difference between your results and the controller’s results.

Required

Analyze the data and your results and state your reasons for supporting or rejecting your cost equation.

Write a report that informs management about the correct volume that will generate $10,000 per month in operating profits before taxes.

Answer 1

1) Notice the one observation that appears to be unusual. (This is observation 5.) Without knowing more about the reasons for the high cost, we might want to treat it as an "outlier" meaning we would estimate the regression without this observation. The results of that regression are:
Overhead Costs (Y)	Number of Deliveries (X)
$                                                           142,860.00	11,430
$                                                           151,890.00	12,180
$                                                           192,600.00	15,660
$                                                           141,030.00	11,250
$                                                           180,630.00	14,730
$                                                           159,630.00	12,510
$                                                           183,990.00	15,060
$                                                           194,430.00	15,450
$                                                           150,120.00	11,970
$                                                           154,080.00	12,630
$                                                           184,800.00	15,300
$                                                           183,120.00	14,580
SUMMARY OUTPUT
Regression Statistics
Multiple R	0.992130931
R Square	0.984323784
Adjusted R Square	0.982756162
Standard Error	2635.659661
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	4361896882	4361896882	627.909039	2.3451E-10
Residual	10	69467018.5	6946701.85
Total	11	4431363900
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	9776.561937	6370.43427	1.53467747	0.15587261	-4417.6502	23970.774	-4417.6502	23970.774
X Variable 1	11.68578345	0.4663473	25.0581132	2.3451E-10	10.6466969	12.72487	10.6466969	12.72487
2) Using the result from improved regression the new cost equation would be
Monthly overhead = $$9776.56  + $11.69 x number of deliveries
This implies a contribution margin per delivery of $8.31 (= $20.00 – $11.69).To earn operating profits of $10,000, the company needs approximately 2,380 (= [$10,000 + $9,777] - $8.31) deliveries, this level of deliveries is outside the range of the observations used to develop the regression estimates. Therefore, this estimate needs to be used with caution.