Question

Table 13.6 Inventory Holdings: Home Improvement Stores Standard Deviation in Company Name Inventory Sales (%) 10.74 17.46 14.58 20.88 16.50 19.96 14.91 21.27 18.43 16.91 12.72 24.76 14.79 9.24 16.65 in (Revenues) Operating Earnings"(%) Building Materials Catalina Lighting Continental Materials Corp. Eagle Hardware Emco Limited Fastenal Co. The Home Depot HomeBase Inc. Hughes Supply Lowe's Cos. National Home Centers Waxman Industries, Inc. Westburne Inc. Wolohan Lumber Average 6.59 5.09 4.59 6.88 7.14 5.99 10.09 7.30 7.54 9.22 5.02 4.66 7.76 6.05 35.82 52.76 25.15 45.50 39.68 43.41 24.15 36.93 35.90 33.72 70.93 112.57 25.14 24.56 43.30 This standard deviation was computed using five years of quarterly operating earnings for each of these firms and was based on percent changes in operating income from year to year Source: Value Line database.

QUESTIONS

1) CALCULATE THE WORKING CAPITAL AS % OF REVENUES FOR EACH COMPANY

2) FIND OUT WHETHER EACH COMPANY IS OVER INVESTED OR UNDER INVESTED

3) WHAT IS THE STATUS OF EACH COMPANY IN TERMS OF WORKING CAPITAL INVESTMENT COMPARED TO INDUSTRY AVERAGE

Answer 1

In order to answer the questions, we will have to perform the regression analysis on the data give. Assume Inventory / Sales (%) as dependent variable i.e. Y and IN (Revenues) & Standard Deviation (%) as two dependent variables X₁ & X₂ respectively. I have performed regression using excel and the output is shown below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.606138683
R Square	0.367404103
Adjusted R Square	0.252386667
Standard Error	3.683505305
Observations	14
ANOVA
	df	SS	MS	F	Significance F
Regression	2	86.68279677	43.3414	3.194334	0.080574022
Residual	11	149.2503247	13.56821
Total	13	235.9331214
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	5.610433786	6.468254097	0.86738	0.404259	-8.626097492	19.84696506	-8.626097492	19.84696506
X Variable 1	0.817710178	0.734829572	1.112789	0.289526	-0.799638805	2.435059162	-0.799638805	2.435059162
X Variable 2	0.128343814	0.05108084	2.512563	0.028855	0.015915643	0.240771985	0.015915643	0.240771985

Based on the Coefficients as shown in the regression output above, So, the equation of regression is:

Y = 5.6104 + 0.8177X₁ + 0.1283X₂

That is Inventory / Sales (%) = 5.6104 + 0.8177 x IN (Revenues) + 0.1283 x Standard Deviation (%)

Based on this equation, let's calculate the Inventory / Sales (%) for each of the company.

If actual Inventory / Sales (%) > Inventory / Sales (%) as predicted by regression equation then the compnay is over invested otherwise it's underinvested.

Industry average Inventory / Sales (%) = 16.65.

If actual Inventory / Sales (%) of a company > 16.65 = Industry average Inventory / Sales (%) then status with respect to industry average is "More" otherwise it's "Less".

Please see the table below now:

Company name	Inventory / Sales (%)	In (Revenues)	Standard Deviation	Inventory / Sales (%) as predicted by Regression Equation	Over invested / under invested	More or less than industry average
	Y	X1	X2	Yp=5.6104+0.8177X1+0.1282X2	If Y > Yp then "Over invested" otherwise "Under invested"	If Y > 16.65 then "More" otherwise "Less"
Building Materials	10.74	6.59	35.82	15.60	Under invested	Less
Catalina Lightings	17.46	5.09	52.76	16.54	Over invested	More
Continental	14.58	4.59	25.15	12.59	Over invested	Less
Eagle	20.88	6.88	45.5	17.08	Over invested	More
Emco	16.5	7.14	39.68	16.54	Under invested	Less
Fastenal	19.96	5.99	43.41	16.08	Over invested	More
The Home Depot	14.91	10.09	24.15	16.96	Under invested	Less
Homebase	21.27	7.3	36.93	16.32	Over invested	More
Hughes	18.43	7.54	35.9	16.38	Over invested	More
Lowe's Co.	16.91	9.22	33.72	17.48	Under invested	More
National Homes	12.72	5.02	70.93	18.82	Under invested	Less
Waxman	24.76	4.66	112.57	23.87	Over invested	More
Westburne	14.79	7.76	25.14	15.18	Under invested	Less
Wolohan	9.24	6.05	24.56	13.71	Under invested	Less
Average	16.65		43.30