Justifying an Increased Line of Credit
This case illustrates the use of multiple regressions to estimate a com¬pany's demand function. The estimated demand function is used to calculate the price and cross-elasticities of demand, and the regres¬sion coefficients of the advertising and time trend variables are ana¬lyzed. These elasticities and coefficients are then interpreted in terms of their bearing on whether its bank should increase the company's line of credit.
The Assignment
You are the manager of a chain of 12 discount men's clothing stores. Sales have risen by 25 percent over the past 6 months and appear likely to remain at high levels. However, you are up against your credit limits and need a 25 to 30 percent increase in your line of credit to finance larger orders and inventories. The loan officer at ale bank is not convinced that an increase is reasonable. If the high sales of the past 6 months cannot be maintained, serious inventory problems might result. About 18 months ago the bank had to pro¬vide an emergency 40 percent increase in your line of credit when sales fell unexpectedly. A clearance sale retired this added line of credit, but the company ran a loss that year. The banker feels that the extended line of credit must be justified through a study of the demand for your principal product, men's suits, including its re¬sponse to changes in your price, your competitors' prices, and your advertising. He wants empirical evidence supporting your contention that present sales levels can be maintained with lower prices than those of your principal competitors and relatively little advertising. A department store executive recently told the banker that department store prices for men's suits were going to fall about 5 percent next year. This price decline is expected to increase department store sales at the expense of discount clothing chains. You were dubious of this, but had no evidence to support your view.
The Available Data
The number of suits sold each month and their average price is in your monthly accounting reports. One section of each manager's monthly sales report deals with the store's competitive environment. Each store manager surveys prices at nearby stores selling compara¬ble suits and records them in this section. You obtained a 36-month time series for the average prices of nearby discount and department stores. The account executive at your advertising agency provided the agency's estimates of your percentage of total discount clothing store advertising. You thought about gathering data on consumer in¬comes and general economic conditions. However, to save time and, reduce costs you decided to first try the data you have already located.
These data are in Table 4.4. The average monthly sales of 12,778 suits for the last 6 months are substantially greater than for any other 6-month period in the last 3 years.
Table 4.4 Demand Curve Data for Clothing Store Chain
|
Chain's
Sales
|
Chain's
Price
|
Competitor's
Price
|
DeparTment
Store Price
|
Chain's
Advertising
|
Time
Trend
|
|
11,127
|
$89.90
|
$91.48
|
$147.12
|
14.0%
|
1
|
|
8,250
|
92.60
|
92.64
|
143.08
|
14.6
|
2
|
|
11,370
|
94.22
|
89.43
|
138.22
|
20.0
|
3
|
|
9,064
|
99.35
|
104.45
|
139.10
|
10.7
|
4
|
|
10,172
|
90.10
|
89.75
|
142.46
|
17.0
|
5
|
|
13,231
|
95.46
|
97.29
|
141.00
|
19.1
|
6
|
|
10,111
|
99.05
|
97.63
|
131.51
|
19.7
|
7
|
|
8,690
|
. 98.91
|
95.05
|
133.05
|
13.5
|
8
|
|
13,029
|
93.66
|
98.32 '
|
140.88
|
13.9
|
9
|
|
.12,331
|
93.54
|
98.81
|
133.02
|
11.1
|
10
|
|
9,380
|
90.36
|
87.57
|
147.46
|
13.6
|
11
|
|
10,662
|
89.57
|
96.27
|
139.08
|
17.1
|
12
|
|
10,533
|
101.30
|
91.83
|
150.94
|
20.4
|
13
|
|
11,451
|
99.26
|
97.68
|
144.81
|
17.2
|
14
|
|
8,722
|
95.88
|
89.33
|
148.11
|
12.4
|
15
|
|
9,921
|
98.62
|
97.16
|
143.17
|
17.5
|
16
|
|
12,737
|
90.04
|
97.20
|
136.94
|
13.6
|
17
|
|
12,333
|
90.41
|
89.13
|
135.15
|
13.6
|
18
|
|
10,793.
|
93.11
|
.86.35
|
146.91
|
17.5
|
19
|
|
9,89r
|
105.74
|
96.94
|
135.66
|
14.5
|
20
|
|
8,467
|
104.12
|
99.41
|
137.74
|
17.7
|
21
|
|
6,820
|
105.70
|
96.67
|
140.60
|
12.0
|
22
|
|
11,841
|
94.92
|
98.45
|
139.11
|
14.3
|
23
|
|
10,892
|
102.69
|
104.96
|
143.86
|
11.2
|
24
|
|
10,087
|
100.50
|
95.63
|
132.08
|
19.7
|
25
|
|
7,512
|
107.60
|
101.74
|
147.62
|
13.6
|
26
|
|
8,207
|
101.70
|
.97.42
|
144.02
|
14.0
|
27
|
|
9,667
|
102.81
|
96.16
|
145.44
|
19.7
|
28
|
|
13,531
|
96.40
|
97.21
|
152.00
|
16.3
|
29
|
|
9,687
|
103.11
|
100.80
|
141.15
|
12.6
|
30
|
|
14,692
|
90.92
|
97.88
|
148.05
|
16.9
|
31
|
|
11,072
|
100.03
|
100.11
|
146.12
|
11.8
|
32
|
|
12,657
|
92.61
|
98.63
|
155.71
|
17.2
|
33
|
|
13,728
|
89.96
|
99.33
|
147.54
|
15.5
|
34
|
|
12,388
|
99.44
|
99.68
|
140.81
|
12.6
|
35
|
|
12,134
|
97.80
|
101.73
|
144.11
|
10.1
|
36
|
Average sales for the other five 6-month periods, starting with the most recent one, were 9,782, 9,785, 10,950, 10,700, and 10,536. Your prices were below the average price for your competitors during the last 6 months. Over all 3 years, the average of your prices and those of your competitors Are $96.98 and $96.39. Your advertising is below its average for the 3-year period - 14.0 percent in the last 6 months compared to 15.2 percent for the 3-year period. This makes the sales performance for the last 6 months seem all the more remarkable since advertising is generally felt to be very important in your business.
QUESTIONS
1. A monthly regression analysis is to be conducted using the monthly data for each demand variable. Formulate your empirical model using the additive functional form.
2. Using economic theory, what are the hypothesized signs of the parameters in the demand model? Explain.
3. Using the results from your regression analysis, interpret your estimated parameters. Are they statistically significant? Compare your hypothesized parameter signs with your estimated signs. If there are discrepancies, provide an appropriate-explanation.
4. Using average values for the most recent 6-month period, what are your estimated elasticities with respect to each independent variable (excluding the time trend variable). Interpret each elasticity.
5. As stated, your banker wants empirical evidence supporting your contention that current sales volume can be maintained with lower prices than those of your principal competitors and relatively little advertising (recall, your recent relative advertising effort has fallen compared to its average for the 3-year period). Also, your banker is concerned about the impact on your volume of a likely 5 percent decline in department store suit prices. Using appropriate parameter and elasticity estimates from your demand model, address your banker's concerns.
6. Your Singapore-based supplier can ship you between 10 and 15 thousand suits per month at a per unit cost of $54.50. Does your most recent 6-month average price represent an optimal pricing strategy? Explain.