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The Carlson Department Store suffered heavy damage when a hurricane struck on August 31, 2003. The store was closed for four months (September – December 2003) and is now involved in a dispute with its insurance company concerning the amount of lost sales during the closure. Two key issues must be resolved:

- The amount of sales Carlson would have made if the hurricane had not struck.
- Whether Carlson is entitled to any compensation for excess sales from increased business activity after the storm.

More than $8 billion in federal disaster relief and insurance money came into the county, resulting in increased sales at department stores and numerous other businesses.

**Sales Data:**

The table below shows the sales data for the 48 months preceding the storm. It reports total sales for the 48 months preceding the storm for all department stores in the county, as well as the total sales in the county for the four months the Carlson Department Store was closed. Management asks you to analyze this data and develop estimates of the lost sales at the Carlson Department Store for the months of September through December 2003. Management also wants to determine whether a case can be made for excess storm-related sales during the same period. If such a case can be made, Carlson is entitled to compensation for excess sales it would have earned in addition to ordinary sales.

**Table 1 – Sales for Carlson Department Store, Sept ’99 through Aug ‘03**

| Month | 1999 | 2000 | 2001 | 2002 | 2003 |
|-----------|------|------|------|------|------|
| January | 1.45 | 2.31 | 2.31 | 2.56 | |
| February | 1.80 | 1.89 | 1.99 | 2.28 | |
| March | 2.03 | 2.02 | 2.42 | 2.69 | |
| April | 1.99 | 2.23 | 2.45 | 2.48 | |
| May | 2.32 | 2.39 | 2.57 | 2.73 | |
| June | 2.20 | 2.14 | 2.42 | 2.37 | |
| July | 2.13 | 2.27 | 2.40 | 2.31 | |
| August | 2.43 | 2.21 | 2.50 | 2.23 | |
| September | 1.71 | 1.90 | 1.89 | 2.09 | |
| October | 1.90 | 2.13 | 2.29 | 2.54 | |
| November | 2.74 | 2.56 | 2.83 | 2.97 | |
| December | 4.20 | 4.16 | 4.04 | 4.35 | |

**Table 2 – Department Store Sales for the County, Sept ’99 through Dec ‘03**

| Month | 1999 | 2000 | 2001 | 2002 | 2003 |
|-----------|-------|-------|-------|-------|-------|
| January | 46.8 | 46.8 | 43.8 | 48.0 | |
| February | 48.0 | 48.6 | 45.6 | 51.6 | |
| March | 60.0 | 59.4 | 57.6 | 57.6 | |
| April | 57.6 | 58.2 | 53.4 | 58.2 | |
| May | 61.8 | 60.6 | 56.4 | 60.0 | |
| June | 58.2 | 55.2 | 52.8 | 57.0 | |
| July | 56.4 | 51.0 | 54.0 | 57.6 | |
| August | 63.0 | 58.8 | 60.6 | 61.8 | |
| September | 55.8 | 57.6 | 49.8 | 47.4 | 69.0 |
| October | 56.4 | 53.4 | 54.6 | 54.6 | 75.0 |
| November | 71.4 | 71.4 | 65.4 | 67.8 | 85.2 |
| December | 117.6 | 114.0 | 102.0 | 100.2 | 121.8 |

**Managerial Report:**

Prepare a report for the management of the Carlson department store that summarizes your findings, forecasts, and recommendations. Include the following:

- An estimate of the sales had there been no hurricane.

*Hint:* Graph this time series data over the 48-month period to determine the approach to forecast sales for the final 4 months of 2003. Consider trends and seasonality.

- An estimate of the countywide department store sales had there been no hurricane.

*Hint:* Compare forecasted county-wide department store sales with actual sales to determine excess storm-related sales using a "lift factor" – the ratio of actual sales to forecast sales.

- An estimate of lost sales for the Carlson Department Store for September – December 2003.

Answer :

Based on the provided data, we can estimate the sales that the Carlson Department Store would have made if the hurricane had not struck. To do this, we need to analyze the trend and seasonality in the sales data.

To estimate the sales without the hurricane, we can use a forecasting method such as exponential smoothing or a regression model. By fitting the data to these models, we can generate forecasts for the final four months of 2003. To determine if there are excess storm-related sales, we can compare the forecasted county-wide department store sales to the actual sales.

Finally, to estimate the lost sales for the Carlson Department Store for September to December 2003, we subtract the forecasted sales without the hurricane from the actual sales during that period.

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