dolution

Analytics Exercise 20-4 (Algo)

The firm has considered the idea of making the sweaters in their own factory, but for now they purchase them from a supplier in China. The prices are great, but service is a problem since the supplier has a 20-week lead time for each order and the minimum order size is 5,000 sweaters. The order can consist of a mix of the different logos, such as 2,000 for OSU, 1,500 for UM, 750 for MSU, 500 for PU, and 250 for IU. Within each logo sub lot, sizes are allocated based on percentages and the supplier suggests 20 percent X-large, 50 percent large, 20 percent medium, and 10 percent small based on their historical data.

Once an order is received, a local subcontractor applies the monograms and ships the sweaters to the customer. They store the inventory of sweaters for the company in a small warehouse area located at the subcontractor.

This is the company’s second year of operation. Last year they only sold sweaters for three of the schools, OSU, UM, and PU. They ordered the minimum 5,000 sweaters and sold all of them, but the experience was painful since they had too many UM sweaters and not enough for OSU fans. Last year they ordered 2,260 OSU, 1,840 UM, and 900 PU sweaters. Of the 5,000 sweaters, 434 had to be sold at a steep discount on eBay after the season. They were hoping not to do this again.

For the next year, you have collected some data relevant to the decision. Exhibit 20.12 shows cost information for the product when purchased from the supplier in China. Here we see that the cost for each sweater, delivered to the warehouse of our monogramming subcontractor, is $66.03. This price is valid for any quantity that we order above 5,000 sweaters. This order can be a mix of sweaters for each of the five schools we are targeting. The supplier needs 20 weeks to process the order, so the order needs to be placed around April 1 for the upcoming football season.

Exhibit 20.12

COST INFORMATION FOR THE BIG TEN SWEATERS
China supplier cost
Material		$	36.00
Labor			11.50
Overhead			1.25
Transportation within China			1.00
Supplier profit			9.10
Agent’s fee			2.68
Freight (ocean carrier)			1.50
Duty, insurance, etc.			3.00
Total supplier cost					$	66.03
Domestic subcontractor cost
Monogram material		$	5.00
Labor			9.00
Total subcontractor cost					$	14.00
Total (per sweater)					$	80.03

Exhibit 20.13

FORECAST DATA FOR THE BIG TEN SWEATERS
	AVERAGE FOOTBALL GAME ATTENDANCE	LAST YEAR’S ACTUAL SALES (FULL PRICE)	RHONDA’S FORECAST FOR NEXT YEAR	STEVE’S FORECAST FOR NEXT YEAR	MARKET RESEARCH FORECAST FOR NEXT YEAR	AVERAGE FORECAST	STANDARD DEVIATION
Ohio State	105,261	2,260	2,420	2,260	2,760	2,480	255
Michigan	108,933	1,431	1,830	1,470	2,030	1,777	284
Purdu	50,457	875	1,040	890	1,050	993	90
Michigan State	74,741	–	1,770	1,470	1,520	1,587	161
Indiana	41,833	–	570	480	490	513	49
Penn State	107,008
Wisconsin	80,109
Iowa	70,214
Illinois	59,545
Minnesota	50,805
Northwestern	24,190
Nebraska	85,071
Total		4,566*	7,630	6,570	7,850	7,350	427**

*434 sweaters were sold through eBay for $49 each (the customer pays shipping on all orders).

**Calculated assuming the demand at each school is independent = Si?=?1N?s2iSi??=?1N??si2

Our monogramming subcontractor gets $14 for each sweater. Shipping cost is paid by the customer when the order is placed.

In addition to the cost data, you also have some demand information, as shown in Exhibit 20.13. The exact sales numbers for last year are given. The exhibit indicates the retail or “full price” sales for the sweaters that were sold for $133 each. Sweaters that we had at the end of the season were sold through eBay for $49 each and were not monogrammed. Keep in mind that the retail sales numbers do not accurately reflect actual demand since they stocked out of the OSU sweaters toward the end of the season.

As for advertising the sweaters for next season, Rhonda is committed to using the same approach used last year. The firm placed ads in the football program sold at each game. These worked very well for reaching those attending the games, but she realized there might be ways to advertise that would open sales to more alumni. She has hired a market research firm to help identify other advertising outlets but has decided to wait at least another year to try something different.

Forecasting demand is a major problem for the company. You have asked Rhonda and Steve to predict what they think sales might be next year. You have also asked the market research firm to apply their forecasting tools. Data on these forecasts are given in Exhibit 20.13. To generate some statistics you have averaged the forecasts and calculated the standard deviation for each school and in total.

Based on advice from the market research firm, you have decided to use the aggregate demand forecast and standard deviation for the aggregate demand. The aggregate demand was calculated by adding the average forecast for each item. The aggregate standard deviation was calculated by squaring the standard deviation for each item (this is the variance), summing the variance for each item, and then taking the square root of this sum. This assumes that the demand for each school is independent, meaning that the demand for Ohio State is totally unrelated to the demand at Michigan and the other schools.

You will allocate your aggregate order to the individual schools based on their expected percentage of total demand. You discussed your analysis with Rhonda and Steve and they are OK with your analysis. They would like to see what the order quantities would be if each school was considered individually.

You are curious as to how much Rhonda and Steve made in their business last year. You do not have all the data, but you know that most of their expenses relate to buying the sweaters and having them monogrammed. You know they paid themselves $50,000 each and you know the rent, utilities, insurance, and a benefit package for the business was about $16,000.

They are paying you $36,000 and you expect your benefit package addition would be about $1,000 per year. Assume that they order based on the aggregate forecast.

a. what is the expected pre-tax profit for this year, after deducting salary and overhead? Use average forecast for each school. Assume sales materialize per the average forecasts and the entire safety stock amount (computed based on aggregate demand) must be sold on EBay. (Round your answer to the nearest dollar amount.)

b. If they must pay 50% in taxes after deducting their venture capital firm payment, how much do you expect their business cash to increase this year? (Round your answer to the nearest dollar amount.)