Exhibit $20\mathrm{.}12$

COST INFORMATION FOR THE BIG TEN SWEATERS

China supplier cost

Material $ $34\mathrm{.}00$

Labor $12\mathrm{.}00$

Overhead $1\mathrm{.}25$

Transportation within China $1\mathrm{.}00$

Supplier profit $8\mathrm{.}85$

Agent's fee $2\mathrm{.}68$

Freight $($ocean carrier$)1\mathrm{.}50$

Duty, insurance, etc. $3\mathrm{.}00$

Total supplier cost $ $64\mathrm{.}28$

Domestic subcontractor cost

Monogram material $ $5\mathrm{.}00$

Labor $10\mathrm{.}00$

Total subcontractor cost $ $15\mathrm{.}00$

Total $($per sweater$)$ $ $79\mathrm{.}28$

Exhibit $20\mathrm{.}13$

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 $105,2612,4402,4902,3102,8902,563297$

Michigan $108,9331,3761,9001,5201,9801,800246$

Purdue $50,4577451,0809001,1101,030114$

Michigan State $74,741-1,8201,5201,5401,627168$

Indiana $41,833-61058046055079$

Penn State $107,008000000$

Wisconsin $80,109000000$

Iowa $70,214000000$

Illinois $59,545000000$

Minnesota $50,805000000$

Northwestern $24,190000000$

Nebraska $85,071$

Maryland $37,767$

Rutgers $46,193000000$

Total $4,561*7,9006,8307,9807,570443**$

$*439$ sweaters were sold through eBay for $$45$ each $($the customer pays shipping on all orders$).$

$**$Calculated assuming the demand at each school is independent $=\backslash$Sigma i$=1$N$\backslash$sigma $2$i$$

Our monogramming subcontractor gets $$15\mathrm{.}00$ 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 information, as shown in Exhibit $20\mathrm{.}13.$ The exact sales numbers for last year are given. Sweaters sold at full retail price were sold for $$131$ each. Sweaters left over at the end of the season were sold through eBay for $$45$ each and these sweaters were not monogrammed by our subcontractor. Keep in mind that the retail sales numbers do not accurately reflect actual demand because the company 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 may be ways to advertise that may 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 $20\mathrm{.}13.$ 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 $$50,000$ each and you know the rent, utilities, insurance, and a benefit package for the business was about $$23,000.$

What was the net pre$-$tax profit for their business last year, after deducting salary and overhead?

Note: Do not round intermediate calculations. Round your answer to the nearest dollar amount.

If they must pay $50\%$ in taxes after deducting their venture capital firm payment, what was the increase in cash that their business accrued last year?

Note: Do not round intermediate calculations. Round your answer to the nearest dollar amount.