ANALYTICS EXERCISE: Inventory Management at Big$10$Sweaters.com

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$1.$ 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 $$50,000$ each and you know the rent, utilities, insurance, and a benefit package for the business was about $$20,000.$ About how much do you think they made $$before taxes$$ last year?$$ If they must make their payment to the venture capital firm, and then pay $50\%$ in taxes, what was their increase in cash last year?

Last Year$$s Pre$-$Tax Profit

$$

Unit

Unit

Sales

Sale Price

Cost

Revenue

Cost

Margin

Ohio

$2,300$

$$120$

$73\mathrm{.}88$

$$276,000$

$$169,924$

$$106,076$

Michigan

$1,468$

$$120$

$73\mathrm{.}88$

$$176,160$

$$108,456$

$$67,704$

Purdue

$890$

$$120$

$73\mathrm{.}88$

$$106,800$

$$65,753$

$$41,047$

eBay

$342$

$$50$

$60\mathrm{.}88$

$$17,100$

$$20,821$

$($$$3,721)$

Totals

$5,000$

$$576,060$

$$364,954$

$$211,106$

Overhead:

$$120,000$

Net Profit:

$$91,106$

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If they pay $25\%$ to the venture capital firm, this is $$\_\_\_\_\_\_\_\_\_,$ their profit before taxes is $$\_\_\_\_\_\_\_\_\_.$ They then pay $$\_\_\_\_\_\_\_\_\_\_$ in taxes leaving them with an increase in cash of about $$\_\_\_\_\_\_\_\_\_.$

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$2.$ What was your reasoning behind using the aggregate demand forecast when determining the size of your order rather than the individual school forecasts?$$ Should you rethink this or is there a sound basis for doing it this way?

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$3.$ How many sweaters should you order next year?$$ Break down your order by individual school. Document your calculations in your spreadsheet.$$ Calculate this based on the aggregate forecast and also the forecast by individual school.

Here the single period model is applicable.$$ The cost of underestimating demand is the lost profit.$$ In this case a sweaters would be sold for $$120$ and it would cost $$73\mathrm{.}88($supplier plus subcontractor cost$),$ so the return is $$46\mathrm{.}12$ per sweater. The cost of overestimating demand is the difference between the supplier cost of $$60\mathrm{.}88$ and the eBay price of $$50$ which is $$10\mathrm{.}88.$

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The critical probability then is Cu$/($Co$+$Cu$)=\_\_\_\_/(\_\_\_\_+\_\_\_\_)=$

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Now, using the aggregate demand forecast, which has a mean of $7,400$ and standard deviation of $430$ units, you should order NORMINV$(\mathrm{.}809123,7400,430)=7,776$ units.$$

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If we base this on the individual forecasts we would order the following:

Ohio State $=$ NORMINV$(\mathrm{.}809123,\_\_\_,\_\_\_=$

Michigan $=$ NORMINV$(\mathrm{.}809123,\_\_\_,\_\_\_=$

Purdue $=$ NORMINV$(\mathrm{.}809123,\_\_\_,\_\_\_=$

Michigan State $=$ NORMINV$(\mathrm{.}809123,\_\_\_,\_\_\_=$

Indiana $=$ NORMINV$(\mathrm{.}809123,\_\_\_,\_\_\_=$

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Total order size would be $\_\_\_\_\_-7,767=\_\_\_\_$ sweaters.

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$4.$ What do you think they could make this year?$$ They are paying you $$40,000$ and you expect your benefit package addition would be about $$1,000$ per year.$$ Assume that they order based on the aggregate forecast.

We base this on the expected average sales from our forecast and an aggregate order size of $7,767$ sweaters.$$ Assuming sales are as forecast, the safety stock would be sold on eBay.$$ We also need to adjust overhead to account for the $$41,000$ increase due to the new employee.

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This Year$$s Expected Pre$-$Tax Profit

$$

Unit

Unit

Sales

Sale Price

Cost

Revenue

Cost

Margin

Ohio

$$

$$120$

$73\mathrm{.}88$

$$

$$

$$115,300$

Michigan

$$

$$120$

$73\mathrm{.}88$

$$

$$

$$81,494$

Purdue

$$

$$120$

$73\mathrm{.}88$

$$

$$

$$46,120$

Michigan State

$$

$$120$

$73\mathrm{.}88$

$$

$$

$$74,576$

Indiana

$$

$$120$

$73\mathrm{.}88$

$$

$$

$$23,844$

eBay

$$

$$50$

$60\mathrm{.}88$

$$

$$

$($$$3,982)$

Totals

$7,767$

$$906,420$

$$569,068$

$$337,352$

Overhead:

$$\_\_\_\_\_\_\_$

Net Profit:

$$176,352$

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Using the same logic as before, the venture capital people get $25\%\_\_\_\_\_\_\_$leaving us with $$\_\_\_\_\_\_\_$ to pay taxes on$.$ Taxes would be $$\_\_\_\_\_\_\_\_\_.$ This creates an increase in our cash of about $$\_\_\_\_\_\_\_.$

$5.$ How should the business be developed in the future?$$ Be specific and consider changes related to your supplier, the monogramming subcontractor, target customers, and products.

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