# Math

We are asked to find the estimated profit from the extended warranty program.

(1) 2006 sales were 320,000 units at \$710.7 million. With a 4% increase in unit sales the sales for 2007 will be 320000(1.04)=332800 units.

The average cost per unit was 710700000/320000=2220.94 so the sales in 2007 will be 2220.9375*332800=\$739.128 million.

This assumes that the prices remained the same year over year.

(2) The company expects to sell warranties on 75% of sales, and warranties are a flat 8% of sales. So the total income from warranty sales is:

739128000*.75*.08=\$44347680

(3) The company pays employees a 10% commission for warranty sales so after commission the company receives 44347680*.9=\$39,912,912

(4) Since the customers have paid for a warranty the company must pick up any repair costs. ** These warranties are extensions -- above and beyond the original warranty. I am assuming that the company factors in all repair costs to determine profit on warranty sales.**

(a) 4% of all units fail, so we can expect 332800*.04=13312 failures.

- Of these 95% require minor repairs. So about 12646 will require minor repairs. Each minor repair takes on average 1.5 hours to fix for a total of 18970 hours. It costs the company \$100 per repair hour so the company has \$1896960 in costs.

- For the remaining 5%, these are outsourced at an average cost of \$800 per unit. There will be 666 units for a total cost of \$532480.

So the cost to the company of the warranty service is 1896960+532480=\$2,429,440

(5) The profit from the warranty service will be the income less commission minus the costs.

P=\$39912912-\$2429440=\$37,483,472

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The profit from warranty sales is approximately \$37,483,472

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As a quick check this is about 5% of sales which seems reasonable.