Tuesday
June 18, 2013

# Homework Help: Math/Biz Math

Posted by Jose on Monday, November 9, 2009 at 12:34am.

I am so lost.

Did I answer these problems right?
Bud Ray is the owner of an automatic car wash located in a busy side of town. He currently has all the business he can handle and then some. His business has grown steadily over the years. His current car wash equipment is in need of a complete overhaul. Jim Dandy is a sales rep. for Magic Wash and sells equipment for rebuilding car wash systems or new start up car wash systems. Jim however would rather sell the new system as he knows there will be less problems in the future since there would be no make-shift conversions to adapt to his current system. The cost difference is substantial. In order to rebuild Bud’s current system, it will cost \$114,000.00. To purchase a new Magic Wash Sparkle II system, the cost is \$250,000.00. The rebuilt system would have the capacity to wash 40 cars per day at \$3.95 per car. In addition, it will cost \$.48 per car in detergent and rinsing agents. The new Magic Wash Sparkle II would have a capacity of 60 cars per day, and the detergent and rinsing agents would only cost \$.23 per car because of the special “soap saver” feature. This feature is only available on the new system. Both systems have an expected 10 year life span. The car wash operates 200 days per year.

1.For the expected life expectancy of the Magic Wash Sparkle II, how would you justify the purchase using the “Price Vs Cost” method? (Show your work) Use profit for each.

The Magic Wash Sparkle II costs \$250,000. It can handle 60 cars per day @ \$3.95. Thanks to the special “soap saver,” the cost of detergent and rinsing agents is only \$.23 per car.

\$3.95 – \$.23 (cost of soap to car wash)

From this we can assume the real profit per car is \$3.72.
\$3.95 – \$.23 (cost of soap to car wash)

Since the car wash can handle 60 washes per day, assuming there are a total of 60 washes, the profit per day will be the total number of car washes times the profit per car.

\$3.72 x 60 = \$223.2

If the car wash operates at 200 days per year, we need to find the total profit. If one day yields \$223.20 we just multiply by 200 to find the total profit.
\$223.20 x 200 days = \$44,640/year(200 days).

Then, backed by the 10 year life expectancy warranty. We take the profit per year of the Magic Wash II by 10 years.

\$44,640 x 10 = \$446,400

The profit is \$446,400. The initial cost was \$250,000.

Subtract both to find price vs cost.

\$446,400 - \$250,000 = \$196,400

**********************************************************************

The rebuilt system costs \$114,000. It can handle 40 cars per day @ \$3.95. Yet, the cost is \$.48 per car from the soaps and detergents.

From this we can assume the real profit per car is \$3.47.
\$3.95 – \$.23 (cost of soap to car wash)

Since the car wash can handle 40 washes per day, assuming there are a total of 40 washes, the profit per day will be the total number of car washes times the profit per car.

\$3.47 x 40 = \$138.80

If the car wash operates at 200 days per year, we need to find the total profit. If one day yields \$138.80 we just multiply by 200 to find the total profit.
\$138.80 x 200 days = \$27,760/year(200 days).

Then, backed by the 10 year life expectancy warranty. We take the profit per year of the Magic Wash II by 10 years.

\$27,760 x 10 = \$277,600.

The profit is \$277,600. The initial cost was \$114,000.
Subtract to find price vs cost.
\$277,600 - \$114,000 = \$163,600

In reality, the Magic Wash Sparkle II is a better buy. Remember in 10 years it made \$446,400. The original cost was \$250,000. Then, the real profit was \$196,400.
The rebuilt system seemed like a smaller cost upfront. Yet, it only made \$277,600 in 10 years, when the initial cost was \$114,000. Leaving a profit of \$163,000.

4.Assume the same 10 year life expectancy, using the previous case, justify the purchase using the Cost-per-Unit method. (Show your work) Use profit per car.

\$163,000 / 10 / \$16,300 profit per year / 200 days / \$81.5 per day / 40 washes / \$2.0375 profit per car.

\$196,400 / 10 / \$19,640 per year / 200 days / \$98.2 per day / 60 / \$1.63666667 profit per car.

• Math/Biz Math - Trevor, Monday, November 9, 2009 at 3:39am

Argh too much!!! Who has time to read all this!

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