## Weighted Average for Multiple Products

WHAT ARE WEIGHTED AVERAGES

If you plan to sell more than one type of product, you should consider calculating a weighted average selling price and a weighted average product cost. The weighted average selling price reduces all your selling prices (of each product you plan to sell) down to one single selling price.

For instance, if you plan to sell 10 products, then you will have 10 selling prices. The weighted average method will reduce those ten selling prices down to one single selling price. On the other end of the continuum, the weighted average product cost reduces all your product costs (of each products you plan to sell) down to one single product cost. For instance, if you plan to sell 10 products, then you will have 10 product costs. The weighted average method will reduce those ten product costs down to one single product cost.

Developing weighted averages essentially reduces the quantity of numbers you have to work with, thereby reducing the chance for error. In addition, weighted averages generally enhance the presentation of the forecasted financial statements.

Before we show you how to calculate weighted average, lets discuss the concept of Averaging. Reflect back to your school days for a moment. Remember back to when your math instructor was teaching you the average of numbers. She would ask "what is the average of 6, 4, 7, and 3?" To find the average of these numbers, you would simply add all the numbers together and divide by the number of numbers added together. In this case, the average is 5. That is; 6+4+7+3 = 20 divide by 4 equals 5.

For most of us, finding the average of numbers was rather simple, however, understanding what it meant was an entirely different story. Let me break it to you gently - you will have to understand the concept of Averages before you can understand the concept of Weighted Averages. The consolation, however is that both use the same principals. Lets get started.

Averages use the principal of percentages. In theory, percentages can not exceed 100%. For instance, if you have a glass of water in front of you and it is 100% full, how much more water can you pour into the glass? You wouldn't be able to pour any more into the water because the glass is already 100% full. Numbers work in the same fashion. To prove this point, substitute the word water with the number 6. You have a full glass of 6 in front of you, how much more 6 can you put into the glass. You can not put any more 6 into the glass because the glass is already 100% full of 6.

Lets assume, you have a full glass of 4 in front of you, how much more 4 could you put into the glass. That's correct, no more 4 can fit into the glass because the glass is already 100% full of 4. Therefore, we can say that any number represents 100% of itself - no more or no less. When you try to calculate an AVERAGE, it attempts to break the 100% down into smaller, equal percentages. For example, lets find the average of 6 and 4. The formula is:

Sum of the numbers                 =     6 + 4    =     10 =     5
The # of numbers you are adding                 2               2

Therefore, the average of 6 and 4 is 5. What really took place is simple; the 100% was broken down into two equal percentages (2 is our denominator - the # of numbers we added together).  The equal percentage is 50%. In essence, the 100% is divided by the 2 (in our example) to produce 50% (which is half of 100%). Both 4 and 6 are multiplied by 50% and the sum becomes the average.

4   x   50%   =   2
6   x   50%   =   3

The sum of 2 and 3 equals 5 which is our average of 4 and 6. Lets now find the average of 40, 60, 80, and 100.

Sum of the numbers             =      40+60+80+100   =   280  =  70
the # of numbers you are adding                      4                    4

In this example, the average of 40, 60, 80, and 100 is 70. In other words, 100% of each number is broken down into 4 equal parts of 25% (100% divided by 4 = 25%) and are then added together to produce an answer of 70.

40   x   25%   =   10
60   x   25%   =   15
80   x   25%   =   20
100  x    25%   =   25

The sum of 10, 15, 20, and 25 is 70 (which is the average of the 4 numbers).

Now lets assume you plan to establish a business selling only two models of television sets. Model A will sell for \$200 and Model B will sell for \$400. What is the average selling price of the televisions sets?

Sum of the numbers             =   \$200 + \$400 =   \$600  =  \$300
the # of numbers you are adding                 2                  2

Therefore, the average selling price of the televison sets is \$300. Lets calculate the average selling price another way.

\$200   x   50%   =   100
\$400   x   50%   =   200

The sum of 100 and 200 produces an average selling price of \$300. What does this average selling price mean? If you sell the SAME QUANTITY of Model A and Model B televison sets, your average selling price will be \$300. In other words, in order to have an average selling price of \$300, 50% of all the television sets you sell will have to be Model A televisions and 50% of all the television sets you sell will have to be Model B televisions. Assume for a moment, you feel 1,000 television sets will sell during your first year of operation. Therefore, 500 Model A and 500 Model B television sets would have to be sold in order to have an average selling price of \$300. Remember, averaging breaks numbers down into EQUAL percentages. In this example, the equal percentage is 50% because we are finding the average of two numbers (100% divide by 2 equals 50%). The equal percentage for finding the average of 3 numbers would be 33.3% (100% divided by 3 = 33.3%) The equal percentage for finding the average of 4 numbers is always 25% (100% divided by 4 equals 25%). The equal percentage for finding the average of 5 numbers would be 20% (100% divided by 5 = 20%) and so on...

Chances are, however, one Model will sell better than the other Model. ( IE not at equal rates of 50% and 50%). As a result, you will want to find the weighted average of all the selling prices. Lets assume you estimate that 70% of the televisions sold in your first year of operation will consist of Model A televisions, while the remaining 30% is expected to be Model B sales (70% +30% = 100% or ALL the television sets you will sell in your first year of operation). Therefore, if you expect to sell 1,000 televisions during the first year of operation, 700 will be Model A televisions and 300 will be Model B televisions (IE 70% x 1,000 = 700 and 30% x 1,000 = 300).  Asuming the selling price of Model A is \$200 and the selling price of Model B is \$400, we can determine the weighted average of the two selling prices to be \$260.

\$200 (selling price of Model A)     x     70%    =    140
\$400 (selling price of Model B)     x     30%    =    120

The sum of 140 and 120 is \$260. Therefore, the weighted average selling price of the two Models, at the expected selling rates of 70% and 30%, is \$260. Remember earlier, we calculated the Average Selling Price to be \$300. The Average selling price assumes an equal selling rate for each model (that is; 50% Model A and 50% Model B). The Weighted Average selling price, on the other hand, applies unequal selling rates to each Model ( 70% to Model A and 30% to Model B). These unequal selling rates are more realistic, since in the world of business, products do not sell at equal amounts.

Businesses can also forecast their weighted average product cost. Assuming, each Model A televison set is purchased from your supplier for \$100 and each Model B television set is purchased from the same supplier for \$200, what will your average cost be and what will your weighted average cost be?

 AVERAGE COST: Cost Rate Model A \$100 x 50% = 50 Model B \$200 x 50% = 100 Average Product Cost \$150

Therefore, your Average Cost is \$150. The rate is 50% since averaging breaks numbers down into EQUAL percentages (100% divided by two numbers equals 50% each).  Below calculates the weighted average product cost.

 WEIGHTED AVERAGE PRODUCT COST: Cost Selling Rate Model A \$100 x 70% = 70 Model B \$200 x 30% = 60 Weighted Average Product Cost \$130

Therefore, the Weighted Average Product Cost is \$130; assuming the selling rate of TV Model A is 70% and the selling rate of TV Model B is 30%. Notice, the selling rate used to determine the weighted average selling price is also used to determine the weighted average product cost (IE 70% and 30%). The reason is simple - if you anticipate to SELL more Model A televisions than Model B televisions then, you will BUY more Model A and fewer Model B television sets.

The most powerful application for the weighted average selling price and the weighted average product cost is seen when a company's sell many products or provide many services. Once again , if you plan to sell 10 products, then you will have 10 selling prices and 10 product costs. The weighted average method will reduce your ten selling prices down to one single selling price (weighted average selling price). In addition, the weighted average method reduces all your product costs (of each products you plan to sell) down to one single product cost (weighted average product cost). In essence, one single selling price is much easier to "work" with than 10 selling prices. And one singe product cost is much easier to work with than 10 product costs. Developing weighted averages essentially reduces the quantity of numbers you have to work with, thereby reduces the chance for error.

In conclusion, if you plan to sell more than one product, you should consider calculating a weighted average selling price and a weighted average product cost. The importance of calculated a weighted average selling price and weighted average product cost will become apparent as you familiarize yourself with the process of forecasting financial statements. Below takes you through the entire process of calculating a weighted average selling price and a weighted average product cost. The example used below relates to a retail clothing company who intends to sell thirteen (13) clothing products.

WEIGHTED AVERAGES - EXPLAINED & ILLUSTRATED

As you'll see later in our retail clothing store example, John Smith plans to sell thirteen (13) separate clothing products, each having their own selling prices and product costs. As a result, John will calculate a weighted average selling price that reduces his thirteen (13) selling prices down to one selling price. In addition, he will calculate a weighted average product cost that reduces his thirteen (13) costs down to one product cost. This will ultimately alleviate any errors arising from working with so many numbers. It will also improve the presentation of his forecasted financial statements.

Below illustrates the steps necessary in calculating a single selling price and a single product cost (IE weighted average selling price and weighted average product cost).   Each step must be completed in sequence.

The steps needed to develop a weighted average selling price and a weighted average product cost can summarized by saying;

You will list all the major product groups in which you plan to sell. Next you will list the brand names, models or services within each major product group. Then you will assign forecasted percentages to each product group and to each brand name, model or service. These percentages will represent the rate at which your customers buy your products and product groups. Then you will determine your costs and selling prices of the products you plan to sell. These calculations will then be used to calculate your weighted average selling price and your weighted average product cost.

Categories: Financial