A weighted average is the average value of a set of numbers, with different levels of relevance. This relevance of each number is referred to as its weight, and is represented as a percentage of the total relevancy. All weights in a weighted average formula calculation should be equal to 100%, or 1.

$$Weighted\space Average_{x} = w_{1}x_{1} + w_{2}x_{2}…+ w_{n}x_{n}$$

Where w = the relevant weight in %, and x = the value.

The easiest way to calculate an average is the arithmetic mean formula. In this formula, you add all of the numbers together and divide by the total amount of numbers. So, for the average of the numbers 1, 3 and 3, it would be ( 1 + 2 + 3)/2 which equals 2.

The weighted average formula takes into account how relevant each number is. Each number in the data set is multiplied by a number denoting its relative importance or weight. The result is then added up to get the weighted average. The weight is assigned to each number to specify the relative importance of them in the data set

So for example, if 1 is used 20% of the time while 2 and 3 happen 40% of the time, the percentages become the weight and the weighted average would be 2.2.

While the weighted average formula is a general mathematical formula, it has many uses when applied to finance.

### Uses of weighted average formula in finance

Weighted average finds extensive use in many areas of finance. Some of its frequent applications are briefly described below:

• The concept of Weighted Average is incorporated in Weighted Average Cost of Capital (WACC). A business might have numerous sources of financing and each source has its cost. So, in order to determine the cost of capital the concept of Weighted Average Cost of Capital is used.
• Investors use the measure of Weighted Average Cost of Capital (WACC) to evaluate projects of a company before possibly investing in them. If the risk factor of different an ongoing and new starting projects of a company involving same capital structure remains stable or same, then it is an indication that it is safe to invest in those projects. But, if the risk factor and structure of capital indicate vivid instability then the investment can turn out to be nightmare and chance of return are bleak as well.
• The Weighted Average Cost of Capital (WACC) measure is also used to determine Economic Value Addition (EVA). It is calculated by subtracting cost of capital from the profits made by the company. The Weighted Average Cost of Capital (WACC) is used in place of cost of capital in the above scenario.

#### Weighted average formula example

Stuart has saved $25,000, and he wants to invest in four projects. The projects are named as A, B, C and D. He has decided to invest 20% in project A, 40% in project B, 10% in project C and 30% in project D. He also knows that the return on investment of the projects is 5%, 4%, 6% and 3% respectively. Determine the possible amount which he is expected to earn as a result of this investment. • Total Amount to be Invested =$25,000
• Amount to be invested in project A = $5,000 • Amount to be invested in project B =$10,000
• Amount to be invested in project B = $2,500 • Amount to be invested in project D =$7,500
• Return on Investment in A = 5%
• Return on Investment in B = 4%
• Return on Investment in C = 6%
• Return on Investment in D = 3%
$$Weighted\space Average =(0.05)(20\%) + (0.04)(40\%) + (0.06)(10\%) + (0.03)(30\%)$$

So, Stuart is expected to earn a total weighted average of 4.1% on the total amount, for a total of $1,025. If Stuart had used the arithmetic mean, he would have calculated an average return of 4.5% and expected$100 more return. With small numbers, this may not be important, but when dealing with larger numbers in business finance it’s easy to see that this considerable difference highlights the importance of using the best formula to have accurate analysis on how profitable the investment may be.