Weighted Average Formula

Formula to Calculate Weighted Average

Weighted average is a type of an average that takes into account the relative importance of each value under consideration and is calculated by multiplying the respective weights (in percentage terms) with its corresponding value.

Weighted Average Formula = W₁X₁ + W₂X₂ +……+W_nX_n

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For eg:
Source: Weighted Average Formula (wallstreetmojo.com)

Here, w = respective weight (in percentage), x = value

Example

Let’s take a simple weighted average example to illustrate how we calculate a weighted average.

Ramen has invested his money into four types of investments. He has invested 10% of his money in Investment A, 20% in Investment B, 30% in Investment C, and 40% in Investment D. The rates of return for these investments are 5%, 10%, 15%, and 20%. Calculate weighted avg of the rates of return Ramen would receive.

In this weighted average example, we are given both w and x.

Using the weighted average formula, we get –

• Weighted Avg = w₁x₁ + w₂x₂ + w₃x₃ + w₄x₄
• Weighted Avg = 10% * 5% + 20% * 10% + 30% * 15% + 40% * 20% = 0.005 + 0.02 + 0.045 + 0.08 = 15%.

Explanation

On a simple average, we don’t pay heed to the weight. That’s why when we calculate the simple average, the result becomes too generic. However, in the weighted average, we pay the right emphasis on the right weight, and we portray the weight in terms of percentages.

If you look at the weighted average formula, you would see that the value is being multiplied by the right amount of weight, and that is the beauty of the wt average.

• For example, if we need to find out the average of 10, 13, and 25, on a simple average, we will add three numbers and divide it by 3. Simple average of the above three numbers would be = (10 + 13 + 25) / 3 = 48 / 3 = 16.
• If we take the same example with weight; then the result would be quite different. Let’s say that the weight of number 10 is 25%, 13 is 30%, and 25 is 45%. Wt average of the above three numbers of would be = (10 * 25%) + (13 * 30%) + (25 * 45%) = 2.5 + 3.9 + 11.25 = 17.65.

Use

The usage of the weighted average is quite broad.

As for the weighted average example, we can talk about the weighted average cost of capital. In calculating the weighted average cost of capital, we take the cost of equity and the cost of debtCost Of DebtCost of debt is the expected rate of return for the debt holder and is usually calculated as the effective interest rate applicable to a firms liability. It is an integral part of the discounted valuation analysis which calculates the present value of a firm by discounting future cash flows by the expected rate of return to its equity and debt holders.read more into account. And depending on the capital structure of the company, we calculate the WACC.

Another example where we use the weighted average cost of capital is the issuance of outstanding shares. Let’s say that a firm has issued 100 shares on the 1st of January. And then another 100 shares are issued on the 1st of July.

Now, while calculating the outstanding sharesCalculating The Outstanding SharesOutstanding shares are the stocks available with the company's shareholders at a given point of time after excluding the shares that the entity had repurchased. It is shown as a part of the owner's equity in the liability side of the company's balance sheet.read more available during the year, we will use the weighted average method. Since the first 100 shares are issued on the 1st of January, it would be applicable for the whole year. But the next 100 shares are only issued in the middle of the year; that’s why the next 100 shares would be available only for 6 months. And here would be the calculation of weighted average of outstanding sharesWeighted Average Of Outstanding SharesWeighted Average Shares Outstanding is a calculation used to estimate the variations in a Company’s outstanding shares during a given period. It is determined by multiplying the outstanding number of shares (consider issuance & buybacks) in a given reporting period with their individual time-weighted portions. read more = (100 * 1) + (100 * 0.5) = 100 + 50 = 150.

Weighted Average in Excel (with excel template)

Let us now do the same example as above in Excel.

This is very simple. You need to provide the values of “X” and “Y.”

You can easily calculate the ratio in the Weighted Average in the ExcelWeighted Average In The ExcelIn Excel, we calculate Weighted Average by assigning weights to each data set. It is generally used to compute robust observations in statistics or portfolios and is calculated as (w1x1+w2x2+....+wnxn)/(w1+w2+..wn), where w is the weight allocated to the x value and the sumproduct function is used.read more template provided.

Recommended Articles

This article is a guide to Weighted Average Formula. Here we learn how to calculate the weighted average using its formula and practical examples, a calculator, and a downloadable excel template. You may also take a look at the following useful articles –

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