How to do average of shares?

However, if you bought your shares in several transactions at different price points, and bought a different number of shares each time, evaluating your investments' performance is a little more complicated. In this case, the best method is to calculate a "weighted average" of the prices you paid. Your broker can probably help you sort things out -- and if you don't have a broker, be sure to check out our Broker Center -- but in the meantime, let's take a closer look a weighted average.

What is a weighted average? A weighted average is a method of finding the average value of a group of numbers, which takes into account how many times each number occurs, or its importance. A common real-world example is the calculation of a grade-point average in schools, where an "A" carries a greater weight than a "B", which carries a greater weight than a "C", and so on.

How to calculate your weighted average price per share When it comes to buying stock, a weighted average price can be used when shares of the same stock are acquired in multiple transactions over time. This is necessary if the transactions were for different numbers of shares, since the larger purchases contribute more to the average. For example, the mathematical average of $100 and $200 is $150, but if you bought 10 shares of stock at $100 and only one share at $200, the lower-priced shares carry more weight when calculating the average price you paid.

In order to calculate your weighted average price per share, you can use the following formula:

In words, this means that you multiply each price you paid by the number of shares you bought at that price. Then, add up all of these results. Finally, divide by the total number of shares you purchased.

This may sound a little complicated, so let's look at an example to illustrate how it works.

An example Let's say that you own 500 shares of Microsoft, and you acquired your shares in three separate transactions. You bought the following number of shares at each of the following price points.

In order to calculate your weighted average price per share, simply multiply each purchase price by the amount of shares purchased at that price, add them together, and then divide by the total number of shares. Written as an equation, it looks like this:

Why it's useful Knowing the weighted average price you paid for each share of stock can help you determine how your investment is performing as a whole, relative to the current share price.

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If you bought all of your stock in a single transaction, it's easy to determine how your investment is performing. Simply look at the current share price and compare it to the price you paid.

However, if you bought your shares in several transactions at different price points, and bought a different number of shares each time, evaluating your investments' performance is a little more complicated. In this case, the best method is to calculate a "weighted average" of the prices you paid.

What is a weighted average?A weighted average is a method of finding the average value of a group of numbers, which takes into account how many times each number occurs, or its importance. A common real-world example is the calculation of a grade-point average in schools, where an "A" carries a greater weight than a "B", which carries a greater weight than a "C", and so on.

How to calculate your weighted average price per shareWhen it comes to buying stock, a weighted average price can be used when shares of the same stock are acquired in multiple transactions over time. This is necessary if the transactions were for different numbers of shares, since the larger purchases contribute more to the average. For example, the mathematical average of $100 and $200 is $150, but if you bought 10 shares of stock at $100 and only one share at $200, the lower-priced shares carry more weight when calculating the average price you paid.

In order to calculate your weighted average price per share, you can use the following formula:

In words, this means that you multiply each price you paid by the number of shares you bought at that price. Then, add up all of these results. Finally, divide by the total number of shares you purchased.

This may sound a little complicated, so let's look at an example to illustrate how it works.

An exampleLet's say that you own 500 shares of Microsoft, and you acquired your shares in three separate transactions. You bought the following number of shares at each of the following price points.

In order to calculate your weighted average price per share, simply multiply each purchase price by the amount of shares purchased at that price, add them together, and then divide by the total number of shares. Written as an equation, it looks like this:

Why it's usefulKnowing the weighted average price you paid for each share of stock can help you determine how your investment is performing as a whole, relative to the current share price.

This article is part of The Motley Fool's Knowledge Center, which was created based on the collected wisdom of a fantastic community of investors based in theFoolsaurus. Pop on over there to learn more about our Wiki andhow you can be involvedin helping the world invest, better! If you see any issues with this page, please email us atknowledgecenter@fool.com. Thanks -- and Fool on!

The article How to Calculate Weighted Average Price per Share originally appeared on Fool.com.

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The average cost basis method considers the total cost of your investment, factoring in purchases, reinvested dividends, capital gains and returns of capital. From that figure, it calculates the average purchase price of your shares. Your average cost basis can help you calculate whether or not your investment gained or lost value.

Average cost isn’t the only method to calculate cost basis. Unless you elect an alternative, the average cost method is used help calculate the money you made (or lost) and how much you owe in taxes.

When you sell a share, the net proceeds from the sale are compared to your average cost basis. If your net proceeds are greater than the average cost basis, then the sale is generally considered a gain. If it’s less than what you paid for it, it may be a loss.

A shareholder opens an account with a $2,500 initial purchase and invests $100 into the same fund at different times during the same year. Then the fund paid a taxable capital gain distribution of $50, which was reinvested into the fund. The result is an addition to the cost basis of $50.

The same shareholder sold five shares the following year on May 1 at $70 per share for a total sale of $350.

Average Cost per share = Total purchases ($2,750) ÷ total number of shares owned (56.61) = $48.58.

To calculate the average cost, divide the total purchase amount ($2,750) by the number of shares purchased (56.61) to figure the average cost per share = $48.58.

Cost basis = (p1 * q1 + p2 * q2 + ... + pi * qi) / n

where:

If you're familiar with the notion of weighted average, you've most probably noticed that the cost basis is precisely the weighted average of consecutive prices, with the weights given by the number of shares bought at each step.

Now, we will take the previous example and determine the average stock price.

Then, the total number of shares is:

Consequently, the average stock price, or the stock cost basis, is:

Average Cost per share = Total purchases ($2,750) ÷ total number of shares owned (56.61) = $48.58. To calculate the average cost, divide the total purchase amount ($2,750) by the number of shares purchased (56.61) to figure the average cost per share = $48.58.

The weighted average of outstanding shares is a calculation that incorporates any changes in the number of a company's outstanding shares over a reporting period. The reporting period usually coincides with a company's quarterly or annual reports. The weighted average is a significant number because companies use it to calculate key financial measures with greater accuracy, such as earnings per share (EPS) for the time period.

Calculating a weighted average of outstanding shares is important because it allows a company to calculate its earnings per share (EPS), which is a measurement of how much money a company makes for each share of its stock. Potential investors in a company look at the EPS as an indicator of the company's profitability and compare this metric with the EPS of other companies before making an investment decision.

For example, let's say a company has 100,000 shares outstanding at the start of the year. Halfway through the year, it issues new shares in the amount of an additional 100,000 shares. Thus, the total amount of shares outstanding increases to 200,000.

If at the end of the year the company reports earnings of $200,000, which amount of shares should be used to calculate earnings per share (EPS): 100,000 or 200,000? If the 200,000 shares were used, the EPS would be $1, and if 100,000 shares were used, the EPS would be $2—this is quite a large range! To avoid the confusion caused by such a large range, the company must calculate the weighted average of outstanding shares to arrive at a more accurate EPS for the given time period.

This potentially large range is the reason why a weighted average is used, as it ensures that financial calculations will be as accurate as possible in the event that the amount of a company's shares changes over time. The weighted average number of shares is calculated by taking the number of outstanding shares and multiplying the portion of the reporting period those shares covered, doing this for each portion and, finally, summing the total.

The weighted average number of outstanding shares in our example would be 150,000 shares.

The earnings per share calculation for the year would then be calculated as earnings divided by the weighted average number of shares ($200,000/150,000), which is equal to $1.33 per share.

Understanding how to calculate a weighted average can also be useful to individual investors who want to calculate their cost basis. The cost basis refers to the original purchase price of an asset or investment for tax purposes. Investors calculate the cost basis to determine if their investment has been profitable or not, along with any possible taxes they might owe on the investment.

Because investors frequently purchase shares of a company at various times and in various amounts as they build their position in a stock, it can be a challenge to keep track of the cost basis of those shares. One method is for the investor to calculate a weighted average of the share price paid for the shares. The investor would multiply the number of shares acquired at each price by that price and then add those values together. Lastly, divide the total value by the total number of shares purchased to arrive at the weighted average share price.