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When we calculate a simple average of a given set of values, the assumption is that all the values carry an equal weight or importance.

For example, if you appear for exams and all the exams carry a similar weight, then the average of your total marks would also be the weighted average of your scores.

However, in real life, this is hardly the case.

Some tasks are always more important than the others. Some exams are more important than the others.

And that’s where Weighted Average comes into the picture.

Here is the textbook definition of Weighted Average:

Now let’s see how to calculate the Weighted Average in Excel.

In this tutorial, you’ll learn how to calculate the weighted average in Excel:

Using the SUMPRODUCT function.

Using the SUM function.

So let’s get started.

There could be various scenarios where you need to calculate the weighted average. Below are three different situations where you can use the SUMPRODUCT function to calculate weighted average in Excel

Below are three different situations where you can use the SUMPRODUCT function to calculate weighted average in Excel

Suppose you have a dataset with marks scored by a student in different exams along with the weights in percentages (as shown below):

In the above data, a student gets marks in different evaluations, but in the end, needs to be given a final score or grade. A simple average can not be calculated here as the importance of different evaluations vary.

For example, a quiz, with a weight of 10% carries twice the weight as compared with an assignment, but one-fourth the weight as compared with the Exam.

In such a case, you can use the SUMPRODUCT function to get the weighted average of the score.

Here is the formula that will give you the weighted average in Excel:

=SUMPRODUCT(B2:B8,C2:C8)

Here is how this formula works: Excel SUMPRODUCT function multiplies the first element of the first array with the first element of the second array. Then it multiplies the second element of the first array with the second element of the second array. And so on..

And finally, it adds all these values.

Here is an illustration to make it clear.

In the above case, the weights were assigned in such a way that the total added up to 100%. But in real life scenarios, it may not always be the case.

Let’s have a look at the same example with different weights.

In the above case, the weights add up to 200%.

If I use the same SUMPRODUCT formula, it will give me the wrong result.

In the above result, I have doubled all the weights, and it returns the weighted average value as 153.2. Now we know a student can’t get more than 100 out of 100, no matter how brilliant he/she is.

The reason for this is that the weights don’t add up to 100%.

Here is the formula that will get this sorted:

=SUMPRODUCT(B2:B8,C2:C8)/SUM(C2:C8)

In the above formula, the SUMPRODUCT result is divided by the sum of all the weights. Hence, no matter what, the weights would always add up to 100%.

One practical example of different weights is when businesses calculate the weighted average cost of capital . For example, if a company has raised capital using debt, equity, and preferred stock, then these will be serviced at a different cost. The company’s accounting team then calculates the weighted average cost of capital that represents the cost of capital for the entire company.

Also read: How to Calculate Percentage Increase in Excel

In the example covered so far, the weights were specified. However, there may be cases, where the weights are not directly available, and you need to calculate the weights first and then calculate the weighted average.

Suppose you are selling three different types of products as mentioned below:

You can calculate the weighted average price per product by using the SUMPRODUCT function. Here is the formula you can use:

=SUMPRODUCT(B2:B4,C2:C4)/SUM(B2:B4)

Dividing the SUMPRODUCT result with the SUM of quantities makes sure that the weights (in this case, quantities) add up to 100%.

While the SUMPRODUCT function is the best way to calculate the weighted average in Excel, you can also use the SUM function.

To calculate the weighted average using the SUM function, you need to multiply each element, with its assigned importance in percentage.

Using the same dataset:

Here the formula that will give you the right result:

=SUM(B2*C2,B3*C3,B4*C4,B5*C5,B6*C6,B7*C7,B8*C8)

This method is alright to use when you have a couple of items. But when you have many items and weights, this method could be cumbersome and error-prone. There is shorter and better way of doing this using the SUM function.

Continuing with the same data set, here is the short formula that will give you the weighted average using the SUM function:

=SUM(B2:B8*C2:C8)

The trick while using this formula is to use Control + Shift + Enter, instead of just using Enter. Since SUM function can not handle arrays, you need to use Control + Shift + Enter.

When you hit Control + Shift + Enter, you would see curly brackets appear automatically at the beginning and the end of the formula (see the formula bar in the above image).

Again, make sure the weights add up to 100%. If it does not, you need to divide the result by the sum of the weights (as shown below, taking the product example):

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Calculating Profit Or Loss Using Python

In this article, we will learn a Python Program to calculate Profit Or Loss.

The following are the different methods to accomplish this task −

Using If Conditional Statements

Using the abs() function.

What are the selling price, cost price, and Profit and Loss?

The price a consumer pays to purchase a product or a commodity is known as the selling price. It is a price that is higher than the cost price and also includes a portion of the profit.

Cost price is the cost at which the seller buys the product or the commodity. He follows that by adding a portion of gain or profits.

The amount gained from selling an item for more than its cost price is known as the profit.

Profit = Selling Price – Cost Price.

Loss is the amount lost by selling an item for less than its cost price.

Loss = Cost Price - Selling Price Method 1: Using If Conditional Statements

Algorithm (Steps)

Following are the Algorithms/steps to be followed to perform the desired task. −

Create a function to calculate Profit that accepts the cost price(cp) and selling price(sp) as arguments.

Use the mathematical formula sp – cp to calculate profit and create a variable to store it.

Return the above-calculated profit using the return keyword.

Create another function to calculate Loss that accepts the cost price(cp) and selling price(sp) as arguments.

Use the mathematical formula cp – sp to calculate loss and create a variable to store it.

Return the above-calculated loss using the return keyword.

Create two separate variables to store the input cost price and selling price.

Use the if conditional statement and ‘==’ operator to check whether the input selling price is equal to the cost price.

Print Neither profit nor Loss if the condition is true.

Use the elif conditional statement to check whether the selling price is greater than the cost price.

Print profit if the condition is true by calling calculateProfit function by passing cost price and selling price as arguments to get the profit value.

Else print Loss by calling calculateLoss function by passing cost price and selling price as arguments to it to get the loss value.

Example

The following program calculates the profit or loss using the if conditional statements −

# creating a function to calculate Profit that # accepts the cost price(cp) and selling price(sp) as arguments def calculateProfit(cp, sp): # formula for calculating profit resultProfit = (sp - cp) # returning the resulting profit return resultProfit # creating a function to calculate Loss that # accepts the cost price(cp) and selling price(sp) as arguments def calculateLoss(cp, sp): # formula for calculating loss resultLoss = (cp - sp) # returning the resultant loss. return resultLoss # input cost price cost_price = 500 # input selling price selling_price = 1000 # checking whether the selling price is equal to the cost price if selling_price == cost_price: # printing Neither profit nor loss if the condition is true print("Neither profit nor Loss") # checking whether the selling price is greater than the cost price # Calling calculateProfit function by passing cost price and selling price # as arguments and printing profit if the condition is true print("The Profit is", calculateProfit(cost_price, selling_price)) else: # Else calling calculateLoss function by passing cost price and # selling price as arguments and printing Loss print("The Loss is", calculateLoss(cost_price, selling_price)) Output

On execution, the above program will generate the following output −

The Profit is 500 Method 2: Using the abs() function Algorithm (Steps)

Following are the Algorithms/steps to be followed to perform the desired task. −

Create a function to calculate the difference between the selling price and cost price that accepts the cost price(cp) and selling price(sp) as arguments.

Use the abs() function to calculate the difference between the selling price and the cost price.

Return the difference between the selling price and the cost price.

Create two separate variables to store the input cost price and selling price.

Print the profit/loss like the previous method.

Example

The following program calculates the profit or loss using the abs() function −

# creating a function to calculate the difference between sp and cp that # accepts the cost price(cp) and selling price(sp) as arguments def calculateDifference(cp, sp): # calculating the difference between the selling price and the cost price difference = abs(sp - cp) # returning the absolute difference of selling and cost price return difference # input cost price cost_price = 500 # input selling price selling_price = 1000 # checking whether the selling price is equal to the cost price if selling_price == cost_price: # printing Neither profit nor Loss if the condition is true print("Neither profit nor Loss") # checking whether the selling price is greater than the cost price # printing profit if the condition is true, by calling calculateDifference # function by passing cost price and selling price as arguments print("The Profit is", calculateDifference(cost_price,selling_price)) # Else this is the case of loss else: # Else printing Loss if the condition is true by calling calculateDifference # function by passing cost price and selling price as arguments to it print("The Loss is", calculateDifference(cost_price,selling_price)) Output

On execution, the above program will generate the following output −

The Loss is 200 Conclusion

In this article, we learned what selling and cost prices are as well as how to create a Python program to determine profit or loss when selling and cost prices are given. As an alternative to using two different functions, we learned how to calculate the absolute difference between selling and cost prices using the abs() function.

Calculate Average Per Customer Transaction Using Dax In Power Bi

What I want to demonstrate in this tutorial is how we can calculate average sales, profits, or transactions per certain dimension inside of DAX in Power BI. You may watch the full video of this tutorial at the bottom of this blog.

In this particular example we’re going to look at it from a customer’s perspective. We’re going to try and analyze what the average sales are we make per transaction per customer?

This is going to enable us to understand who our best customers are, but also who are our customers that come in and buy a substantial amount.

From here we can ultimately understand what the margins are we’re extracting per transaction from our customers. Are they good in some regions compared to other regions? Are they good for some products compared to other products?

We are going to look at the average amount of products purchased per transaction. Then, I’m also going to show you how to derive even more so you can find even more interesting insights based on this initial one. We’re going to branch out into other things and I’m going to show you how to do it efficiently.

First, we will work out a value per transaction by jumping into the Sales table. We have an order ID column on the left side.

So every order ID equates to every transaction in this particular table. We need to find a way to evaluate every single one of these transactions and essentially average up the sales that we have made for every single transaction.

This is going to give us – depending on the context – the average per transaction. This could be from a regional perspective, a customer perspective, or a sales person perspective.

Some data tables have an Order ID, and then within that Order ID, you might have a number of different transactions. Depending on what average calculation you want to do you’ll probably want to input that column into the calculations. First, let’s calculate average sales.

Let’s create a measure and call this one Average Sales per Transaction. I’m going to use the AVERAGEX function because this will allow us to do these averages by iterating through something. Within AVERAGEX, I’m going to use VALUES and put in my Order ID. Then, I want to average up the Total Sales for every single order.

Once I drag this measure with my Customer Name context, this is the table I come up with:

This will show us on average how much each person makes per transaction every time they come into a store.

This is already a pretty good insight by itself, but we can make this look better using conditional formatting and data bars.

We don’t have to stop here; we can we can go even further. We have some other core calculations like Total Profits and Total Costs. With these calculations, I can find out the average profits per transaction. All I have to do is copy and paste the measure I just used into a new measure, and instead of Total Sales, I’m going to put in Total Profits.

With this new measure, we can work out what our profits are out of every single transaction and then average those up.

I can just drag the new measure into my table to come up with new insights. For example, our customer Chris Fuller has greater profitability per transaction then Philip Foster, who actually made greater sales. This is a pretty good insight, right?

We can also deal with average margins per transaction. We won’t be needing to reference anything from the table because we can actually just use measures within measures.

All we have to do is divide Average Profits per Transaction by Average Sales per Transaction, then input 0 as an alternative result. We also have to make sure that it’s formatted correctly.

Once I drag this into the table, you’ll see now why we have higher profits for Chris Fuller than for Philip Foster’s. Chris has higher margins compared to Philip.

This is a very interesting insight for this particular customer, as well as the rest of our customers.

What’s cool is that we can use this technique on any context. Currently, we’re just using a filter from our Customers table. If you think about it, we can use filters from any of these tables in our data model and see how things change.

We can also take a look at our Average Margins per Transaction over time. I’ll just quickly whip this up using Month & Year and Average Margins per Transaction as values, then put them out into a graph.

We can see how the average margins change through time and see the seasonality.

Overall, it is a lot easier now to see our high margin versus low margin customers. For instance, customer Juan Collins has a 40% Margin. This one sticks out clear as day.

We can also save filter to see which are the most profitable customers per transaction; this could possibly indicate the salesperson assigned to these parts is very good.

We can look further into the insight using DAX in Power BI and determine our best customers on a regional basis. Is there something happening regionally? We can switch from a map visual to a filled map.

We can drill in and have a more in-depth look. In my example, New Hampshire has low margins while every other region is pretty evenly distributed.

You can also select customers from the table, and determine from this a subset of customers where the breakdown was.

We can extract so many great insights when we calculate averages using DAX in Power BI. They also add a lot of value to what we might do within a business from a marketing perspective and allocating sales resources perspective.

You obviously want to be focusing on the clients who purchase the most at the highest margins. And through this type of analysis, you can align your resources to where you feel you’re going to optimize the best results.

In this tutorial, we worked on one thing and then branched out into lots of other things. You can do many calculations and techniques using DAX in Power BI, and find some really good insights.

This type of analytical work is so powerful. If you want to review more examples just like it, check out the Business Analytics Series module at Enterprise DNA Online. This module contains contents around solving real-world business problems using the best practices of DAX in Power BI.

All the best,

Sam

How To Apply A 2D Average Pooling In Pytorch?

We can apply a 2D Average Pooling over an input image composed of several input planes using the torch.nn.AvgPool2d() module. The input to a 2D Average Pooling layer must be of size [N,C,H,W] where N is the batch size, C is the number of channels, H and W are the height and width of the input image.

The main feature of an Average Pooling operation is the filter or kernel size and stride. This module supports TensorFloat32.

Syntax torch.nn.AvgPool2d(kernel_size) Parameters

kernel_size – The size of the window to take an average over.

Along with this parameter, there are some optional parameters also such as stride, padding, dilation, etc. We will take examples of these parameters in detail in the following Python examples.

Steps

You could use the following steps to apply a 2D Average Pooling −

Import the required library. In all the following examples, the required Python library is torch. Make sure you have already installed it. To apply 2D Average Pooling on images we need torchvision and Pillow as well.

import torch import torchvision from PIL import Image

Define input tensor or read the input image. If an input is an image, then we first convert it into a torch tensor.

Define kernel_size, stride and other parameters.

Next define an Average Pooling pooling by passing the above defined parameters to torch.nn.AvgPool2d().

pooling = nn.AvgPool2d(kernel_size)

Apply the Average Pooling pooling on the input tensor or image tensor.

output = pooling(input)

Next print the tensor after Average Pooling. If the input was an image tensor, then to visualize the image, we first convert the tensor obtained # Import the required libraries import torch import chúng tôi as nn

”’input of size = [N,C,H, W] or [C,H, W] ”’ input = torch.empty(3, 4, 4).random_(256) print(“Input Size:”,input.size())

# pool of square window of size=3, stride=1 pooling1 = nn.AvgPool2d(3, stride=1)

# Perform Average Pooling output = pooling1(input) print(“Output Size:”,output.size())

# pool of non-square window pooling2 = nn.AvgPool2d((2, 1), stride=(1, 2))

# Perform average Pool output = pooling2(input) print(“Output Size:”,output.size())

Output Input Tensor: tensor([[[194., 159., 7., 90.], [128., 173., 28., 211.], [252., 123., 248., 147.], [144., 107., 28., 17.]], [[122., 140., 117., 52.], [252., 118., 216., 101.], [ 88., 121., 25., 210.], [223., 162., 39., 125.]], [[168., 113., 53., 246.], [199., 23., 54., 74.], [ 95., 246., 245., 48.], [222., 175., 144., 127.]]]) Input Size: torch.Size([3, 4, 4]) Output Tensor: tensor([[[145.7778, 131.7778], [136.7778, 120.2222]], [[133.2222, 122.2222], [138.2222, 124.1111]], [[132.8889, 122.4444], [155.8889, 126.2222]]]) Output Size: torch.Size([3, 2, 2]) Output Tensor: tensor([[[161.0000, 17.5000], [190.0000, 138.0000], [198.0000, 138.0000]], [[187.0000, 166.5000], [170.0000, 120.5000], [155.5000, 32.0000]], [[183.5000, 53.5000], [147.0000, 149.5000], [158.5000, 194.5000]]]) Output Size: torch.Size([3, 3, 2]) Example 2

In the following Python example, we perform 2D Avg Pooling on an input image. To apply 2D Avg Pooling, we first convert the image to a torch tensor and after Avg Pooling again convert it to a PIL image for visualization

# Python 3 program to perform 2D Average Pooling on image # Import the required libraries import torch import torchvision from PIL import Image import torchvision.transforms as T import torch.nn.functional as F # read the input image img = Image.open('panda.jpg') # convert the image to torch tensor img = T.ToTensor()(img) print("Original size of Image:", img.size()) #Size([3, 466, 700]) # unsqueeze to make 4D img = img.unsqueeze(0) # define avg pool with square window of size=4, stride=1 pool = torch.nn.AvgPool2d(4, 1) img = pool(img) img = img.squeeze(0) print("Size after AvgPool:",img.size()) img = T.ToPILImage()(img) img.show() Output Original size of Image: torch.Size([3, 466, 700]) initialization of the weights and biases.

Return On Average Assets Formula

Return on Average Assets Formula

The Formula of Return on Average Assets can be calculated by dividing Company’s Annual Net Income to its Average Total Assets.

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Average Total Assets is calculated using the below formula

In every case, it is not mandatory to have average total assets. In most of the cases return on asset is also used. It is given below.

Generally, banks and other financial institutions utilize a return on average assets to evaluate their performance. It is calculated at period ends, like quarters, years, etc. The return on average assets does not show all the lows and highs. It is, rather, just an average of the period under consideration.

Explanation of Return on Average Assets

A return on average assets ratio is shown as a percentage of all average assets. The return on Average assets ratio often called the return on total assets, is a profitability ratio that calculates the net income produced by total assets during a given period by comparing the net income to the average total assets of the company. In simple words, the ROA or return on assets ratio calculates how efficiently a firm or management of a company can manage its assets to produce profits during a given period. In short, the return on Average assets ratio measures how profitable a firm’s assets are.

Examples of Return on Average Assets Formula

Suppose ABC Company earns $ 4,000 as annual net income while average assets are $40,000.

You can download this Return on Average Assets Template here – Return on Average Assets Template

Return on Average Asset can be calculated as:

Return on Average Asset = (Net income)/(Total Average Asset)

Return on Average Asset = ($ 4,000)/($ 40,000)

Return on Average Asset = 10 %

This indicates that the ABC Company has $0.1 of net income for every dollar of invested assets. Return on assets should be compared with peers in the same industry as a return on assets has stark differences in different industries. So it is wise to compare the return on assets with its peer for a good comparison.

Assume that XYZ company earns a total annual Net Income of $ 100,000 while beginning total assets are $600,000 and ending total assets are $500,000 to calculate Return on Average Assets,

Average Total Assets=(Beginning Total Assets+ Ending Total Assets)/2

The average total assets = ($ 600,000 + $ 500,000) / 2

The average total assets = $ 550,000

According to the Return on Average Assets formula, we get

Return on Average Assets = Net Income / Average Total Assets

Return on Average Assets = $ 100,000 / $ 550,000

Return on Average Assets = 18.18 %

Company XYZ earns 18.18 % on its total assets.

Suppose company ABC & XYZ operates in the same industry. If we compare company ABC & company XYZ, company XYZ utilizes its assets more efficiently than company ABC. As company XYZ has more earnings on assets than company ABC. As an investment analyst, investing in a company that utilizes its assets efficiently makes more sense.

Significance and Use of Return on Average Assets Formula

The return on Average Assets formula is an indicator that helps to assess how profitable a company is relative to its total annual assets. Return on Average Assets is a type of Return on investments, so it helps to indicate a company’s performance. Return on Average Assets gives an idea to an analyst, investors, and managers of how efficiently management uses its assets to improve earnings. It generates the profitability of a business in relation to its total annual assets.

Return on Average Assets shows how efficiently management or a company can convert the money used to purchase total assets into profits or net income. It makes sense that a higher ratio is more favorable to the management and investors because it shows that the firm is more effectively operating its assets to produce greater amounts of net profit. For the management, the return on Average Assets ratio is also important because the ratio can tell a lot about the firm’s performance; and by comparing the ratio with similar companies under one industry, management should be able to understand how well the firm is doing.

Return on Average Assets Calculator

You can use the following Return on Average Assets Calculator

Annual Total Income Average Total Assets Return on Average Assets Formula Return on Average Assets Formula = Annual Total Income =

Average Total Assets

= 0

Return on Average Assets Formula in Excel (With Excel Template)

Here we will do the same example of the Return on Average Assets formula in Excel. It is very easy and simple. You need to provide the three inputs i.e. Net Income and Total Average Asset.

In the First Example, We calculate the Return on Average Assets using Formula

In the Second Example

first, we calculate the Average total assets.

Then, we calculate the Return on Average Assets using Formula

Return On Average Capital Employed

Definition of Return on Average Capital Employed

The term “return on average capital employed” refers to the performance metric that determines how well a company can leverage its capital structure to generate profit. To put it simply, this metric determines the dollar amount that a company is able to produce in net operating profit for each dollar of the capital (both equity and debt) utilized.

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The return on average capital employed is abbreviated as ROACE. This metric is the improved version of ROCE as it takes into account the opening and closing value of the capital employed. ROACE can be used to compare peer performance of a similar scale and with different capital structures as it compares the profitability relative to both equity and debt.

The formula for ROACE can be derived by diving the operating profit or earnings before interest and taxes (EBIT) by the difference between average total assets and average total current liabilities, which is then expressed in terms of percentage. Mathematically, it is represented as,

ROACE = EBIT / (Average Total Assets – Average Total Current Liabilities) * 100

The formula for ROACE can also be expressed as operating profit divided by the summation of average shareholder’s equity and average long term liabilities. Mathematically, it is represented as,

ROACE = EBIT / (Average Shareholder’s Equity + Average Long Term Liabilities) * 100

Examples of Return on Average Capital Employed (With Excel Template)

Let’s take an example to understand the calculation of Return on Average Capital Employed in a better manner.

You can download this Return on Average Capital Employed Excel Template here – Return on Average Capital Employed Excel Template

Example #1

Let us take the example of a company that is engaged in the manufacturing of mobile phone covers. During 2023, the company booked an operating profit of $22.5 million. Its total assets at the start and end of the year were $140 million and $165 million respectively, while its corresponding total current liabilities were $100 million and $120 million respectively. Based on the given information, calculate the ROACE of the company for the year.

Solution:

Average Total Assets is calculated using the formula given below

Average Total Assets = (Total Assets at the Start of the Year + Total Assets at the End of the Year)/2

Average Total Assets = ($140 million + $165 million) / 2

Average Total Assets = $152.5 million

Average Current Liabilities is calculated using the formula given below

Average Current Liabilities = (Total Current Liabilities at the Start of the Year + Total Current Liabilities at the End of the Year) / 2

Average Current Liabilities = ($100 million + $120 million) / 2

Average Current Liabilities = $110.0 million

Return on Average Capital Employed is calculated using the formula given below

ROACE = $22.5 million / ($152.5 million – $110.0 million)

ROACE = 52.94%

Therefore, the company’s ROACE for the year 2023 stood healthy at 52.94%.

Example #2

Let us take the example of Walmart Inc.’s annual report for the year 2023 to illustrate the computation of ROACE. During 2023, its operating income was $20.44 billion, its total assets at the start and at the end of the year was $198.83 billion and $204.52 billion respectively and its total current liabilities at the start and at the end of the year was $66.93 billion and $78.52 billion respectively. Calculate Walmart Inc.’s ROACE for the year 2023.

Solution:

Average Total Assets is calculated using the formula given below

Average Total Assets = (Total Assets at the Start 2023 + Total Assets at the End of 2023) / 2

Average Total Assets = ($198.83 billion + $204.52 billion) / 2

Average Total Assets = $201.68 billion

Average Current Liabilities is calculated using the formula given below

Average Current Liabilities = (Total Current Liabilities at the Start of 2023 + Total Current Liabilities at the End of 2023) / 2

Average Current Liabilities = ($66.93 billion + $78.52 billion) / 2

Average Current Liabilities = $72.73 billion

Return on Average Capital Employed is calculated using the formula given below

ROACE = EBIT / (Average Total Assets – Average Total Current Liabilities) *100

ROACE = $20.44 billion / ($201.68 billion – $72.73 billion)

ROACE = 15.85%

Therefore, Walmart Inc.’s ROACE stood at 15.85% during the year 2023.

Source: Walmart Annual Reports (Investor Relations)

Advantages of Return on Average Capital Employed

It measures the return on both equity and debt.

It is used to compare the profitability of companies with different capital structures.

Limitations of Return on Average Capital Employed

One of the limitations of return on average capital employed is that it can be manipulated through accounting forgery, such as the classification of long-term liabilities as current liabilities.

Conclusion

So, ROACE is an important financial metric that helps in the evaluation of the overall profitability of a company. However, it is also risks of accounting manipulations and so it is essential that you are cautious while analyzing companies based on ROACE.