Athabasca University



Slide 1: Lecture 1 - Du Pont IdentityWelcome to Lecture 1 on the Du Pont Identity.Slide 2: Financial ratiosWhat is a Du Pont Identity? Basically, Du Pont Identity is a way for us to look at the different components of the financial ratios: Return on Assets (ROA) and Return on Equity (ROE). The Return on Assets (ROA) is calculated as:ROA = Net Income / Total Assets = NI / AThe Return on Equity (ROE) is calculated as:ROE = Net Income / Total Equity = NI / EIt is good to always memorize these two formulas for ROA and ROE, because they are the basic formulas from which all the Du Pont Identities are derived. And so, if you know these two basic formulas by heart, you will be able to derive the Du Pont Identities yourself, without having to memorize all the identities.Slide 3: Du Pont Identity (DPI) for ROALet’s start with the Du Pont Identities for the ROA. How do we get from the basic formula of ROA = NI/A to a more involved formula/identity for the ROA. We do this by formula manipulation. Taking the basic formula:ROA = NI/AWe multiply and divide the right-hand-side of the formula by S, giving usROA = (NI/A) x (S/S)(Note that S/S = 1, which means that we are multiplying the right-hand-side by 1, which gives us the original formula of NI/A.) Switching the denominators on the right-hand-side of the new formula, we getROA = (NI/S) x (S/A)This is the first identity for the ROA formula. Looking closely at this new formula, we see that (NI/S) is what we normally call the profit margin, and (S/A) is what we normally call the asset-use efficiency ratio (AUE). Therefore, ROA can also be written as:ROA = Profit margin x Asset-use efficiencyThat’s it! With a few strokes of the pen, we now have two identities for the ROA formula.Slide 4: Numerical ExampleLet’s work through a simple numerical example of calculating ROA using one of the identities. Given the following data:NI/S = 0.1S/A = 2Calculate the ROA.ROA = (NI/S) x (S/A) Plugging the numbers for NI/S and S/A into the ROA identity, we getROA = 0.1 x 2 = 0.2 This gives us a Return on Assets of 20%.Slide 5: What is S/A?Remember when we were looking at the first identity for ROA, we haveROA = (NI/S) x (S/A)What does the second term on the right-hand-side of the formula, S/A, represent? Again, S/A is what is referred to as Asset-use efficiency. What it literally means is the dollar amount of sales generated per dollar amount invested in assets. Slide 6: DPI for ROENext, let’s move on to the Du Pont Identities for ROE. How do we get from the very basic ROE formula of ROE = NI/E to a more involved form of the formula such as this one:ROE = (NI/S) x (S/A) x (1 + D/E)?Again, this is done by formula manipulation. First, multiply and divide the right-hand-side of the basic ROE formula by S:ROE = (NI/E) x (S/S)Switch the denominators in this new formula, and we getROE = (NI/S) x (S/E)This is the first identity for the ROE formula. Going one step further, multiply and divide the right-hand-side of this first identity by A:ROE = (NI/S) x (S/E) x (A/A)Switch the denominators between (S/E) and (A/A), and we getROE = (NI/S) x (S/A) x (A/E)This is the second identity for the ROE formula.An aside: Why do we call these formulas identities? This is because we should get the same answer for ROE when we calculate it using any of these formulas/identities.Looking closely at the second identity for ROE, we see that NI/S is what is commonly referred to as the profit margin, S/A represents asset-use efficiency, and A/E (Total Assets / Total Equity) is what is commonly referred to as the equity multiplier. Therefore, we now have the third identity for ROE:ROE = Profit margin x Asset-use efficiency x Equity multiplier.Again, with just a few strokes of the pen, we have derived three different identities for the ROE formula.Slide 7: Variables in ROELet’s take a closer look at the second ROE identitiy.ROE = (NI/S) x (S/A) x (A/E)What are the variables we will need in order to calculate the ROE using this formula? We will need the values of Net Income (NI), Sales (S), Total Assets (A), and Total Equity (E). Slide 8: One step furtherWe could stop at three identities for the ROE and be satisfied, but we finance people are adventurous. So, we go on. We know from the accounting balance sheet identity that the value of the total assets (A) must equal the sum of the values of total debt (D) and total equity (E):A = D + ESo, given this balance sheet identity, we can rewrite the equity multiplier, A/E, as follows:A/E = (D + E)/E = (D/E) + (E/E) = (D/E) + 1 = 1 + D/ESlide 9: One step further (cont.)Going one step further with the second ROE identity ofROE = (NI/S) x (S/A) x (A/E),we plug A/E = 1 + D/E into this ROE formula to getROE = (NI/S) x (S/A) x (1 + D/E)This is the fourth identity for ROE. Now, looking closer at this new identity, we see that NI/S is profit margin, S/A is asset-use efficiency, and D/E is the familiar debt-equity ratio. Therefore, we have our fifth identity for ROE:ROE = Profit margin x Asset-use efficiency x (1 + Debt-equity ratio)Slide 10: Summary – ROA DPITo sum up, we have found three Du Pont Identities for calculating ROA:ROA = NI/A (basic formula)ROA = (NI/S) x (S/A)ROA = Profit margin x Asset-use efficiencySlide 11: Summary – ROE DPIAs well, we have found seven Du Pont Identities for calculating ROE:ROE = NI/E (basic formula)ROE = (NI/S) x (S/E)ROE = (NI/S) x (S/A) x (A/E)ROE = Profit margin x Asset-use efficiency x Equity multiplierROE = ROA x (A/E) ROE = (NI/S) x (S/A) x (1 + D/E)ROE = Profit margin x Asset-use efficiency x (1 + Debt-equity ratio)Note: The fifth identity is derived by plugging ROA = (NI/S) x (S/A) into the third identity: ROE = (NI/S) x (S/A) x (A/E).Slide 12: What does it mean?What does all this mean? It means that, when we calculate ROA and ROE, we get to see the different components that contribute to the return on assets and return on equity. For example, with the ROE formula:ROE = Profit margin x Asset-use efficiency x (1 + Debt-equity ratio)we see that the return on equity is affected by three variables: the profit margin, the asset-use efficiency, and the debt-equity ratio. If a company wants to increase its return on equity, it will have to increase profit margin, improve asset-use efficiency, or increase debt-equity ratio. In fact, given that the debt-equity ratio is calculated as the value of total debt divided by the value of total equity, to increase ROE, the company will have to increase debt or reduce equity.So, the model says, to increase ROE, we must do one or more of the followings:Increase profit marginIncrease asset-use efficiencyIncrease debtDecrease equitySlide 13: Numerical Example - ROANow, without further ado, let’s work through a numerical example. Let’s start with one of calculating the ROA.Given the following information, find the return on Income = $1,000Total Assets = $10,000Sales = $15,000Writing down the information given in the symbols we have used in this lecture, we haveNI = $1000A = $10000S = $15000The ROA identity we could use is:ROA = (NI/S) x (S/A) Plugging the numbers for NI, A, and S into this formula, we getROA = (1000/15000) x (15000/10000) = 0.1 = 10%The return on asset is therefore 10%.Slide 14: Numerical Example - ROENow let’s move on to a numerical example for ROE. Given the following information, calculate the ROE.Profit margin = 8%Sales = $20,000Total Assets = $50,000Total Equity = $30,000Net Income = $1,600Rewriting the information given in the symbols we have used in this lecture, we haveNI/S = 0.08S = 20000A = 50000E = 30000NI = 1600Which ROE identity should we use? The decision is usually based on what information we have on hand. In this case, because we have the numbers for A and E, the easiest ROE formula to use is:ROE = (NI/S) x (S/A) x (A/E)Plugging the numbers we know into this formula, we getROE = 0.08 x (20000/50000) x (50000/30000) = 0.05333333This gives us a return on equity of approximately 5.33%.Slide 15: Numerical Example - ROE calculation (cont.)Left blank – unused as the space was not needed during the lecture.Slide 16: Numerical Example – missing variableLet’s move on to the next numerical example. Here, we are given an ROE and a bunch of information, and we are then asked a slightly different question: What is the value of one of the missing variables? Given the following information, calculate the value of total debt, D.Profit margin = 8%Total equity = $30,000Net Income = $5,000ROE = 16.67%Asset-use efficiency = 0.5Writing down the information in the symbols we have been using, we haveNI/S = 0.08E = $30000NI = $5000ROE = 0.1667S/A = 0.5Where do we start? First, we know the value for ROE, and we also know how ROE is calculated. Which ROE identity to use though? The ROE formula that is often used is:ROE = (NI/S) x (S/A) x (A/E)We know that ROE = 0.1667, NI/S = 0.08, S/A = 0.5, and E = $30000. With these numbers, we can figure out the value for A, the total assets. Once we obtained A, we can calculate the value for debt, D, by using the balance sheet identity: A = D + E. So, without further ado, let’s do this. Plugging the numbers for all the known variables into the ROE formula, we get0.1667 = 0.08 x 0.5 x (A / 30000)Dividing both sides by 0.08 x 0.5 = 0.04, we get0.1667 / 0.04 = A / 30000Multiplying both sides by 30000, we get(0.1667 / 0.04) x 30000 = AThis gives us A = 125000.Slide 17: Numerical Example - Missing variable (cont.)We now haveA = $125000E = $30000We also have the balance sheet identity:A = D + EPlugging the numbers for A and E into this formula, we get125000 = D + 30000Subtracting 30000 from both sides, we getD = 125000 – 30000 = 95000Therefore, the total debt value is $95,000.Slide 18: Numerical Example - Missing variable (cont.)Left blank – unused as the space was not needed during the lecture.Slide 19: Practice, Practice, PracticePractice is the secret to passing any finance course. In this practice problem, you are given a whole bunch of information. Net Income = $5,000Sales = $62,500Total Assets = $125,000Total Equity = $30,000Total Debt = $95,000ROE = 16.67%The exercise is to pretend that you do not have the value for one of the variables. For example, let’s say that we forgot what the value of Net Income is. Can you find it using the ROE Du Pont Identity? The answer is, as always, yes we can! Try this exercise on your own, and see if you can derive each of the numbers by using the other numbers given and the ROE Du Pont Identities.Here ends the lecture on the Du Pont Identities. Thank you for attending. ................
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