DuPont Analysis

While making my way through the Chartered Financial Analysis (CFA) level 1 curriculum in the Financial Reporting and Analysis (FRA) section, I encountered one of the most important tools in financial statement analysis--the DuPont Analysis. I’d like to take a moment to explain not only the process for completing this analysis but also breakdown the potential usefulness of it.

We will begin the conversation with the ratio known as return on equity or ROE. This is a measure of the total return based on the amount of book equity the firm has in its capital structure. Return is simply net income as this is the allocation of earnings that equity investors have title to. The simplest form of the DuPont analysis breaks the ROE calculation into two portions, the first is return on assets (ROA) and the second is the financial leverage ratio. ROA can be viewed as a measure of how efficiently the firm is utilizing the assets they have while the financial leverage ratio (sometime called the equity multiplier) is the amount of debt in proportion to the amount of equity a firm has within this capital structure.

 This shows us that changes in ROE can be linked to either a change in the return on assets or the amount of leverage used within the business. While this is a base line equation, we can continue to break this down further. We can next break the ROA into two separate factors, net profit margin and asset turnover.

In doing this breakout, we are not able to determine that changes in ROE can be attributed to changes in net margins, asset efficiency (asset turnovers) and use of leverage.

The last step to breaking out the DuPont equation is taking a look at net profit margin. We can view net profit margin as a function thee key areas, the first of which is the earnings before interest and taxes (EBIT) margin, sometime referred to as the operation margin. This is the income the firm earned from normal operations without consideration of capital structure. The second factor is the interest burden which takes earnings before taxes (after interest) and compares it to EBIT. This will indicate how much of the firm’s earnings are being used to service the debt within the capital structure. The last factor is the tax burden which shows us the firm’s tax rate. 

This allows us to analyses changes in the net profit margin of the firm based on operating changes (EBIT margin) changes in debt service costs (interest burden) and tax rates. Finally, we can combine all these calculations to end with the five step DuPont analysis of ROE.

Apply simply cross multiplication and this equation breaks down to net income over equity, or ROE. As analyst, we are able to look at ROE of a firm and determine what factors have helped the firm achieve their given ROE. More importantly, we can analyses time-series data and determine what is causing changes in ROE form one period to another. For example, if a firm has a 10% increase in ROE year over year and you apply the DuPont analysis to determine that this change is caused by an increase in the use of leverage it will be much less favorable than an identical firm which had the same 10% increase due to improved efficiency or margins (asset turnover or EBIT margin). 

Control Premiums

In valuation, there are times that some practitioners believe it is appropriate to apply the so-called “control premium” to their valuation process. While I have mixed thoughts on the use of this control premium, I would like to explain the concept along with my thoughts on when and when not to apply it. I will also shed some light as to the reasons for my mixed thoughts on the use of control premiums in practice.

To begin this discussion, I’d like to talk about what a control premium theoretically is. To help better explain this think about yourself as an investor in Microsoft; as an individual shareholder it is likely that you have little to no influence over the direction of the company. This is because of the sheer size of the firm and your likely minority position. In the event that you had the ability to control the firm you would theoretically be able to make certain decisions that are in your best interest, as an equity owner, and thus be willing to pay a premium. While this is a very simplified explanation, I would like to take a closer look at why one might be willing to pay this premium.

Take for example a firm such as Jos A Bank, a men’s clothing retailer who has a balance sheet loaded with cash and virtually no debt. Corporate Finance 101 teaches us that the cost of debt is almost always cheaper than the cost of equity. The second part of this lesson is that adding debt to the capital structure, to the extent that the additional risk of bankruptcy is offset by the cheaper capital and tax benefits associated with debt, will lower the cost of capital for the firm. Taking this lesson and applying it to the Jos A Bank situation, a controlling owner could increase the use of leverage within the firm and therefore lower the cost of capital and increase the number of profitable projects the firm can pursue or the net present value of their current projects. In essence, having this controlling interest allows for an increase in the value of the firm and thus the purchaser would theoretically be willing to pay a premium from the current minority stake price.

In valuation, there are three primary models used in practice to determine your final valuation: discounted cash flow, comparable companies and precedent transactions. While I do not want to get into the details in this post, I would like to discuss each of the three and why or why not you would potentially apply a control premium.

When looking at a discounted cash flow valuation model, one is forecasting future economic benefits to an ownership stake and then discounting these benefits to today’s dollars using an appropriate rate that reflects the risk associated with the cash flows. Now if one believed that they would be able to achieve more economic benefit from the firm by gaining a controlling interest, and intended to gain this control, they would be able to forecast the additional economic benefit into the model. This would then be discounted and the final value would already factor in the added value for control, thus a control premium would not be appropriate for the discounted cash flow model.

Comparable companies model takes a set of firms which are similar to the firm being valued and analyses key multiples. For example, if firm A is comparable to firm B and firm A is currently trading for 7.5 times EBITDA, then it might be safe to say that firm B is also worth 7.5 times EBITDA. There are many details to this valuation process that I will not cover in this post, but the key take away is that you are comparing the current trading price of comparable firms. Back to the original discussion about Microsoft, most shareholders are minority shareholders. Thus, the currently trading price would generally represent a minority interest and thus one who intended to purchase a controlling interest would then apply the control premium to the comparable companies model.

Lastly, precedent transactions takes a look at historical deals done in the open markets in which a buyer purchases a firm similar to the firm you are valuing. For example, firm C was purchased for 8.0 times EBIT, and firm D is similar to firm C. Thus, firm D might be worth 8.0 times EBIT to a purchaser. Now the key here is that this is based on a purchase price; implying that control is achieved. Therefore, the price paid would already have a control premium factored in and thus a control premium should not be added to the precedent transactions model.

To summarize thus far, it would theoretically be appropriate to apply a control premium to the comparable companies model only, but not to the discounted cash flow or present transactions model. Now enters the question as to what premium to add if you do intend to apply this. In practice many will rely on the data that is provided by Mergerstat for control premium. This can range from about 20-30% on average and is based on the premiums paid on historic transactions over a selected time horizon. This is where I find myself torn on the control premium.

I’d like to reflect on what a control premium is; recall that is the additional price one would pay for control due to the added value that comes from control of the firm. Also recall that if we used intrinsic valuation methods such as a discounted cash flow, we would factor this added value into the cash flows. One could value the company as it stands using the discounted cash flow model then value the same firm again but this time applying the added future income from the ability to control the firm. The differences in these two valuations would theoretically be the value of control, or the control premium. Mergerstat data on the other hand is simply historical premiums paid, but fully independent of the current firm and potential control benefits. I believe that it would be more advantageous to use the intrinsic valuation method to determine the value of control rather than simply applying the historical average. Also, remember that Mergerstat data is a statistic that has its own standard error which can be quite large and make confidence intervals wide.

This is not to say that the other side of the argument is not strong as well. First, conducting two discounted cash flow valuations with any level of accuracy will likely be very time consuming. Secondly, these models are based completely on forecasted data, which has a level of uncertainty associated with it. Lastly, it is very common in practice to apply the control premium based on Mergerstat data, thus it is hard to ignore widely-accepted practices.

In conclusion, I have used the terms “theoretical” often in this post to stress that I do not have a clear view on the proper way to handle this in practice. However, I do believe that this helps explain the basis for both sides of the argument and allows one to make their own decision on the use of control premiums in valuation. 

Beta

Anyone who has ever dealt with valuation or modern corporate finance has probably encountered the use of beta. In modern finance beta is the key relative risk measure used in the Capital Asset Pricing Model (CAPM) to determine the risk premium demanded by equity investors. I’d like to take a minute to talk about what exactly beta is measuring along with methods by which to determine the beta used in CAPM.

Let’s begin with what exactly beta is meant to measure. Beta is a measure of systemic risk of a security versus the market as a whole. It is generally viewed as the covariance between the returns of the security and the returns of the aggregate market divided by the variance of returns of the aggregate market. Or rewritten as the correlation between the returns of the stock and the aggregate market multiplied by the standard deviation of the stock returns dividend by the standard deviation of aggregate market returns. 

Most commonly these calculations are done using a simple regression with the returns of the aggregate market being the independent variable and the returns of the stock being the dependent variable. The regression result will provide the coefficient of the x variable which will represent beta. In essence, if we apply the simple linear equation (Y = mX + B) the “m” is beta which show how much of a movement can be expected in the given stock based on the movement of the aggregate market. It is common to use the returns of the S&P 500 to represent the market and between a 3-5 year time horizons for return data.

While much more could be said regarding the technical side of regressing to find beta, I would like to look at one simple fact. In any regression the coefficient of determination (R²) indicates how much of the data can be explained by the regression model. Put simply, it is a measure of accuracy within the regression model. In almost any regression model to find beta, the R² will be very low (0.30 or less), this leads us to question the accuracy of using this method to calculate such an important variable when calculating the cost of equity capital.

Before I get into an alternative method for beta, I would like to shift our focus back to what beta measures for a moment. Beta is the measure of systemic risk of a firm, and part of this risk is both operating risk and financial risk. Operating risk can be defined as the risk inherent in a firm that is fully financed with equity, essentially the risk of the business if it had not required debt payments. The firm’s operating risk is impacted by the amount of fixed versus variable costs. The other part of this risk is financial risk, which is the risk as firm’s equity holder bear due to the use of leverage and thus required debt payments. Now in calculating a regression beta we will have a result of levered beta, which is the beta that includes both operating risk and financial risk. Let’s now jump to an alternative method for calculating beta. 

An alternative that is commonly used is to first identify the firm’s industry and collected data on a group of comparable companies. Then take these firms and run a simple regression to calculate beta. The betas collected, as described above, are levered betas. Since our firm, and each firm in the group of comparable companies will most likely have different uses of leverage, we must “unlever” these betas. The process of unlevering beta is essentially factoring in both the amount of debt capital used as compared to equity capital along with the benefits provided by the tax shield offered from interest payments. Levered beta can also be calculated from unlevered beta. The calculations for both are described below.

To continue with the alternative beta calculation, you first must take the levered betas found through regression and unlevered each of these based on each firms respective debt to equity capital structure and corporate marginal tax rate. Then a mean or median of these unlevered betas can be used to determine and estimate for the industry beta; the choice of mean of median will be a judgment based on variance of these betas. Once the industry’s unlevered beta is found, the beta can be relevered using our given firm’s debt to equity structure and marginal tax rate to determine the beta used within the CAPM.

Now you may ask “what is the benefit of completing this process versus using a simple regression?” Well as discussed above, simple regressions have very low predictability value and can lead to misleading betas. By using this alternative, you are collecting date on multiple firms within the industry which can eliminate some of the risk of having an outlier. Is it perfect? No, but I do believe that it can provide a better estimate of the true systemic risk of a firm. 

Hope you found this interesting. 

Financial Statement Flow

Having a strong understanding of the “flow” through financial statements is essential in the valuation process. One must create forecasts and make assumptions that will impact pro-forma financials and should be able to identify how these will flow through the three primary financials. I thought it would be worthwhile to create a post covering the basic flow between each of the primary financials. As with many of my posts, this will have an emphasis on valuation uses and therefore will include certain details that are of particular concern to valuation modeling. Enjoy.

To help guide our conversations, I have created a simple graphic that outlines the most important flows between statements.  I will reference these flows and their colors through the post to help the reader gain a better understanding.

 

Due to the web of flows that is created here, I will start at the top of the income statement and work my way through these in what will hopefully be a coherent manner. Let’s get started.

The income statement starts with revenue less Cost of Goods Sold (COGS) to get gross income and then Sales, General and administrative (SG&A) along with Depreciation and Amortization (D&A) expenses are subtracted to get earnings before interest and tax (EBIT). In some financials D&A in consolidated within SG&A so be on the lookout for this. D&A (purple line) has two primary flows, first of which is to the balance sheet into the Accumulated Depreciation account. The amount of D&A expense will be added to the accumulated depreciation account to calculate Net PP&E. Remember too that only the “D” portion will flow into accumulated depreciation account, not the amortization. If a firm has no intangible assets to amortize, this is easy; however if they consolidate this you might have to dig into the footnotes to determine what amount is actually attributable to depreciation. The second flow for D&A is into the Statement of Cash Flows as an add-back to operating cash flow. Since D&A is a non-cash expense, it must be added back to net income.

Now let’s look at Interest Expense and Income (orange and brown lines). Interest Expense/Income can be found as a line item on historical financials, thus this commentary only applies to forecasting future financials. The general rule of thumb is to calculate interest expense as the average debt—(beginning balance+endining balance)/2—multiplied by the interest expense for the given debt. The same calculation is used for interest income but based on the average cash balance. You can also see the dark orange flow line from payments and issuance of Long-Term Debt (LTD), this will impact the balance and thus the interest expense.

Net Income (NI) is arguable the most important flow to understand. NI is represented by the light-red line and flows into two primary areas. First, NI is used as the starting basis for the indirect cash flow statement creation. The second flow is one that is most often forgotten, NI flows into the Retained Earnings on the balance sheet. Jumping over to the statement of cash flows, we can also see the flow between dividends under the cash flow from financing section to retained earnings (dark red line). Dividends paid will reduce the retained earnings balance while net income will increase it.

Let’s now turn out attention to some balance sheet accounts that have yet to be addressed. The Accounts Receivable (A/R), Inventory, and Accounts Payable (A/P) are all considered working capital (W/C). There may be other items such as accruals, however this is a simplified example. The change in these account balance (light blue) will flow into the statement of cash flows under the cash flow from operations section. I used the term “delta in W/C” to indicate that the change in these could either be an increase in cash flow or a decrease in cash flow. If there is an increase in net working capital (current assets less current liabilities) then this will be a use of cash and therefore a subtraction from net income; the opposite applies if it was a decrease in net working capital. We must also remember that in this instance the net working capital calculation does not include cash.

Next let’s look at the Property, Plant and Equipment (PP&E) account on the balance sheet. We can see the flow between the investing section of the statement of cash flows and the PP&E account on the balance sheet (yellow). If a firm has CapEx it will be an outflow of cash on the statement of cash flow but will be capitalized as an asset and added to PP&E on the balance sheet. Conversely, if a firm sells a piece of equipment it will be a cash inflow on the statement of cash flows while it will reduce the PP&E account on the balance sheet (both the PP&E and accumulated depreciation will be reduced as they relate to the asset being sold).

Lastly, we take a look at the bottom of the statement of cash flows to see that the ending cash balance (green line) will flow back to the balance sheet for the respective period ending. The beginning cash balance comes from the cash balance on the opening balance sheet (not shown in the image).

While this is a very simplified explanation of the flow between the statements, I do hope it puts its all in prospective and helps you better understand the process. Again, I did not list every single flow, only those most important to creating pro-forma forecasted financials. If you have questions or need clarifications, feel free to ask. 

DCF Model #1

The Discounted Cash Flow model is a staple in any valuation tool kit. While these tend to vary from model to model depending on the user’s specific needs, there are a few common aspects. A DCF generally includes as assumptions section that is used to model the forecasted pro-forma financials. It is also common to include a sensitivity analysis for certain key metrics; these are Weighted Average Cost of Capital (WACC) and Discount Rate for most DCF models. Despite difference between models, at heart all DCFs are intended to estimate intrinsic value of an asset based on expected future cash flows discounted to present value.

To help me gain a better understanding of DCF models and to improve my Excel skills, I started with a blank spread sheet and went to work. I used sample DCF models that I have seen elsewhere for some of the formatting ideas, however I did fully create every aspect of this model. 

At this time, I am simply going to post the model for review. However, I do plan to have future posts that explain specific parts of this model. As a note, I used rough inputs for Microsoft to help better demonstrate the functionality of the model; however, there was no rigor put into the assumptions, they are for illustrative purposes only. 

DCF Model #1

Simple Deferred Tax Asset & Liability Explanation

If you have ever taken a look at the balance sheet of almost any publicly traded firm, you will probably notice either a deferred tax asset or a deferred tax liability. While these are relatively simple to understand, I wanted to take a few moments to talk about how these are created and how they will impact not only the GAAP financials, but also the valuation process.

To begin with, what is a deferred tax account? In the U.S. all public companies are required to follow U.S. Generally Accepted Accounting Principles (GAAP) for financial reporting. However, for tax purposes, they follow a slightly different system of accounting. The difference in treatment for certain items can leave a firm actually having different amount of taxable income for accounting books purposes than for tax. Some of these differences are permeate other are simply temporary. Let’s discuss the differences and see some examples.

Permanent Differences

Certain expense are never taxable or are never tax deductible under U.S. Tax law. Take for example the investment in a municipal bond; the coupon stream for muni bonds is never taxable at the Federal level. If a firm is invested in a muni bond, they will show a higher book income versus a taxable income. Now let’s look at a federal fine for pollution. While the firm will use this as an expense for accounting purposes (hopefully extraordinary) they are not allowed to write it off on their tax income and therefore will have a higher tax income than book income. Since issues like these are never reversed, the income tax expense associated with these is factored in on the tax expense for the respective period.

Temporary Differences

While permanent differences are relatively simply and straight forward, temporary differences can be much trickier. Take for example the differences in depreciation methods. Most firms will choose to depreciate an asset under the straight line method, however under U.S. Tax law a system of depreciation called MACRS is used. This is essentially and accelerated deprecation system. This will generally cause the firm to have higher book taxable income in the early years and lower book taxable income in the later years versus the tax accounting income.

If a firm has a book taxable income of $1,000 but a tax accounting taxable income of $800 with a 40% tax rate what will they expense and what will they pay? For accounting purposes they will have income tax expense of $400; however, they will actually only have a tax liability of $320. Now since the difference is temporary and will reverse at a later time, they must account for this. To do this they will create an account-either an asset or a liability. From a valuation stand point, we must remember that the cash flows will be effected due to the differences between actual tax expense and tax liabilities paid in cash.

Since I think some of this can be a bit hard to explain in writing, I have decided to create a short screen cast. I hope this helps make this issue a bit clear.

I do understand that this is not an extensive explanation of deferred tax assets or liability, but I do hope it lays the foundation for a better understanding. 

Excel Model: Defered Taxes & Valuation Example

Leases and Their Role in Valuation

A lease is a contractual agreement in which one party (the lessor) agrees to allow another party (the lessee) use an asset for a stated period of time. In return, the lessee agrees to make fixed cash payments to the lessor. Since the title does not transfer to the lessee, this is not considered a sale and thus the asset is not recorded on the books of the lessee, rather it stays on the books of the lessor. While this makes sense, there is a problem. Leases are allowing a firm to obtain an asset in return for a future commitment of payments, this is essentially adding an asset to the firm and a corresponding liability. When a firm accounts for this transaction as a lease rather than a sale, it is essentially able to avoid putting the liability on their balance sheet; this is often referred to as “off-balance sheet financing”. This can lead to investors underestimating the liabilities a firm has and therefore poses a risk to the investing community.

Enter capital leases. Under U.S. GAAP, two forms of leasing exist. The first is an operating lease and the second being a capital lease; with the former reflecting the above discussion. Capital leases on the other hand are required to be accounting for in a different manner in which the asset and corresponding liability are reflected on the lessee’s balance sheet. A lease will be classified as a capital lease if it satisfies any one of the following requirements.

1. The life of the lease exceeds 75% of the economic life of the asset.
   (Lease a truck for 9 years that has a useful life of 10 years)
     
2. The present value all future lease commitments is greater than 90% of the current fair market value of the asset.
   (The PV of lease payments is $1,000, when the FMV of the asset is $850)  
   
   
3. The title of the asset transfers from the lessor to the lessee at the conclusion of the lease.
   (After 10 years of leasing a computer, the title of ownership transfers to the lessee) 
         
4. There is bargain purchase price option included in the lease.
   (At the end of a machinery lease, the lessee can purchase the asset for $100, despite the FMV at that time being significantly higher)

In essence, a lease that meets any of the criteria above--while not meeting the legal requirements of a sale--is an economic sale. Since this is the case, the asset being leased is removed from the books of the lessor and placed on the books of the lessee. In addition, the present value of all lease payments are considered a liability on the lessee’s balance sheet and an asset on the lessor’s. This does have a valid reasoning since these type of leases are essentially a form of capital financing and thus should be included in the liabilities section of the balance sheet. Rather than the lessee considering the payment to the lessor an expense, it is now an amortization of the liability with the difference between the payment and the amortized amount classified as interest expense (another indication of debt financing). In addition, the lessee can now depreciate the asset over its useful life.

While much more could be said about capital lease (a possible future topic), I believe from a valuation stand point it is relatively clear as to the treatment. Since they are already classified as assets and a corresponding liability, not too much more needs deep consideration. However, I do not feel the same for operating leases.

If a lease agreement does not meet any of the four criteria outlined above, it will be considered an operating lease. Under this treatment, the lessee does not record the asset nor the corresponding liability. The payments are simply considered lease expense. This is a preference for many firms, as it will give the appearance of a stronger balance sheet (lower debt); thus, it is common for firms to attempt to structure leases in a manner that will allow operating lease treatment under U.S. GAAP. One of the most common assets to be classified as operating leases, while taking on more of an appearance as capital financing, is retail real estate. Since the economic life can be very long for a retail location and the lessor generally has no interest in transferring title at the end of the lease, it is relatively easy to structure a deal in such a way that it will be classified as an operating lease.

With the above said, think about industries such appear retailers and restaurants. In these industries, many operating leases are created for the real estate being used in the ordinary course of business. While these leases are structured in such a way that they are treated as operating leases, they do constitute a large portion of the operating expenses and, in my opinion, represent a form of debt financing. I say this due to the fact that they allow the firm the use of an asset in return for a requirement of a fixed payment; sounds a whole lot like debt financing to me.  

From my perspective, it would be necessary to take the expected future payments of these leases (in many cases this figure can be found on the firm’s 10-K) and discount them to their present value and capitalize them, adding both an asset and liability to the pro-forma statements. The discount factor should be the firm’s pre-tax cost of debt for the firm (pre-tax since the payment being discounted is a pre-tax item). In addition, these payments should no longer be treated as lease expense, but as interest expense. The net effect of this process would be an increase to EBIT, EBITDA, and the weight of debt in the WACC calculation.

Since the EBIT, EBITDA and WACC all play a very important role in a DCF valuation, this process can be key to an accurate calculation in some cases. Is this always right? As with most valuation topics, there can be a long debate about how valid this theory is. However, I do believe that in certain industries that rely heavily on operating leases, not creating pro-forma financials with these operating leases capitalized will create an error in your final valuation.

As a last note, while I believe this process to be an accurate treatment for many operating leases, in cases where the operating leases do not represent a major portion of the firm’s expenses, I do not believe this process will yield a material difference the final valuation.