Levering and Unlevering Beta - Mechanics of the Model

It occurs to me that I didn't really describe the formula for levering and unlevering Beta and why it works. Let's have a closer look:

First think of any given industry. There are some major assumptions required to get levering and unlevering beta to work. For instance, a dollar invested in an industry will give a constant return proportional to it's risk (beta). This is one of the fundamental assumptions in CAPM.

Levering beta is the idea that I can amplify the result of a deal by using debt. Let's look at an example:

I'm in an industry that has a beta of 1.2

ERP is 5%

RFR is 4%

ke = RFR + beta * ERP = 4% + (1.2) 5%

= 10%

So if I invest a dollar, I can expect to get a return of 10%.

However, I can use leverage (borrow money) so that I want to experience an amplified result:

I'll invest 1 dollar, but allow borrow another dollar to invest with. So I have two dollars in play, but only one of those is mine. My return? Well, assuming you can borrow at RFR (a huge assumption), you'll gain another 10% on that additional dollar, but have to pay 4% (RFR) so you'll gain another 6% on top of your original 10% for a total of 16%. You've doubled your systematic risk by having two dollars in play. Let's check with CAPM:

Beta = 2*1.2 (twice as much exposure)

ke = RFR + beta * ERP

= 4% + 2.4 * (5%) = 16%

This makes sense. For every additional dollar you borrow at RFR and invest in the industry, you will make the spread between their returns (or the beta * ERP).

So if you borrow D, dollars (D in this case stands for Debt), versus E dollars of your own money (Equity), and because CAPM is a linear function, you can expect:

• Your exposure will be based off of D+E dollars (total capital in the game - systematic risk, exposure)
• But off a base of E dollars invested (the money you have invested yourself, or Equity)

So if an industry has a beta of Ba, and you use leverage D on your initial investment E, you can expect your new beta of Be, to be:

Be = Ba * (E+D)/E

Note, however, that (E+D)/E = 1 + (D/E)

Look familiar? It's the levering formula:

Be = Ba * (1 + D/E)

But there is still one piece missing. The (1-t) portion of the formula is to simply account for the fact that debt that you borrow provides a tax shield, so the final version of the formula replaces D with (1-t)*D to get:

Be = Ba * (1 + (1-t)*D/E)

Hope this decomposition helps. I noticed this relationship is very prevalent in financial calculations as Anita McGahan clarified in one of her lectures on Starbucks in first year when talking about Operating Strategy versus Financial Strategy in the Dupont Decomposition. This was something I had also wondered about previously.

Accounting – The Story Behind the Numbers

It seems like the major topic for this week has been related to working capital. In our financial management course, however, there was a great example case where simply knowing the numbers is not enough.

Simplified Case Info (expressed in thousands):

Revenue = 17805
AR = 6000
Average Day’s Receivable in the industry = 59 days

Analysis:

Company’s Average Day’s Receivable = 123 days

Proposed financing solution: Collect on AR to reduce Day’s Receivable to industry average of 59 days.

If Days Receivable = 59 days, implied new AR is 2878. The change in AR would be 6000 – 2878 or 3122.

So looking at this *mathematical* solution, it seems as if the company can get a free 3 million dollars just by tightening its AR, right? Well as it turns out probably not. The reason?

Most companies define default as non-payment of debts of 90 days or more. Previously, we’ve talked about how debts decay in value as they are outstanding for longer and longer (probability of collection and bad debt expense). If you look at this number, essentially what it is saying that the many of your accounts are in default with an average age of 120 days!

Sometimes you can’t just assume you can make operational changes to reflect a reality that you want. The truth of the matter is that those funds are probably lost. The firm probably won’t collect those accounts and will incur a significant bad debt expense.

In reading more of the case, it also mentioned that the company had a “no returns” policy with its distribution channel partners. Looking at this number not only meant that they probably weren’t going to collect, but that their distributors were telling them that they didn’t want to do business with them any more (affecting their potential future revenue growth). Not only will they not be able to pull 3 million dollars out of working capital, there are some critical red flags appearing about their ability to continue as an ongoing concern.

Unlevered Beta

A quick recap:
Beta of a company is determined by a statistical regression of returns of a given security against returns of the market.

As a result, "beta" usually refers to a company's equity beta or observable beta. Using CAPM, we can calculate the expected cost of equity (ke) using:

ke = RFR + beta * ERP

Where ERP is Equity Risk Premium

So what is unlevered beta and why is it important?

Well, recall from CAPM that you can change a company's capital structure in order to add leverage to increase beta and thereby increase expected return of equity (with a company's cost of equity being the investors return on equity).

Unlevered beta tells you how much a company's industry is expected to return, regardless of the leverage employed by looking at the systematic risk of an industry regardless of the financing decisions. Theoretically, the unlevered beta should be constant across companies in an industry.

Why is this important? Here is one example. You are trying to determine the cost of equity (so you can determine WACC for DCF) of a new company in an industry. However, because it is a new company, there is no previous history in terms of what they can be expected to return relative to the market. So it is impossible to calculate its equity beta. So what can you do?

You can look at a variety of other companies in the space, unlever all their betas to get asset betas and average them (as they should be theoretically the same, but will most likely differ slightly) and then relever it to the new company’s capital structure to approximate its expected equity beta. Armed with its equity beta, you can calculate its cost of equity using CAPM.

While this is how it would work in theory, there are some major problems with this model, the most obvious being:

• How do you do “comps”? How do you define “a variety of companies in the space”, especially if few or none of the companies are exactly the same?
• CAPM has its own issues which make it a less than perfect model
• As a new company, they will probably not behave in the same manner as more mature companies in the space.

Here is an example:

There are four companies with different betas and leverage levels. By unlevering all the equity betas, you can have various approximations for what the asset beta should be. An average of all four gives you a decent approximation for the beta of the industry.


Now assume we have a new company in this space that will have a D/E of 50% at the same tax rate. We can use the leverage formula to calculate what the beta equity should be:

Equity Beta = Asset Beta * (1+(1-Tax)*D/E)

In this case, the equity beta would be approximately 1.3, which makes sense as it has a leverage between B and C and therefore should have an equity beta in between.

Excess Cash isn't always just from cash

Putting together the last few posts (House analogy for EV, FCFF and NOWC and N[O]WC as a source of funds), let's look at an example of how they are all interrelated.

Target Company:
Total Assets = $100M
AR = $10M
Inventory = $15M
AP = $10M

Industry Average
Total Assets* = $100M
AR = $5M
Inventory = $10M
AP = $20M

* Total Assets for each company are deliberately the same to make percentage calculations convenient.

Let's also assume that looking only at the company's operations, you are planning on bringing the balance sheet accounts closer in line with industry average. Implicitly, you are improving the company's operations (reducing days receivable, days on hand and increasing days payables).

Therefore:
Change in AR = -5M (cash inflow)
Change in Inventory = -5M (cash inflow)
Change in AP = +10M (cash inflow)

Total cash inflow from Operating Working Capital = +5M +5M + 10M = +20M

This change in accounts reflects a type of excess which can be converted into "excess cash". These changes would be manifested in operations through:

• Collecting on debts sooner, reducing credit terms
• Selling out of inventory without replenishment (reducing inventory size and implicit days on hand)
• Taking longer to pay our suppliers, using more supplier credit
• Essentially, running "leaner"

This excess cash would be captured in a financial DCF model as a change in net operating working capital in the first year of operation and built into the company's EV calculation.

Enterprise Value - House Analogy with Excess Cash

Another common question that comes up is related to enterprise value, particularly as it relates to excess cash. Recall that enterprise value is the value of the entire company and should be capital structure neutral.

EV = Equity + Debt - Excess Cash
or
EV = DCF Value + Excess Cash

The initial reaction is: "Wait, how can that be?" How is it that in one formula excess cash detracts from EV whereas in the other it increases? Does that make sense? In explaining, I find that a house analogy is helpful for understanding how to calculate EV.

Scenario 1:
Imagine Steve ownes a house worth $100k. Over the years, Steve has paid down his mortgage to $50k. Therefore, Steve's house's capital structure is $50k debt and $50k equity.

Dave is interested in buying Steve's house. For simplicity, let's say the house hasn't appreciated in value and is still worth $100k. Dave doesn't care what Steve's mortgage is, how much he's paid down etc. After all, that is Steve's capital structure. Dave is a new home buyer and is starting with a $20k downpayment and $80k mortgage.

The main point is that it doesn't matter who is buying the house (over simplified assumption), the house is worth $100k. It is an attempt to understand an unbiased (unlevered) way of looking at value of the company.

Scenario 2:

Let's assume a few changes:

• The $100k price of the house includes $10k in cash which is sitting on the floor of a room
• The house is being rented out as an investment property for $4k per year forever and the appropriate discount rate is 5%

Using the following formula:

EV = Equity + Debt - Cash = $100k - $10k = $90k

Does this make sense? Dave buys the house with $80k of debt, $20k of equity for a total price of $100k. However, immediately upon buying the house, Dave takes the $10k sitting on the floor and pays down his mortgage. Effectively, Dave has only paid $90k for the house.

Using the alternate formula (using a perpetuity formula for DCF):

EV = DCF Value + Excess Cash = $4,000 / 5% + $10k = $80k + $10k = $90k

That is to say, forgetting the cash, the house is worth $80k only from the income it generates. However, because the cash sitting on the floor is not integral to operating the house, it can be taken out of the house without affecting the income stream.

While it isn't an entire conicidence that the end numbers are the same (I've deliberately selected convenient numbers), it should hopefully demonstrate how excess cash in one formula decreases EV whereas in another in increases EV.

Free Cash Flow to Firm and Net Change in [OPERATING] Working Capital

A few of my classmates have been asking me a very common question so I thought I would post the answer. Particularly because I think it is a fantastic question and is something I’ve wrestled with for sometime.

In Corporate Finance, Financial Management and Mergers & Acquisitions, one of the most important metrics of a company’s performance is it’s free cash flow. Or more specifically, it’s free cash flow to firm (aka. Unlevered free cash flow). This is the cash flow metric that is used to value the entire enterprise. It’s defined as:

FCFF = EBIT (1 – tax) + DA – NWC – Capex

Where:
EBIT is Earnings Before Interest and Tax (otherwise known as operating income)
DA is Depreciation and Amortization (which is actually a place holder for all non-cash expenses, but DA is the largest and most common one)
NWC – Change in net working capital (*NOTE* This is the tricky part that people are asking about)
Capex – Capital Expenditures

So while this formula is not new to most, what I want to focus on is NWC. If you have read my post on the difference between OPERATING working capital and working capital will know what I’m getting at.

First, before we even get to that, I want to emphasize a lesson taught in Anita McGahan’s first year strategy course relating to Dupont analysis (one of my favourite frameworks). Dupont analysis looks at Return on Equity and Anita made a fantastic point about how to look at the formula:

ROE = NI / Equity

ROE = (NI / A) * (A / E)

ROE = ROA * FLA

Where:
ROA is return on assets (Operational Strategy)
FLA is financial leverage (Financial Strategy)

In a discounted cash flow, a company’s value is calculated as it’s enterprise cash flows discounted at the appropriate enterprise cost of capital (it’s weighted average cost of capital).

In other words: In the summation formula, the numerator is operating (FCFF) and the denominator is financial (WACC).

This is another good way to think about the difference between OPERATING working capital (OWC) and working capital (WC) as I explained previously.

While the commonly accepted formula for FCFF is as explained above, anyone who has done a proper financial model is quick to learn that it isn’t change in net working capital which is important, but rather change in OPERATING net working capital (excluding financing items such as cash and short term debt).

FCFF = EBIT (1 – tax) + DA – NOWC - Capex

But the next logical question is what is the difference between something like short term debt (a quantifiable liability) and accounts payable (also a quantifiable liability which is equally a debt of sorts – a debt to a supplier). The answer? Interest.

The reason why something would be considered OPERATING working capital (or particularly an operating current liability) versus a normal working capital (or current liability) is that a financial current liability *bears interest* whereas an operating liability does not.

This raises the next interesting question: How do you treat pension liabilities? As you may recall, I mentioned previously how the CFA treat’s pensions as if they are interest bearing liabilities (or specifically, debts of the company owed to it’s workers which is expected to grow at the company’s cost of debt). This is a perfect example of a judgment call. Some of the top equity research analysts will consider pensions to be part of operating a business (not included in enterprise value as a financial consideration) whereas others will consider pensions to be a type of financing (don’t take my word for it, check out the research reports of companies with sizable pensions and see how different analysts treat different companies). Some will consider current pension obligations as debt (as it has to be financed to be paid out) whereas others will treat the entire long and short term obligation as debt.

Study Tour Applications - Latin America Study Tour Series

Applications for study tour have been submitted for January tours and students are getting emails for interviews over the next period. It seems like there are a lot of keen students who are interested in participating and it looks like there will be some strong candidates representing Rotman in the Middle East and China study tours.

Anticipating the release of applications for the May international study tours for Latin America, I've cleaned up my Latin America Study Tour Series and posted a link in the navigation bar for your reading pleasure.