Discounted Cash Flow

You're looking at two companies, both of which produce identical total Free Cash Flows over a 5-year period. Company A generates 90% of its Free Cash Flow in the first year and 10% over the remaining 4 years. Company B generates the same amount of Free Cash Flow in each year. Which one has the higher net present value?

Company A, because money today is worth more than money tomorrow. All else being equal, generating higher cash flow earlier on will always boost a company's value in a DCF.

What's an appropriate growth rate to use when calculating the Terminal Value?

Normally you use the country's long-term GDP growth rate, the rate of inflation, or something similarly conservative. For companies in developed countries, a long-term growth rate over 5% would be quite aggressive since most developed economies are growing at less than 5% per year.

Why do you use 5 or 10 years for the "near future" DCF projections?

That's about as far as you can reasonably predict for most companies. Less than 5 years would be too short to be useful, and more than 10 years is too difficult to project for most companies.

Is there a valid reason why we might sometimes project 10 years or more anyway?

You might sometimes do this if it's a cyclical industry, such as chemicals, because it may be important to show the entire cycle from low to high.

What about Net Income from Equity Interests?

Again, this should have no net impact on Free Cash Flow because you add it at the bottom of the Income Statement and then subtract it out on the Cash Flow Statement.

Let's say that we want to analyze all these factors in a DCF. What are the most common sensitivity analyses to use?

Common sensitivities: • Revenue Growth vs. Terminal Multiple • EBITDA Margin vs. Terminal Multiple • Terminal Multiple vs. Discount Rate • Terminal Growth Rate vs. Discount Rate

Why do you add back non-cash charges when calculating Free Cash Flow?

For the same reason you add them back on the Cash Flow Statement: you want to reflect the fact that they save the company on taxes, but that the company does not actually pay the expense in cash.

How do Pension Obligations and the Pension Expense factor into a DCF?

If you're running an Unlevered DCF and you're counting Unfunded Pension Obligations as Debt, you should exclude pension-related expenses from Unfunded obligations on the Income Statement and Cash Flow Statement, for the same reason you exclude interest payments on Debt. For a Levered FCF you would do the opposite and leave in these expenses because they're a form of "interest expense."

Which tax rate should you use when calculating Free Cash Flow - statutory or effective?

Normally you use the effective tax rate because you want to capture what the company is actually paying out in taxes, not what it "should" be paying out according to standard federal and state rates. Sometimes you may adjust the tax rate if it's an unusual situation (e.g. the company is a sole proprietorship LLC and therefore income is taxed at the owner's personal income tax rate, but a large corporation is considering acquiring the company).

How do you know if a DCF is too dependent on future assumptions?

Some people claim that if over 50% of a company's value comes from the present value of the Terminal Value, the DCF is too dependent on future assumptions. The problem, though, is that in practice this is true in almost all DCFs. If the present value of the Terminal Value accounts for something like 80-90%+ of the company's value, then maybe you need to re-think your assumptions.

An alternative to the DCF is the Dividend Discount Model (DDM). How is it different in the general case (i.e. for a normal company, not a commercial bank or insurance firm?)

The setup is similar: you still project revenue and expenses over a 5-10 year period, and you still calculate Terminal Value. The difference is that you do not calculate Free Cash Flow - instead, you stop at Net Income and assume that Dividends Issued are a percentage of Net Income, and then you discount those Dividends back to their present value using the Cost of Equity. Then, you add those up and add them to the present value of the Terminal Value, which you might base on a P / E multiple instead. Finally, a Dividend Discount Model gets you the company's Equity Value rather than its Enterprise Value since you're using metrics that include interest income and expense.

How do you calculate the Terminal Value?

You can either apply an exit multiple to the company's Year 5 EBITDA, EBIT or Free Cash Flow (Multiples Method) or you can use the Gordon Growth method to estimate the value based on the company's growth rate into perpetuity. The formula for Terminal Value using the Gordon Growth method: Terminal Value = Final Year Free Cash Flow * (1 + Growth Rate) / (Discount Rate - Growth Rate). Note that with either method, you're estimating the same thing: the present value of the company's Free Cash Flows from the final year into infinity, as of the final year.

How does Net Income Attributable to Noncontrolling Interests factor into the Free Cash Flow calculation?

It doesn't - or more specifically, it has no net impact because you subtract it at the bottom of the Income Statement but then add it back on the Cash Flow Statement. Just be careful that you do both of those, or that you leave it out altogether - it would be incorrect to only subtract it or to only add it back, which might happen if you're not careful with the calculation.

What's the relationship between Debt and Cost of Equity?

More Debt means that the company is riskier, so the company's Levered Beta will be higher - so all else being equal, Cost of Equity would increase. Less Debt would decrease Cost of Equity.

Let's talk more about how you calculate Free Cash Flow. Is it always correct to leave out most of the Cash Flow from Investing section and all of the Cash Flow from Financing section?

Most of the time, yes, because all items other than CapEx are generally non- recurring, or at least do not recur in a predictable way. If you have advance knowledge that a company is going to sell or buy a certain amount of securities, issue a certain amount of stock, or repurchase a certain number of shares every year, then sure, you can factor those in. But it's extremely rare to do that.

Walk me through a DCF.

"A DCF values a company based on the Present Value of its Cash Flows and the Present Value of its Terminal Value. First, you project a company's financials using assumptions for revenue growth, margins, and the Change in Operating Assets and Liabilities; then you calculate Free Cash Flow for each year, which you discount and sum up to get to the Net Present Value. The Discount Rate is usually the Weighted Average Cost of Capital. Once you have the present value of the Free Cash Flows, you determine the company's Terminal Value, using either the Multiples Method or the Gordon Growth Method, and then you discount that back to its Net Present Value using the Discount Rate. Finally, you add the two together to determine the company's Enterprise Value."

The Free Cash Flows in the projection period of a DCF analysis increase by 10% each year. How much will the company's Enterprise Value increase by?

A percentage that's less than 10%, for two reasons: 1. Remember that we discount all those Free Cash Flows - so even if they increase by 10%, the present value change is less than 10%. 2. There's still the Terminal Value and the present value of that. That has not increased by 10%, so neither has the company's total value. You can't give an exact number for the increase without knowing the rest of the numbers (Discount Rate, Terminal Value, etc.) in the analysis.

Would you expect a manufacturing company or a technology company to have a higher Beta?

A technology company, because technology is viewed as a "riskier" industry than manufacturing.

What's the point of that "Changes in Operating Assets and Liabilities" section? What does it mean?

All it means is that if Assets are increasing by more than Liabilities, the company is spending cash and therefore reducing its cash flow, whereas if Liabilities are increasing by more than Assets, the company is increasing its cash flow. For example, if it places a huge order of Inventory, sells products, and records revenue, but hasn't receive the cash from customers yet, Inventory and Accounts Receivable both go up and represent uses of cash. Maybe some of its Liabilities, such as Accounts Payable and Deferred Revenue, also increase... but think about what happens: if the Assets increase by, say, $100, and the Liabilities only increase by $50, it's a net cash flow reduction of $50. So that is what this section is for - we need to take into account the cash changes from these operationally-linked Balance Sheet items.

Why would you not use a DCF for a bank or other financial institution?

Banks use Debt differently than other companies and do not use it to finance their operations - they use it to create their "products" - loans - instead. Also, interest is a critical part of banks' business models and changes in "Operating Assets and Liabilities" can be much larger than a bank's Net Income. Finally, CapEx does not correspond to re-investment in business for a bank, and is often negligible. For financial institutions (commercial banks and insurance firms), it's more common to use a Dividend Discount Model or Residual Income Model instead of a DCF. See the industry-specific sections of the guide for more.

Let's take a look at companies during the financial crisis (or really, just any type of crisis or economic downturn). Does WACC increase or decrease?

Break it down and think of the individual components of WACC: Cost of Equity, Cost of Debt, Cost of Preferred, and the percentages for each one. Then, think about the individual components of Cost of Equity: the Risk-Free Rate, the Equity Risk Premium, and Beta. • The Risk-Free Rate would decrease because governments worldwide would drop interest rates to encourage spending. • But then the Equity Risk Premium would also increase by a good amount as investors demand higher returns before investing in stocks. • Beta would also increase due to all the volatility. • So overall, we can guess that the Cost of Equity would increase because the latter two increases would likely more than make up for the decrease in the Risk-Free Rate. Now, for WACC: • The Cost of Debt and Cost of Preferred Stock would both increase as it would become more difficult for companies to borrow money. • The Debt to Equity ratio would likely increase because companies' share prices would fall, meaning that Equity Value decreased for most companies while Debt stayed the same... • So proportionally, yes, Debt and Preferred would likely make up a higher percentage of a company's capital structure. • But remember: the Cost of Debt and Cost of Preferred both increase, so that shift doesn't matter too much. • As a result, WACC almost certainly increases because almost all these variables push it up - the only one that pushes it down is the reduced Risk-Free Rate. There's a simpler way to think about it as well: all else being equal, did companies become more valuable or less valuable during the financial crisis? Less valuable - because the market discounted their future cash flows at higher rates. So WACC must have increased.

Let's say we do this and find that the Implied per Share Value is $10.00. The company's current share price is $5.00. What does this mean?

By itself, this does not mean much - you have to look at a range of outputs from a DCF rather than just a single number. So you would see what the Implied per Share Value is under different assumptions for the Discount Rate, revenue growth, margins, and so on. If you consistently find that it's greater than the company's current share price, then the analysis might tell you that the company is undervalued; it might be overvalued if it's consistently less than the current share price across all ranges.

How do you calculate Beta in the Cost of Equity calculation?

First off, note that you don't have to calculate anything - you could just take the company's Historical Beta, based on its stock performance vs. the relevant index. Normally, however, you come up with a new estimate for Beta based on the set of Public Comps you're using to value the company elsewhere in the Valuation, under the assumption that your estimate will be more accurate. You look up the Beta for each Comparable Company (usually on Bloomberg), un-lever each one, take the median of the set and then lever that median based on the company's capital structure. Then you use this Levered Beta in the Cost of Equity calculation. The formulas for un-levering and re-levering Beta are below (see the Rules section above for explanations). • Unlevered Beta = Levered Beta / (1 + ((1 - Tax Rate) x (Total Debt/Equity))) • Levered Beta = Unlevered Beta x (1 + ((1 - Tax Rate) x (Total Debt/Equity)))

Walk me through how you get from Revenue to Free Cash Flow in the projections.

First, confirm that they are asking for Unlevered Free Cash Flow (Free Cash Flow to Firm). If so: Subtract COGS and Operating Expenses from Revenue to get to Operating Income (EBIT) - or just use the EBIT margin you've assumed. Then, multiply by (1 - Tax Rate), add back Depreciation, Amortization, and other non-cash charges, and factor in the Change in Operating Assets and Liabilities. If Assets increase by more than Liabilities, this is a negative; otherwise it's positive. Finally, subtract Capital Expenditures to calculate Unlevered Free Cash Flow. Levered Free Cash Flow (FCFE) is similar, but you must also subtract the Net Interest Expense before multiplying by (1 - Tax Rate), and you must also subtract Mandatory Debt Repayments at the end.

When calculating FCF, you always take into account taxes. But when you calculate Terminal Value, you don't do that - isn't this inconsistent? How should you treat it?

Here's how to think about this one: • First off, if you use the Gordon Growth method to calculate Terminal Value, you are taking into account taxes because you're valuing the company's Free Cash Flow into perpetuity. • And if you're using the Terminal Multiple method, you're implicitly taking into account taxes because you're assuming that [Relevant Metric] * [Relevant Multiple] is the company's present value from that point onward, as of the final year. You're not assuming that the company is actually sold... just estimating what a buyer might pay for it, fully taking into account the value that the buyer would receive from its far-in-the- future, after-tax cash flows.

What about the treatment of other securities, like Mezzanine and other Debt variations?

If interest is tax-deductible, you count them as Debt in the Levered Beta calculation; otherwise they count as Equity, just like Preferred Stock. For WACC itself, you normally look at each type of Debt separately and assume that the "Cost" is the weighted average effective interest rate on that Debt.

Do you think a DCF would work well for an oil & gas company?

If it's an exploration & production (E&P)-focused company, generally a DCF will not work well because: • CapEx needs are enormous and will push FCF down to very low levels. • Commodity prices are cyclical and both revenue and FCF are difficult to project. For other types of energy companies - services-based companies or downstream companies that just refine and market oil and gas - a DCF might be more appropriate. For more on this topic and the alternative to a DCF that you use for oil & gas companies (called a NAV, or Net Asset Value, analysis), see the industry-specific guides.

What do you usually use for the Discount Rate?

In a Unlevered DCF analysis, you use WACC (Weighted Average Cost of Capital), which reflects the "Cost" of Equity, Debt, and Preferred Stock. In a Levered DCF analysis, you use Cost of Equity instead.

Why would you use the Gordon Growth Method rather than the Multiples Method to calculate the Terminal Value?

In banking, you almost always use the Multiples Method to calculate Terminal Value in a DCF. It's easier to get appropriate data for exit multiples since they are based on Comparable Companies - picking a long-term growth rate involves more guesswork. However, you might use Gordon Growth if you have no good Comparable Companies or if you believe that multiples will change significantly in the industry several years down the road. For example, if an industry is cyclical (e.g. chemicals or semiconductors) you might be better off using long-term growth rates rather than exit multiples.

Shouldn't you use a company's targeted capital structure rather than its current capital structure when calculating Beta and the Discount Rate?

In theory, yes. If you know that a company's capital structure is definitely changing in a certain, predictable way in the future, sure, go ahead and use that. In practice, you rarely know this information in advance, so it's not terribly practical to make this kind of assumption.

What about if we change revenue growth to 1%? Would that have a bigger impact, or would changing the Discount Rate to 9% have a bigger impact?

In this case the change in revenue growth is likely to have a bigger impact because you've changed it by 90% but you've only changed the Discount Rate by 10% - and that lower revenue growth will push down the present value of the Terminal Value (EBITDA and the FCF growth rate will both be lower) as well as the present value of the Free Cash Flows.

We're creating a DCF for a company that is planning to buy a factory for $100 in Cash in Year 4. Currently the net present value of this company, according to the DCF, is $200. How would we change the DCF to account for the factory purchase, and what would the new Enterprise Value be?

In this scenario, you would include additional CapEx spending of $100 in Year 4 of the DCF, which would reduce Free Cash Flow for that year by $100. The Enterprise Value, in turn, would decrease by the present value of $100 in Year 4. The math gets messy, but you would calculate the difference by dividing $100 by ((1 + Discount Rate)^4). Then you would subtract this amount from the Enterprise Value.

How do you treat Preferred Stock in the formulas above for Beta?

It should be counted as Equity there because Preferred Dividends are not tax- deductible, unlike interest paid on Debt.

Should Cost of Equity be higher for a $5 billion or $500 million Market Cap company?

It should be higher for the $500 million company, because all else being equal, smaller companies are expected to outperform large companies in the stock market (and are therefore "riskier").

So if you're using Levered FCF to value a company, is the company better off paying off Debt quickly or repaying the bare minimum required?

It's always better to pay the bare minimum. Think about the math for a second: interest rates on Debt rarely go above 10-15%... let's just assume that they're 10%, and that the company has $1,000 in Debt. Initially, it pays $100 in interest expense, and after taxes that's only $60 ($100 * (1 - 40%)). So Levered Free Cash Flow is reduced by $60 each year assuming no principal repayment. What happens if the company decides to repay $200 of that Debt each year? Levered Free Cash Flow is down by at least $200 each year, and the company still pays interest, albeit lower interest, until the end of the period. So the company is always better off, valuation-wise, waiting as long as possible to repay Debt.

Which method of calculating Terminal Value will produce a higher valuation?

It's impossible to say because it could go either way depending on the assumptions. There's no general rule here that always applies, or that even applies most of the time.

What if you have a stub period and you're using the mid-year convention - how does Terminal Value change then?

It's the same as what's described above - a stub period in the beginning does not make a difference.

Let's say that you use Levered Free Cash Flow rather than Unlevered Free Cash Flow in your DCF - what changes?

Levered Free Cash Flow gives you Equity Value rather than Enterprise Value, since the cash flow is only available to Equity Investors (Debt investors have already been "paid" with the interest payments and principal repayments).

Let's say that you use Unlevered Free Cash Flow in a DCF to calculate Enterprise Value. Then, you work backwards and use the company's Cash, Debt, and so on to calculate its implied Equity Value. Then you run the analysis using Levered Free Cash Flow instead and calculate Equity Value at the end. Will the implied Equity Value from both these analyses by the same?

No, most likely it will not be the same. In theory, you could pick equivalent assumptions and set up the analysis such that you calculate the same Equity Value at the end. In practice, it's difficult to pick "equivalent" assumptions, so these two methods will rarely, if ever, produce the same value. Think about it like this: when you use Unlevered FCF and move from Enterprise Value to Equity Value, you're always using the same numbers for Cash, Debt, etc. But in a Levered FCF analysis, the terms of the Debt will impact Free Cash Flow - so simply by assuming a different interest rate or repayment schedule, you'll alter the Equity Value. That's why it's so difficult to make "equivalent assumptions."

How do you factor in one-time events such as raising Debt, completing acquisitions, and so on in a DCF?

Normally you ignore these types of events because the whole point of calculating Free Cash Flow is to determine the company's cash flow on a recurring, predictable basis. If you know for a fact that something is going to occur in the near future, then you could factor that in - issuing Debt or Equity would change Cost of Equity and WACC (and the company's Free Cash Flow in a Levered DCF); completing an acquisition or buying an asset would reduce cash flow initially but perhaps boost it later on.

How do you select the appropriate exit multiple when calculating Terminal Value?

Normally you look at the Public Comps and pick the median of the set, or something close to it. You always show a range of exit multiples and what the Terminal Value looks like over that range rather than picking one specific number. So if the median EBITDA multiple of the set were 8x, you might show a range of values using multiples ranging from 6x to 10x.

What happens in the DCF if Free Cash Flow is negative? What if EBIT is negative?

Nothing "happens" because you can still run the analysis as-is. The company's value will certainly decrease if one or both of these turn negative, because the present value of Free Cash Flow will decrease as a result. The analysis is not necessarily invalid even if cash flow is negative - if it turns positive after a point, it could still work. If the company never turns cash flow-positive, then you may want to skip the DCF because it will always produce negative values.

If I'm working with a public company in a DCF, how do I move from Enterprise Value to its Implied per Share Value?

Once you get to Enterprise Value, ADD Cash and then SUBTRACT Debt, Preferred Stock, and Noncontrolling Interests (and any other debt-like items) to get to Equity Value. Then you divide by the company's share count (factoring in all dilutive securities) to determine the implied per-share price.

Should you ever factor in off-Balance Sheet Assets and Liabilities in a DCF?

Potentially, yes, especially if they have a big impact on Enterprise Value and Equity Value (i.e. if they're something that the acquirer would have to repay). But it's not terribly common to see them, partially because when off-Balance Sheet items are more important (for commercial banks with derivative books, for example), you don't even use a DCF.

How do you determine a firm's Optimal Capital Structure? What does it mean?

The "optimal capital structure" is the combination of Debt, Equity, and Preferred Stock that minimizes WACC. There is no real way to determine this formulaically because you'll always find that Debt should be 100% of a company's capital structure since it's always cheaper than Equity and Preferred Stock... but that can't happen because all companies need some amount of Equity as well. Plus, taking on additional Debt will impact the Cost of Equity and the Cost of Preferred, so effectively it is a multivariable equation with no solution. You may be able to approximate the optimal structure by looking at a few different scenarios and seeing how WACC changes - but there's no mathematical solution.

Let's say that we assume 10% revenue growth and a 10% Discount Rate in a DCF analysis. Which change will have a bigger impact: reducing revenue growth to 9%, or reducing the Discount Rate to 9%?

The Discount Rate change will almost certainly have a bigger impact because that affects everything from the present value of Free Cash Flows to the present value of Terminal Value - and even a 10% change makes a huge impact.

The "cost" of Debt and Preferred Stock make intuitive sense because the company is paying for interest or for the Preferred Dividends. But what about the Cost of Equity? What is the company really paying?

The company "pays" for Equity in two ways: 1. It may issue Dividends to its common shareholders, which is a cash expense. 2. It gives up stock appreciation rights to other investors, so in effect it's losing some of that upside - a non-cash but very real "cost." It is tricky to estimate the impact of both of those, which is why we usually use the Risk-Free Rate + Equity Risk Premium * Beta formula to estimate the company's expected return instead.

What's the basic concept behind a Discounted Cash Flow analysis?

The concept is that you value a company based on the present value of its Free Cash Flows far into the future. You divide the future into a "near future" period of 5-10 years and then calculate, project, discount, and add up those Free Cash Flows; and then there's also a "far future" period for everything beyond that, which you can't estimate as precisely, but which you can approximate using different approaches. You need to discount everything back to its present value because money today is worth more than money tomorrow.

What's the point of Free Cash Flow, anyway? What are you trying to do?

The idea is that you're replicating the Cash Flow Statement, but only including recurring, predictable items. And in the case of Unlevered Free Cash Flow, you also exclude the impact of Debt entirely. That's why everything in Cash Flow from Investing except for CapEx is excluded, and why the entire Cash Flow from Financing section is excluded (the only exception being Mandatory Debt Repayments for Levered FCF).

How does a DCF change if you're valuing a company in an emerging market?

The main difference is that you'll use a much higher Discount Rate, and you may not even necessarily link it to WACC or Cost of Equity... because there may not even be a good set of Public Comps in the country. You might also add in a premium for political risk and uncertainty, and you might severely reduce management's growth or profit expectations, especially if they have a reputation for being overly optimistic.

Walk me through a Dividend Discount Model (DDM) that you would use in place of a normal DCF for financial institutions.

The mechanics are the same as a DCF, but we use Dividends rather than Free Cash Flows: 1. Project the company's earnings, down to Earnings per Share (EPS). 2. Assume a Dividend Payout Ratio - what percentage of the EPS gets paid out to shareholders in the form of Dividends - based on what the firm has done historically and how much regulatory capital it needs. 3. Use this to calculate Dividends over the next 5-10 years. 4. Do a check to make sure that the firm still meets its required Tier 1 Capital Ratio and other capital ratios - if not, reduce Dividends. 5. Discount the Dividends in each year to their present value based on Cost of Equity - NOT WACC - and then sum these up. 6. Calculate Terminal Value based on P / BV and Book Value in the final year, and then discount this to its present value based on the Cost of Equity. 7. Sum the present value of the Terminal Value and the present values of the Dividends to calculate the company's net present value per share. The key difference compared to a DDM for normal companies is the presence of the capital ratios - you can't just blindly make Dividends per Share a percentage of EPS. See the industry-specific guides for more.

How does a DCF for a private company differ?

The mechanics are the same, but calculating Cost of Equity and WACC is problematic because you can't find the market value of Equity or Beta for private companies. So you might estimate WACC based on the median WACC of its Public Comps, and do the same for Cost of Equity if you're using that as the Discount Rate.

What's the flaw with basing the Terminal Multiple on what the Public Comps are trading at?

The median multiples may change greatly in the next 5-10 years, so they may no longer be accurate by the end of the period you're looking at. This is why you look at a wide range of multiples and run sensitivity analyses to see how these variables impact the valuation.

How can you check whether your assumptions for Terminal Value using the Multiples Method vs. the Gordon Growth Method make sense?

The most common method here is to calculate Terminal Value using one method, and then to see what the implied long-term growth rate or implied multiple via the other method would be. Example: You calculate Terminal Value with a long-term growth rate assumption of 4%. Terminal Value is $10,000. You divide that Terminal Value by the final year EBITDA and get an implied EBITDA multiple of 15x - but the Public Comps are only trading at a median of 8x EBITDA. In this case your assumption is almost certainly too aggressive and you should reduce that long- term growth rate.

Wait a minute, so are you saying that a company that does not take on Debt is at a disadvantage to one that does? How does that make sense?

The one without Debt is not "at a disadvantage" - but it won't be valued as highly because of the way the WACC formula works. Keep in mind that companies do not make big decisions based financial formulas. If a company has no reason to take on Debt (e.g. it is very profitable and does not need funds to expand its business), then it won't take on Debt.

Two companies are exactly the same, but one has Debt and one does not - which one will have the higher WACC?

The one without Debt will generally have a higher WACC because Debt is "less expensive" than Equity. Why? • Interest on Debt is tax-deductible - hence the (1 - Tax Rate) multiplication in the WACC formula. • Debt is senior to Equity in a company's capital structure - debt investors would be paid first in a liquidation or bankruptcy scenario. • Intuitively, interest rates on Debt are usually lower than Cost of Equity numbers (usually over 10%). As a result, the Cost of Debt portion of WACC will contribute less to the total figure than the Cost of Equity portion.

What discount period numbers would you use for the mid-year convention if you had a stub period - e.g. Q4 of Year 1 - in a DCF?

The rule is that you divide the stub discount period by 2, and then you simply subtract 0.5 from the "normal" discount periods for the future years. Example for a Q4 stub: [See diagram] What is the logic here? Think about it like this: let's take the example of the normal discount period for Year 1 being 1.75, representing 3 quarters and then a full year. Now, ask yourself when you receive that cash flow in Year 1. You're still receiving it midway through that first year... in other words, you still use 0.5 for the period. However, you also need to take into account the 3 / 4 of this partial year because 3 quarters pass between now and the start of Year 1. So you still have 0.75 there, and the mid-year discount period with the stub period is 0.75 + 0.5, or 1.25. That is why it's not 1.75 / 2, like you might expect: it's about when you receive that cash flow in Year, from the perspective of the start of Year 1 - and then you add the total amount of time that passes between now and the start of Year 1. There's no mid-year discount applied there because we don't receive any Year 1 cash in this first partial year.

Can Beta ever be negative? What would that mean?

Theoretically, yes, Beta could be negative for certain assets. If Beta is -1, for example, that would mean that the asset moves in the opposite direction from the market as a whole. If the market goes up by 10%, this asset would go down by 10%. In practice, you rarely, if ever, see negative Betas with real companies. Even something labeled as "counter-cyclical" still follows the market as a whole; a "counter-cyclical" company might have a Beta of 0.5 or 0.7, but not -1. ie. Gold

What's an alternate method for calculating Unlevered Free Cash Flow (Free Cash Flow to Firm)?

There are many "alternate methods" - here are a few common ones: • EBIT * (1 - Tax Rate) + Non-Cash Charges - Changes in Operating Assets and Liabilities - CapEx • Cash Flow from Operations + Tax-Adjusted Net Interest Expense - CapEx • Net Income + Tax-Adjusted Net Interest Expense + Non-Cash Charges - Changes in Operating Assets and Liabilities - CapEx The difference with these is that the tax numbers will be slightly different as a result of when you exclude the interest.

How can we calculate Cost of Equity WITHOUT using CAPM?

There is an alternate formula: • Cost of Equity = (Dividends per Share / Share Price) + Growth Rate of Dividends This is less common than the "standard" formula but sometimes you use it when the company is guaranteed to issue Dividends (e.g. Utilities companies) and/or information on Beta is unreliable.

Wait a second, would you still use Levered Beta with Unlevered Free Cash Flow? What's the deal with that?

They are different concepts (yes, the names get very confusing here). You always use Levered Beta with Cost of Equity because Debt makes the company's stock riskier for everyone involved. And you always use that same Cost of Equity number for both Levered Free Cash Flow, where Cost of Equity itself is the Discount Rate, and also for Unlevered Free Cash Flow, where Cost of Equity is a component of the Discount Rate (WACC).

What about WACC - will it be higher for a $5 billion or $500 million company?

This is a bit of a trick question because it depends on whether or not the capital structure is the same for both companies. If the capital structure is the same in terms of percentages and interest rates, then WACC should be higher for the $500 million company for the same reasons as mentioned above. If the capital structure is not the same, then it could go either way depending on how much debt/preferred stock each one has and what the interest rates are.

f a firm is losing money, do you still multiply the Cost of Debt by (1 - Tax Rate) in the WACC formula? How can a tax shield exist if they're not even paying taxes?

This is a good point, but in practice you will still multiply by (1 - Tax Rate) anyway. What matters is not whether the Debt is currently reducing the company's taxes, but whether there's potential for that to happen in the future.

As an approximation, do you think it's OK to use EBITDA - Changes in Operating Assets and Liabilities - CapEx to approximate Unlevered Free Cash Flow?

This is inaccurate because it excludes taxes completely. It would be better to use EBITDA - Taxes - Changes in Operating Assets and Liabilities - CapEx. If you need a very quick approximation, yes, this formula can work and it will get you closer than EBITDA by itself. But taxes are significant and should not be overlooked.

Cost of Equity tells us the return that an equity investor might expect for investing in a given company - but what about dividends? Shouldn't we factor dividend yield into the formula?

Trick question. Dividend yields are already factored into Beta, because Beta describes returns in excess of the market as a whole - and those returns include Dividends.

When you're calculating WACC, do you count Convertible Bonds as real Debt?

Trick question. If the Convertible Bonds are in-the-money then you do not count them as Debt, but instead assume that they contribute to dilution, so the company's Equity Value is higher. If they're out-of-the-money then you count them as Debt and use the interest rate on the Convertible Bonds for the Cost of Debt (and include them in Debt in the formula for Levered Beta).

A company has a high Debt balance and is paying off a significant portion of its Debt principal each year. How does that impact a DCF?

Trick question. You don't account for this at all in an Unlevered DCF because you ignore interest expense and debt principal repayments. In a Levered DCF, you factor it in by reducing the interest expense each year as the Debt goes down and also by reducing Free Cash Flow by the mandatory repayments each year. The exact impact - i.e. whether the implied Equity Value goes up or down - depends on the interest rate and the principal repayment percentage each year; however, in most cases the principal repayments far exceed the net interest expense, so the Equity Value will most likely decrease because Levered FCF will be lower each year.

Can you explain the Gordon Growth formula in more detail? I don't need a full derivation, but what's the intuition behind it?

We actually do have a full derivation if you look in the Key Rules section above. Here's the formula: Terminal Value = Final Year Free Cash Flow * (1 + Growth Rate) / (Discount Rate - Growth Rate). And here's the intuition behind it: Let's say that we know for certain that we'll receive $100 every year indefinitely, and we have a required return of 10%. That means that we can "afford" to pay $1,000 now ($100 / 10%) to receive $100 in year 1 and $100 in every year after that forever. But now let's say that that stream of $100 were actually growing each year - if that's the case, then we could afford to invest more than the initial $1,000. Let's say that we expect the $100 to grow by 5% every year - how much can we afford to pay now to capture all those future payments, if our required return is 10%? Well, that growth increases our effective return... so now we can pay more and still get that same 10% return. We can estimate that by dividing the $100 by (10% - 5%). 10% is our required return and 5% is the growth rate. So in this case, $100 / (10% - 5%) = $2,000. This corresponds to the formula above: $100 represents Final Year Free Cash Flow * (1 + Growth Rate), 10% is the Discount Rate, and 5% is the Growth Rate. The higher the expected growth, the more we can afford to pay upfront. And if the expected growth is the same as the required return, theoretically we can pay an infinite amount (you get a divide by zero error in the equation) to achieve that return. You can test this yourself by plugging the values into a spreadsheet: enter $100, make it grow by 5% each year, and then use NPV(10%, Area With All The Numbers) and you'll see how it approaches $2,000 as you add more to it-

Why do you have to un-lever and re-lever Beta when you calculate it based on the comps?

When you look up the Betas on Bloomberg (or whatever source you're using) they will already be levered because a company's previous stock price movements reflect the Debt they've taken on. But each company's capital structure is different and we want to look at how "risky" a company is regardless of what % debt or equity it has. To do that, we need to un-lever Beta each time. We want to find the inherent business risk that each company has, separate from the risk created by Debt. But at the end of the calculation, we need to re-lever the median Unlevered Beta of that set because we want the Beta used in the Cost of Equity calculation to reflect the total risk of our company, taking into account its capital structure this time as well.

How does the Terminal Value calculation change when we use the mid-year convention?

When you're discounting the Terminal Value back to its present value, you use different numbers for the discount period depending on whether you're using the Multiples Method or Gordon Growth Method: • Multiples Method: You add 0.5 to the final year discount number to reflect that you're assuming the company gets sold at the end of the year. • Gordon Growth Method: You use the final year discount number as is, because you're assuming the free cash flows grow into perpetuity and that they are still received throughout the year rather than just at the end.

Wait a second: why isn't the present value of the Terminal Value, by itself, just the company's Enterprise Value? Don't you get Enterprise Value if you apply a multiple to EBITDA?

Yes, you do get Enterprise Value - but that only represents the company's "far in the future" value. Remember that in a DCF, a company's value is divided into "near future" and "far future." If you leave out the present value of Free Cash Flows in the projection period, you're saying, "For the next 5 years, this company has no value. But then at the end of year 5, the company is miraculously worth something again!" And that doesn't make sense.

What should you do if you don't believe management's projections in a DCF model?

You can take a few different approaches: • You could create your own projections. • You could "hair-cut" management's projections (reduce them by a certain percentage) to make them more conservative. • You could show a sensitivity table based on different growth rates and margins, and show the values using both management's projections and a more conservative set of numbers.

Can you explain how to create a multi-stage DCF, and why it might be useful?

You use a multi-stage DCF if the company grows at much different rates, has much different profit margins, or has a different capital structure in different periods. For example, maybe the company grows revenue at 15% in the first two years, then 10% in years 2-4, and then 5% in year 5, with decreasing growth each year after that. So you might separate that into 3 stages and then make different assumptions for Free Cash Flow and the Discount Rate in each one. Note that a standard DCF, by itself, is actually a two-stage DCF because you divide it into the "near future" and "far future." You can divide it into more periods if you want, and it would just be an extension of this concept.

What's the point of a "stub period" in a DCF? Can you give an example?

You use a stub period when you're valuing a company before or after the end of its fiscal year and there are 1 or more quarters in between the current date and the end of the fiscal year. For example, it's currently September 30th and the company's fiscal year ends on December 31st. In this case it wouldn't be correct to assume that Free Cash Flow only starts on January 1st of the next year - there are still 3 months between now and the end of the year, the company still generates FCF in those 3 months, and you need to account for it somewhere in your model. So you would calculate FCF in that 3-month period, use 0.25 for the discount period, and then use 1.25 for the discount period for the first full year of the model, 2.25 for the next year, and so on.

Explain why we use the mid-year convention in a DCF.

You use it to represent the fact that a company's cash flow does not arrive 100% at the end of each year - instead, it comes in evenly throughout each year. In a DCF without the mid-year convention, we would use discount period numbers of 1 for the first year, 2 for the second year, 3 for the third year, and so on. With the mid-year convention, we would instead use 0.5 for the first year, 1.5 for the second year, 2.5 for the third year, and so on. The end result is that the mid-year convention produces higher values since the discount periods are all lower.

If you use Levered Free Cash Flow, what should you use as the Discount Rate?

You would use Cost of Equity rather than WACC since we're ignoring Debt and Preferred Stock and only care about the Equity Value for Levered FCF.

How do you calculate Cost of Equity?

• Cost of Equity = Risk-Free Rate + Equity Risk Premium * Levered Beta The Risk-Free Rate represents how much a 10-year or 20-year US Treasury (or equivalent "safe" government bond in your own country) should yield; Beta is calculated based on the "riskiness" of Comparable Companies and the Equity Risk Premium is the percentage by which stocks are expected to out-perform "risk-less" assets like US Treasuries. Normally you pull the Equity Risk Premium from a publication called Ibbotson's. Note: Depending on your bank and group, you might also add in a "size premium" and "industry premium" to account for additional risk and expected returns from either of those. Small-cap stocks are expected to out-perform large-cap stocks and certain industries are expected to out-perform others, and these premiums reflect these expectations.

What about alternate ways to calculate Levered Free Cash Flow?

• Net Income + Non-Cash Charges - Changes in Operating Assets and Liabilities - CapEx - Mandatory Debt Repayments • (EBIT - Net Interest Expense) * (1 - Tax Rate) + Non-Cash Charges - Changes in Operating Assets and Liabilities - CapEx - Mandatory Debt Repayments • Cash Flow from Operations - CapEx - Mandatory Debt Repayments

How do you calculate WACC?

• WACC = Cost of Equity * (% Equity) + Cost of Debt * (% Debt) * (1 - Tax Rate) + Cost of Preferred * (% Preferred) In all cases, the percentages refer to how much each component comprises of the company's capital structure. For Cost of Equity, you can use the Capital Asset Pricing Model (CAPM - see the next question) and for the others you usually look at comparable companies and comparable debt issuances and the interest rates and yields issued by similar companies to get estimates.