DCF

Question 1

Terminal Value

Answer 1

Final Year Free Cash Flow * (1 + Terminal FCF Growth Rate) / (Discount Rate - Terminal FCF Growth Rate)

Question 2

Other formula for Cost of Equity

Answer 2

(Dividends Per Share / Share Price) + Growth Rate of Dividends

Question 3

Levered Beta

Answer 3

Unlevered Beta * (1 + (1 - Tax Rate) * (Debt / Equity Value))

Question 4

Unlevered Beta

Answer 4

Levered Beta / (1 + (1 - Tax Rate) * (Debt/Equity Value))

Question 5

What’s the basic concept behind a DCF?

Answer 5

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.

Question 6

Walk me through DCF?

Answer 6

1. Project free cash flows over 5-10 year period
2. Calculate company’s discount rate, usually WACC
3. Discount and sum up company’s FCF
4. Calculate company’s Terminal Value
5. Discount the Terminal Value to its Present Value
6. Add the discounted FCF to the discounted Terminal Value

Question 7

Walk me through how you get from Revenue to FCF in the projections.

Answer 7

1. Make sure its unleveled FCF
2. Subtract COGS and Op Ex from Revenue to get to Operating Income (EBIT)
3. Multiply by (1-TAX Rate), add back DandA, and other non-cash charges, and factor in Change in Operating Assets and Liabilites
4. Subtract CapEX to calculate Unlevered FCF

For Levered FCF: similar, but you must subtract Net Interest Expense before multiplying by (1-Tax Rate), and you must also subtract Mandatory Debt Repayments at the end.

Question 8

What’s the point of FCF, anyway? What are you trying to do?

Answer 8

Idea: you’re replicating Cash Flow Statement, but only recurring, predictable items. In Unlevered Free Cash Flow, exclude impact of debt entirely.

Question 9

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

Answer 9

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.

Question 10

What do you usually for the Discount Rate?

Answer 10

In a Unlevered DCF analysis, you can use WACC, which reflects the “Cost” of Equity, Debt, Preferred Stock. In a Levered DCF analysis, you use Cost of Equity instead.

Question 11

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

Answer 11

Once you get to EV, ADD Cash and then SUBTRACT Debt, Preferred Stock, and Noncontrolling Interests (and any other debt-like items) to get Equity Value.

Then you divide by the company’s share count to determine implied per-share price.

Question 12

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?)

Answer 12

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.

Question 13

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?

Answer 13

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.

Question 14

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

Answer 14

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.

Question 15

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

Answer 15

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.

Question 16

What about alternate ways to calculate Levered Free Cash Flow?

Answer 16

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

Question 17

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?

Answer 17

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.

Question 18

What’s the point of that “Changes in Operating Assets and Liabilities” section? What does it mean?

Answer 18

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.

Question 19

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

Answer 19

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.

Question 20

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

Answer 20

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).

Question 21

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

Answer 21

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.

Question 22

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?

Answer 22

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.”

Question 23

How do you calculate WACC?

Answer 23

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) 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.

Question 24

How do you calculate Cost of Equity?

Answer 24

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.

Question 25

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?

Answer 25

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.

Question 26

How can we calculate Cost of Equity WITHOUT using CAPM?

Answer 26

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.

Question 27

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

Answer 27

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.

Unlevered Beta = Levered Beta / (1 + ((1 - Tax Rate) x (Total Debt/Equity)))

Question 28

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

Answer 28

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.

Question 29

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

Answer 29

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).

Question 30

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

Answer 30

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

Question 31

Can Beta ever be negative? What would that mean?

Answer 31

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.

Question 32

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

Answer 32

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

Question 33

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

Answer 33

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.

Question 34

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?

Answer 34

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.

Question 35

If 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?

Answer 35

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.

Question 36

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

Answer 36

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.

Question 37

How do you calculate the Terminal Value?

Answer 37

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.

Question 38

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

Answer 38

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.

Question 39

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

Answer 39

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.

Question 40

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

Answer 40

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.

Question 41

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

Answer 41

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.

Question 42

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

Answer 42

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.

Question 43

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?

Answer 43

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.

Question 44

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

Answer 44

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.

Question 45

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

Answer 45

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.

Question 46

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?

Answer 46

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.

Question 47

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

Answer 47

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”).

Question 48

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

Answer 48

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.

Question 49

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

Answer 49

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.

Question 50

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

Answer 50

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.

Question 51

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?

Answer 51

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.

Question 52

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%?

Answer 52

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.

Question 53

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?

Answer 53

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.

Question 54

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?

Answer 54

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.

Question 55

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

Answer 55

Common sensitivities:
Revenue Growth vs. Terminal Multiple

EBITDA Margin vs. Terminal Multiple

Terminal Multiple vs. Discount Rate

Terminal Growth Rate vs. Discount Rate

Question 56

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?

Answer 56

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.

Question 57

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?

Answer 57

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.