Discounted Cash Flow REFINED

Question 1

Walk me through a DCF.

Answer 1

• 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 FCF for each year, which you discount and sum up to get to the NPV. The Discount Rate is usually the WACC.
• Once you have the present value of the FCFs, 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 NPV using the Discount Rate.
• Finally, you add the two together to determine the company’s Enterprise Value.

Question 2

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

Answer 2

• First, confirm that they are asking for Unlevered FCF (FCF 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 D&A and other non-cash charges, and factor in the Change in Operating Assets and Liabilities. If Assets increase by more than Liabilities, this is negative; otherwise, it’s positive.
• Finally, subtract CapEx to calculate Unlevered FCF.
• Levered FCF is similar, but you must also subtract the Net Interest Expense before multiplying by the (1 - Tax Rate), and you must also subtract Mandatory Debt Repayments at the end.

Question 3

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

Answer 3

• 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.

Question 4

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

Answer 4

There are many “alternate” methods - here are few common ones:

• EBIT * (1 - Tax Rate) + Non-Cash Charges - Changes in Operating Assets & Liabilities - CapEx • CFO + Tax-Adjusted Net Interest Expense - CapEx • NI + Tax-Adjusted Net Interest Expense + Non-Cash Charges - Changes in Operating Assets and Liabilities - CapEx
• NOTE: The difference with these is that the tax numbers will be slightly different as a result of when you exclude the interest.

Question 5

What’s an alternate method to calculate Levered Free Cash Flow?

Answer 5

• NI + Non-Cash Charges - Changes in Operating Assets & Liabilities - CapEx - Mandatory Debt Repayments
• (EBIT - Net Interest Expense) * (1 - Tax Rate) + Non-Cash Charges - Changes in Operating Assets & Liabilities - CapEx - Mandatory Debt Repayments
• CFO - CapEx - Mandatory Debt Repayments

Question 6

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

Answer 6

Levered FCF 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 7

If you used Levered Free Cash Flow, what should you use as your discount rate?

Answer 7

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 8

How do you calculate WACC?

Answer 8

• WACC = Cost of Equity * (% Equity) + Cost of Debt * (1 - Tax Rate) * (% Debt) + Cost of Preferred Stock * (% 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 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 9

How do you calculate Cost of Equity?

Answer 9

• 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 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 10

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

Answer 10

• 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 of 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 as follows:
• Unlevered Beta = Levered Beta / (1 + [(1 - Tax Rate) x (Total Debt/Equity)])
• Levered Beta = Unlevered Beta * (1 + [(1 - Tax Rate) x (Total Debt/Equity)])

Question 11

Can Beta ever be negative? What would that mean?

Answer 11

• 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 12

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 12

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 13

How do you calculate Terminal Value?

Answer 13

• You can either apply an exit multiple to the company’s Year 5 EBITDA, EBIT, or FCF (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 FCF * (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 FCF from the final year into infinity, as of the final year.

Question 14

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

Answer 14

• Terminal Value = Final Year FCF * (1 + Growth Rate) / (Discount Rate - Growth Rate)
• 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 we can “afford” to pay $1000 now ($100/10%) to receive $100 in Year 1 and $100 in every year after that forever.
• But now let’s say that the stream of $100 were actually growing each year - if that’s the case, then we could afford to invest more than the initial $1000.
• 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 the same 10% return. We can estimate the $100 by (10% - 5%). 10% is our required return and 5% is the growth rate. So in this case, $100 / (10% - 5%) = $2000.
• This corresponds to the formula above: $100 represents Final Year FCF * (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.

Question 15

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

Answer 15

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

Question 16

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

Answer 16

The one without Debt will generally have a higher WACC b/c 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 17

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 17

• The one w/o Debt is not “at a disadvantage” - but it won’t be valued as highly b/c of the way the WACC formula works.
• Keep in mind that companies do not make big decisions based on 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 18

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 18

The Discount Rate change will almost certainly have a bigger impact b/c that affects everything from the present value of FCFs to the present value of Terminal Value - and even a 10% change makes a huge impact.

Question 19

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 1% or reducing the discount rate to 9%?

Answer 19

In this case, the change in Revenue is likely to have a bigger impact b/c you’ve change 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 FCFs.

Question 20

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 20

A percentage that’s less than 10%, for two reasons:

1. Remember that we discount all those FCFs - 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 21

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 21

• Trick question. You don’t account for this at all in an Unlevered DCF b/c 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 FCF 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 b/c Levered FCF will be lower each year.

Question 22

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 22

• 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 $1000 in debt.
• Initially, it pays $100 in Interest Expense, and after taxes that’s only $60 [$100 * (1 - 40%)]. So Levered FCF 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 FCF 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.

Question 23

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?

Answer 23

• In this scenario, you would include additional CapEx spending of $100 in Year 4 of the DCF, which would reduce FCF 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.