DCF Flashcards

Question

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

Answer 1

It's an estimate of how changes in operational capital affect cash flows. If Assets increase more than Liabilities, cash flows decrease. If Liabilities increase more than Assets, cash flows increase.

Answer 2

Nothing "happens" bc you can still run the analysis. However, the company's value will decrease if one or both of these are negative, bc the PV of FCF will decrease as a result. If the FCF turn positive during the projection period, the DCF might still work. If not, it won't because it will give you a negative valuation.

Answer 3

1) discount rate is COE 2) resulting valuation is Implied Equity Value

Answer 4

Likely not. In theory you could pick equivalent assumptions and set up the analysis st you calculate the same EqV in the end. In practice, picking "equivalent" assumptions is difficult, and so these two methods will almost never produce the same value. UFCF => TEV => EqV, using the same numbers for Debt, Cash, etc LFCF the terms of the debt affect the FCF

Answer 5

Weighted Average Cost of Capital (proportion Equity) * COE + (proportion Debt) * COD * (1-TaxRate) + (proportion Preferred Stock) * COPS proportions = proportions of each segment in capital structure

Answer 6

Using the Capital-Asset Pricing Model (CAPM) COE = Rf + LeveredBeta*ERP Risk-Free Rate = riskless security like yield of 10 or 20 year US Treasury Beta = calculated based on the "riskiness" of Comparable Companies Equity Risk Premium = percentage by which stocks are expected to outperform riskless assets like US Treasuries - usually found in publication called Ibbotson's - depending on bank/industry, could add a "size" or "industry" premium to account for additional risk - small-cap stocks generally out-perform large-cap stocks, higher COE

Answer 7

Trick question = no, because dividend yield is already factored into Beta. Beta describes the returns in excess of the market as a whole, and those returns INCLUDE dividends.

Answer 8

Alternate formula COE = (Dividends per Share) / (Share Price) + Growth Rate of Dividends This is less common in the "standard" formula, but sometimes you use it when the company is guaranteed to issue Dividends (Utilities) and/or information on Beta is unreliable.

Answer 9

1) you don't have to calculate Beta. You can look up a company's Historical Beta, based on its stock performance vs the relevant index. 2) Public Comps = find a new estimate for Beta by finding comparable companies, look up each Beta, unlever each, pick median of set, then lever the Beta with your company's capital structure. Unlevered Beta = Levered Beta / [1 + (1-TaxRate)(Total Debt/Equity)] Levered Beta = Unlevered Beta * [1 + (1-TaxRate)(Total Debt/Equity)]

Answer 10

When you look up Comps' Betas, they are Levered bc their stock market movement reflects the amount of debt they've taken on/capital structure. Every company's capital structure is different, so we unlever to isolate the inherent business risk of the Comps, then relever the median of the set to reflect the impact of our particular company's debt. Levered Beta now reflects the total risk of our company = both inherent business risk and capital structure risk.

Answer 11

Yes, because Levered Beta reflects the COE of a company, given its inherent business risk and capital structure. UFCF uses COE as part of the Discount Rate WACC.

Answer 12

In calculating Beta, Preferred Stock is treated as Equity because Preferred Dividends are not tax-deductible, unlike interest paid on debt.

Answer 13

Yes. Beta can be negative, which means it has an inverse relationship with the market -- the asset moves in the opposite direction of the market.

Answer 14

Technology companies are generally viewed as "riskier" industry than manufacturing, and therefore would have higher Betas.

Answer 15

In theory, yes. If a company's capital structure is changing in a certain, predictable way then you can use it in a DCF. However, you rarely know capital structure changes in advance. It's not a good assumption to make.

Answer 16

The company "pay" for Equity in two ways 1) Dividends = issuing is a cash expense 2) stock appreciation rights = diluting the ownership of the current shareholders It is tricky to estimate the impact of both of these, which is why we usually use the Rf + Levered Beta(ERP) to estimate the company's expected return instead

Answer 17

1) Consistency – Since UFCF does not depend on the company’s capital structure, you will get the same results even if the company issues Debt or Equity, repays Debt, etc. 2) Ease of Projecting – You do not need to project items such as Debt, Cash, and the interest rates on Debt and Cash because you ignore the Net Interest Expense in the analysis. That means less research and a faster conclusion

Answer 18

No. When projecting FCF you include the impact of RECURRING non-cash expenses only. 1) Most of these other non-cash adjustments are non-recurring (e.g., Gains and Losses, Impairments, and Write-Downs). And when you project Free Cash Flow, you ignore these non-recurring items in future periods. 2) Stock-based compensation, the other common, recurring item in this section, is NOT a real non-cash expense e because it creates additional shares and dilutes the existing investors and should not be added back to calculate UFCF. And, per the definition above, it relates only to a specific investor group (common shareholders). Example: It’s the same with Stock-Based Compensation: if you add it back as a non-cash expense, you’re getting a “free lunch” because you’re not reflecting the existing shareholders’ reduced ownership in the company

Answer 19

Forecast period: 5-10 years Bc want to make sure have predicable cash flows where the assumptions hold. Terminal Growth Rate: 2-3% Bc this is the far-future projected growth rate of the developed US economy. Equity Risk Premium: Rm-Rf = 10 - 4 = 6% Bc average return on the market was around 10% over the last 100 years, average return on 10-year Treasury is about 4% right now Beta: this depends 1) how related is this company's risk to the market? 2) how levered is it?

Answer 20

While the Cost of Debt is usually lower than the cost of equity (for the reasons mentioned above), taking on too much debt will cause the cost of debt to rise above the cost of equity. As a business takes on more and more debt, its probability of defaulting on its debt increases. This is because more debt equals higher interest payments. If a business experiences a slow sales period and cannot generate sufficient cash to pay its bondholders, it may go into default. Therefore, debt investors will demand a higher return from companies with a lot of debt, in order to compensate them for the additional risk they are taking on. This higher required return manifests itself in the form of a higher interest rate. It is also worth noting that as the probability of default increases, stockholders’ returns are also at risk, as bad press about potential defaulting may place downward pressure on the company’s stock price. Thus, taking on too much debt will also increase the cost of equity as the equity risk premium will increase to compensate stockholders for the added risk.

Answer 21

TBD 1) UFCF when risk-free rate increases, interest expense likely increases too. However, UFCF doesn't take into account net interest expense or mandatory debt repayments, so UFCF is likely unaffected. 2) TV when Rf increases, the COE increases, and WACC increases. That means the TV calculated through the GGM would decrease 3) Cost of Debt when risk-free rate increases, interest rates in general usually increase. That means the Kd is likely increasing

Answer 22

Good point, but the DCF and discount rate is about projecting into the future. In practice you would still multiply by (1 - Tax Rate) because what matters is not if Debt is currently reducing taxes, but rather if it will in the future.

Answer 23

An Optimal Capital Structure is the combination of Debt, Equity, and Preferred Stock that minimizes WACC. There is no real way to estimate this via a formula bc you'll always find that Debt should be 100% of the capital structure bc Kd is cheaper than Ke and Kp, but that can't happen bc firms need some amount of Equity as well. You may be able to approximate the optimal structure by looking at a few different scenarios and seeing how the WACC changes, but there's no mathematical solution.

Answer 24

WACC = Ke(%equity) + Kd(%debt) + Kp(%preferred) Ke = Rf + LeveredBeta(ERP) * The Fed might reduce the Rf rate to encourage spending * ERP will increase bc investors will require higher returns to invest in stocks * Beta will increase bc increased volatility Ke in total will probably increase bc 2 increases > 1 decrease Kd and Kp increases (most banks/investors don't want to give out money in times of financial uncertainty) Capital Structure changes - EqV would probably fall bc share prices would fall = Debt is larger total proportion of capital structure, but costs also increase WACC probably increases bc almost all variables push it up Simpler: all else being equal, did companies become more valuable or less valuable during the financial crisis? Less valuable = WACC increases

Answer 25

You can either 1) apply an exit multiple to the company's final year EBITDA, EBIT, or FCF 2) use the growth in perpetuity method (Gordon Growth Method) to estimate the value based on the company's growth rate into perpetuity Note, these two are interrelated and can be used to sanity check each other. HOW? Using the GGM, you have an assumption of terminal growth rate. You plug that into the equation for TVtfinal = FCFtfinal * (1 + terminal growth rate) --------------- discount rate - terminal growth rate Implied Exit Multiple = TV at final projected year / EBITDA at final projected year But using the Multiple Method, you can input the implied TVtfinal into the GGM formula and solve for the terminal growth rate. You can then check the terminal growth rate and exit multiple outputs against reasonable assumptions.

Answer 26

In banking you generally would use the Multiples method to calculate TV bc it's based on Comparable Companies, real data, while picking a terminal growth rate requires more guesswork. However, if you have no good Comparable Companies, or if you believe multiples will change significantly in the industry several years down the road = use GGM. For example, if the industry is cyclical (chemicals, semiconductors).

Answer 27

You build a DCF analysis because a company is worth the Present Value of its expected future cash flows: Company Value = Cash Flow / (Discount Rate – Cash Flow Growth Rate), where Cash Flow Growth Rate < Discount Rate But you can’t just use that single formula because a company’s Cash Flow Growth Rate and Discount Rate change over time. So, in a Discounted Cash Flow analysis, you divide the valuation into two periods: one where those assumptions change (the explicit forecast period) and one where they stay the same (the Terminal Period). You then project the company’s cash flows in both periods and discount them to their Present Values based on the appropriate Discount Rate(s). Then, you compare this sum – the company’s Implied Value – to the company’s Current Value or “Asking Price” to see if it’s valued appropriately.

Answer 28

A DCF values a company based on the Present Value of its Cash Flows in the explicit forecast period plus the Present Value of its Terminal Value. You start by projecting the company’s Free Cash Flows over the next 5-10 years by making assumptions for revenue growth, margins, Working Capital, and CapEx. Then, you discount the cash flows using the Discount Rate, usually the Weighted Average Cost of Capital, and sum up everything. Next, you estimate the company’s Terminal Value using the Multiples Method or the Gordon Growth Method; it represents the company’s value after those first 5-10 years into perpetuity. You then discount the Terminal Value to Present Value using the Discount Rate and add it to the sum of the company’s discounted cash flows. Finally, you compare this Implied Value to the company’s Current Value, usually its Enterprise Value, and you’ll often calculate the company’s Implied Share Price so you can compare it to the Current Share Price.

Answer 29

First, confirm that the interviewer is asking for Unlevered Free Cash Flow (AKA Free Cash Flow to Firm). If so: * Subtract COGS and Operating Expenses from Revenue to get Operating Income (EBIT). * Then, multiply Operating Income by (1 – Tax Rate), add back Depreciation & Amortization, and factor in the Change in Working Capital. If the company spends extra cash as it grows, the Change in Working Capital will be negative; if it generates extra cash flow due to its growth, it will be positive. * Finally, subtract Capital Expenditures to calculate Unlevered Free Cash Flow. Levered Free Cash Flow (Free Cash Flow to Equity) is similar, but you subtract the Net Interest Expense before multiplying by (1 – Tax Rate), and you also factor in changes in Debt principal.

Answer 30

The Discount Rate represents the opportunity cost for the investors – what they could earn by investing in other, similar companies in this industry. A higher Discount Rate means higher risk and potential returns; a lower Discount Rate means lower risk and potential returns. A higher Discount Rate makes a company less valuable because it means the investors have better options elsewhere; a lower Discount Rate makes a company more valuable

Answer 31

You can use the Multiples Method or the Gordon Growth Method (AKA Long-Term Growth Method, Perpetuity Growth Method, etc.). With the Multiples Method, you apply a Terminal Multiple to the company’s EBITDA, EBIT, NOPAT, or FCF in the final year of the forecast period. For example, if you apply a 10x TEV / EBITDA multiple to the company’s Year 10 EBITDA of $500, its Terminal Value is $5,000. With the Gordon Growth Method, you assign a “Terminal Growth Rate” to the company’s Free Cash Flows in the Terminal Period and assume they’ll grow at that rate forever. Terminal Value = Final Year Free Cash Flow * (1 + Terminal Growth Rate) / (Discount Rate – Terminal Growth Rate) The Gordon Growth Method is better from a theoretical perspective because growth always slows down over time; all companies’ cash flows eventually grow more slowly than GDP. If you use the Multiples Method, it’s easy to pick a multiple that makes no logical sense because it implies a growth rate that’s too high. However, many bankers still use and prefer the Multiples Method because it’s “easier” or because they don’t understand that a Terminal Multiple implies a Terminal Growth Rate.

Answer 32

The most common signs of trouble are: 1) Too Much Value from the PV of Terminal Value – It usually accounts for at least 50% of the company’s total Implied Value, but it shouldn’t represent 95% of its value. 2) Implied Terminal Growth Rates or Terminal Multiples That Don’t Make Sense – If you pick a Terminal Multiple that implies a Terminal FCF Growth Rate of 8%, but the country’s long-term GDP growth rate is 3%, something is wrong. 3) You’re Double-Counting Items – If an expense is deducted in FCF, you should not subtract the corresponding Liability in the Enterprise Value → Equity Value “bridge.” And if an expense is not deducted in FCF, you should subtract the corresponding Liability in the bridge at the end (e.g., Interest and Debt in an Unlevered DCF). 4) Mismatched Final Year FCF Growth Rate and Terminal Growth Rate – If the company’s Free Cash Flow is growing at 15% in the final year, but you’ve assumed a 2% Terminal Growth Rate, something is wrong. FCF growth should decline over time and approach the Terminal Growth Rate by the end of the explicit forecast period.

Answer 33

The simplest method is to extend the explicit forecast period so that the company’s Free Cash Flow contributes a higher percentage of the Implied Value and so that there’s more time for the FCF growth to slow down and approach the Terminal Growth Rate. So, if you’re using a 5-year forecast period, extend it to 10-15 years and reduce the company’s FCF growth in those extra years as it approaches maturity. To avoid double-counting items… look at what you’re doing, and don’t double count! Finally, you can reduce the Terminal Value by picking a lower Terminal Growth Rate or lower Terminal Multiple. Terminal Value tends to be overstated in financial models because people don’t understand the theory behind it.

Answer 34

You compare the company’s Implied Enterprise Value, Equity Value, or Share Price to its Current Enterprise Value, Equity Value, or Share Price to see if it might be overvalued or undervalued. You do this over a **range of assumptions because investing is probabilistic**. For example, if you believe that the company’s Implied Share Price is between $15.00 and $20.00, but its Current Share Price is $8.00, that means the company may be undervalued. But if its Current Share Price is $17.00, then it may be valued appropriately

Answer 35

Maybe. A DCF is based on a company’s expected future cash flows, so even if the company is cash flow-negative right now, the analysis could work if the company starts generating positive cash flows in the future. But if the company has no path to positive cash flows, or you can’t reasonably forecast its cash flows, then the analysis doesn’t make sense.

Answer 36

In a Levered DCF, you use Levered FCF for the cash flows (i.e., deduct the Net Interest Expense and include changes in Debt principal) and Cost of Equity for the Discount Rate, and you calculate Terminal Value using Equity Value-based multiples such as P / E. You don’t back into Implied Equity Value at the end because the analysis produces the Implied Equity Value directly. An APV Analysis is similar to a traditional Unlevered DCF, but you value the company’s Interest Tax Shield separately and add the Present Value of this Tax Shield at the end. You still calculate Unlevered FCF and Terminal Value the same way, but you use Unlevered Cost of Equity for the Discount Rate (i.e., Risk-Free Rate + Equity Risk Premium * Median Unlevered Beta from Public Comps). You then project the Interest Tax Shield each year, discount it at that same Discount Rate, calculate the Interest Tax Shield Terminal Value, discount it, and add up everything at the end.

Answer 37

No. The simplest explanation is that an Unlevered DCF does not directly factor the Cost of Debt into the FCF projections, while a Levered FCF does. The Unlevered DCF indirectly accounts for it via the WACC calculation, but it won’t be equivalent to the Levered version. That alone will create differences, but the volatile cash flows in a Levered DCF (due to changes in Debt principal) will also play a role. It’s very difficult to pick equivalent assumptions, and it’s not worth thinking about because no one uses the Levered DCF in real life.

Answer 38

The traditional Unlevered DCF is easier to set up, forecast, and explain, and it produces more consistent results that depend far less on the company’s capital structure. With the other methods, you have to project the company’s Cash and Debt balances, Net Interest Expense, and changes in Debt principal, all of which require more time and effort. The Levered DCF sometimes produces odd results because irregular Debt principal repayments can shift the Levered FCF dramatically in certain years. The APV Analysis is flawed because it doesn’t factor in the main downside of Debt: the increased chance of bankruptcy (unless you make a special adjustment for it). The Unlevered DCF solves this issue because WACC initially decreases with additional Debt but then starts increasing past a certain level, reflecting both the advantages and disadvantages of Debt.

Answer 39

Unlevered FCF must capture the company’s core, recurring line items available to ALL investor groups. That’s because Unlevered FCF corresponds to Enterprise Value, which also represents the value of the company’s core business available to all investor groups. So, if an item is NOT recurring, NOT related to the company’s core business, or NOT available to all investor groups, you ignore it. This rule explains why you ignore these items: * Net Interest Expense = Only available to Debt investors. * Other Income / (Expense) = Corresponds to non-core or non-operating Assets. * Most non-cash adjustments besides D&A = they’re non-recurring. * All Items in Cash Flow from Financing = They’re only available to certain investors. * Most of Cash Flow from Investing = Only CapEx is a recurring, core-business item.

Answer 40

The Change in Working Capital tells you whether the company generates extra cash as it grows or whether it requires extra cash to support its growth. It’s related to whether a company records expenses and revenue before or after paying or collecting them in cash. For example, retailers tend to have negative values for the Change in Working Capital because they usually have to pay for Inventory before delivering it to customers. But subscription-based software companies often have positive values for the Change in Working Capital because they might collect cash from long-term subscriptions upfront and recognize it as revenue over time. The Change in WC could increase or decrease the company’s Free Cash Flow, but it’s rarely a major value driver because it’s fairly small for most companies.

Answer 41

No! You should consider SBC a cash expense in the context of valuation because it creates additional shares and dilutes the existing investors. By contrast, Depreciation & Amortization relate to timing differences: the company paid for a capital asset earlier on but divides that payment over many years and recognizes it over time. Stock-Based Compensation is a non-cash add-back on the Cash Flow Statement, but the context is different: accounting rather than valuation. In a DCF, you should count SBC as a real cash expense or, if you count it as a non-cash add-back, you should assume additional shares by increasing the company’s diluted share count. Either way, the company’s Implied Share Price decreases. Many DCFs get this wrong because they use neither approach: they pretend that SBC is a noncash add-back that makes no impact on the share count (wrong!).

Answer 42

The company’s Free Cash Flows should reflect the cash taxes it pays. So, it doesn’t matter which rate you use as long as the cash taxes are correct. For example, you could use the company’s effective tax rate (Income Statement Taxes / Pre-Tax Income) and then include an adjustment for Deferred Taxes. Or you could calculate and use the company’s “cash tax rate” and skip the Deferred Tax adjustments. You could even use the statutory tax rate and make adjustments for state/local taxes and other items to arrive at the company’s real cash taxes. It’s most common to use the effective tax rate and then adjust for the Deferred Taxes based on historical trends

Answer 43

Just like the company’s Free Cash Flow growth rate should decline in the explicit forecast period, the company’s CapEx and Depreciation, as percentages of revenue, should decrease. High-growth companies tend to spend more on Capital Expenditures to support their growth, but this spending declines over time as they move from “growing” to “mature.” If the company’s FCF is growing, CapEx should always exceed Depreciation, but there may be a smaller difference by the end. CapEx should not equal Depreciation – even in the Terminal Period (again, assuming the company is still growing). That’s partially due to inflation (capital assets purchased 5-10 years ago cost less) and because Net PP&E must keep growing to support FCF Growth in the Terminal Period. If the company’s FCF stagnates or declines, then you might use different assumptions

Answer 44

In most cases, no. Clients and investors tend to think in nominal terms, and assumptions for prices and salaries tend to be based on nominal figures. If you include inflation, you also need to forecast inflation far into the future and adjust all figures in your analysis. That’s rarely worthwhile because of the uncertainty and extra assumptions required.

Answer 45

You’ll reflect it directly in a Levered DCF because the company’s Net Interest Expense and Debt principal will change over time. You’ll also change the Cost of Equity over time to reflect this. The changing capital structure won’t show up explicitly in the projections of an Unlevered DCF, but you will still reflect it with the Discount Rate – WACC will change as the company’s Debt and Equity levels change.

Answer 46

If you subtract a certain expense in FCF, then you should ignore the corresponding Liability when moving from Implied Enterprise Value to Implied Equity Value at the end. For example, with U.S.-based companies, you normally subtract the Rental Expense on Operating Leases in the FCF projections because Rent is a standard operating expense. Therefore, you ignore the Operating Lease Liability in the Enterprise Value bridge at the end. But if you exclude or add back the Rental Expense in FCF, you do the opposite and subtract the Operating Lease Liability in the bridge. This rule also explains why you subtract Debt in the bridge for an Unlevered analysis: UFCF excludes the corresponding Interest Expense on the Debt

Answer 47

For the most part, no. You certainly shouldn’t make speculative projections for these items – they are all non-recurring. If a company has announced plans to sell an asset, make an acquisition, or record a write-down in the near future, then you might factor it into FCF for that year. And if it’s an acquisition or divestiture, you’ll have to adjust FCF to reflect the cash spent or received, and you’ll have to change the company’s cash flow after the deal takes place.

Answer 48

It tells you the average percentage a company’s stock “should” return each year, over the very long term, factoring in both stock-price appreciation and dividends. In a valuation, it represents the average annualized percentage that equity investors might earn over the long term. To a company, the Cost of Equity represents the cost of funding its operations by issuing additional shares to investors. The company “pays for” Equity via potential Dividends (a real cash expense) and by diluting existing investors.

Answer 49

WACC is similar to Cost of Equity, but it’s the expected annualized return if you invest proportionately in all parts of the company’s capital structure – Debt, Equity, and Preferred Stock. To a company, WACC represents the cost of funding its operations by using all its sources of capital and keeping its capital structure percentages the same over time. Investors might invest in a company if its expected IRR exceeds WACC, and a company might decide to fund a new project, acquisition, or expansion if its expected IRR exceeds WACC.

Answer 50

Cost of Equity = Risk-Free Rate + Levered Beta * Equity Risk Premium The Risk-Free Rate represents the yield on "risk-free" government bonds denominated in the same currency as the company’s cash flows. You usually use 10-year or 20-year bonds to match the explicit forecast period of the DCF. Levered Beta represents the volatility of this stock relative to the market as a whole, factoring in both intrinsic business risk and risk from leverage. Equity Risk Premium represents how much the stock market in the company’s country will return above the “risk-free” government bond yield in the long term. Stocks are riskier and have higher potential returns than government bonds, so you take the yield on those government bonds, add the extra returns you could get from the stock market, and then adjust for this company’s specific risk and potential returns.

Answer 51

You should use the yield (to maturity) on the government bonds denominated in the currency of the company’s cash flows. So, if the company reports its financials in USD, you might use the yield on 10-year U.S. Treasuries; if it reports them in EUR or GBP, you might use the yield on 10-year bonds issued by the European Central Bank or the Bank of England

Answer 52

One option is to take the Risk-Free Rate in a country that is “risk-free,” like the U.S. or U.K., and then add a default spread based on your country’s credit rating. For example, you might start with a rate of 1.3% for 10-year U.S. Treasuries and then add a spread of ~7% for Greece based on its current credit rating (this is just an example; these numbers change all the time). This 8.3% Risk-Free Rate represents the additional risk because the government has a significantly higher chance of defaulting.

Answer 53

Stock-market returns differ based on the period and whether you use an arithmetic mean, a geometric mean, or other approaches, so there’s no universal method. Many firms use a publication called “Ibbotson’s” that publishes Equity Risk Premium data for companies of different sizes in different industries each year; some academic sources also track and report this data. You could also take the historical data for the U.S. stock market and add a premium based on the default spread of a specific country. For example, if the historical U.S. premium is 7%, you might add 3% to it if your country’s credit rating is Ba2, and that rating corresponds to a 3% spread. Some groups also use a “standard number” for each market, such as 5-6% in developed countries.

Answer 54

You might take the percentage of revenue earned in each country, multiply it by the ERP in that market, and then add the terms to get the weighted average ERP. To calculate the ERP in each market, you might use one of the methods described in the previous question. The “Historical U.S. stock market returns + default spread” approach is common here.

Answer 55

Levered Beta tells you how volatile a company’s stock price is relative to the stock market as a whole, factoring in both intrinsic business risk and risk from leverage (i.e., Debt). If Beta is 1.0, when the market goes up 10%, this company’s stock price also goes up by 10%. If Beta is 2.0, when the market goes up 10%, this company’s stock price goes up by 20%. Unlevered Beta excludes the risk from leverage and reflects only the intrinsic business risk, so it’s always less than or equal to Levered Beta.

Answer 56

Yes, it’s possible. The company’s stock price must move in the opposite direction of the entire market for Beta to be negative. Gold is commonly cited as an Asset with a negative Beta because it often performs better when the stock market declines, and it may act as a “hedge” against disastrous events. However, negative Betas for traditional companies are quite rare and usually revert to positive figures, even if they’re negative for short periods.

Answer 57

You don’t “have to” un-lever and re-lever Beta: you could just use the company’s historical Levered Beta and skip this step. But in a valuation, you’re estimating the company’s Implied Value: what it should be worth. The historical Beta corresponds more closely to the company’s Current Value – what the market says it’s worth today. By un-levering Beta for each comparable company, you capture the inherent business risk in “the industry as a whole.” Each company might have a different capital structure, so it’s useful to remove the risk from leverage and isolate the inherent business risk. You then take the median Unlevered Beta from these companies and re-lever it based on the capital structure (targeted or actual) of the company you’re valuing. You do this because there will always be business risk and risk from leverage, so you need to reflect both in the valuation. You can think of the result, Re-Levered Beta, as: “What the volatility of this company’s stock price, relative to the market as a whole, should be, based on the median business risk of its peer companies and this company’s capital structure.

Answer 58

Unlevered Beta = Levered Beta / [1 + Debt / Equity * (1 – Tax Rate) + Preferred Stock / Equity] Levered Beta = Unlevered Beta * [1 + Debt / Equity * (1 – Tax Rate) + Preferred Stock / Equity] You use a “1 +” in front of Debt / Equity * (1 – Tax Rate) to ensure that Unlevered Beta is always less than or equal to Levered Beta. You multiply the Debt / Equity term by (1 – Tax Rate) because the tax-deductibility of interest reduces the risk of Debt. The formulas reduce Levered Beta to represent the removal of risk from leverage, but they increase Unlevered Beta to represent the addition of risk from leverage.

Answer 59

Yes, this is one drawback. However: 1) The Debt / Equity ratio is a proxy for interest rates on Debt because companies with higher Debt / Equity ratios have to pay higher interest rates as well. 2) The risk isn’t directly proportional to interest rates. Higher interest on Debt will result in lower coverage ratios (EBITDA / Interest), but you can’t say something like, “Interest is now 4% rather than 1% – the risk from leverage is 4x higher.” A 4% vs. 1% interest rate barely makes a difference if the Debt balance is small, but it will be a much bigger deal with large Debt balances and smaller companies.

Answer 60

Yes. Un-levering and re-levering Beta has nothing to do with Unlevered vs. Levered FCF. A company’s capital structure affects both the Cost of Equity and WACC, so you un-lever and relever Beta regardless of the type of Free Cash Flow you’re using.

Answer 61

Some people argue that you should use the Predicted Beta instead of the Historical Beta because the Cost of Equity relates to expected future returns. If you use the historical data, you could use the company’s Historical Beta or the re-levered Beta based on the comparable companies. And if you re-lever Beta, you could do it based on the company’s current capital structure, its targeted or “optimal” structure, or the capital structure of the comparable companies. Most of these methods produce similar results, but they’re useful for establishing the proper range of values for the Cost of Equity and WACC.

Answer 62

This question tests your ability to make a guesstimate based on common sense and your knowledge of current market rates. You might say, “The Risk-Free Rate is around 4% via yield on 10-year U.S. Treasuries. Industrials' Levered Betas range from 1.5 for Auto to 1.0 for Transportation, so assume 1.25 Levered Beta. So, if you assume an Equity Risk Premium of 6%, the Cost of Equity might be around 11.5%.” 4 + 1.25(6) = 4 + 7.5 = 11.5%

Answer 63

The formula for WACC is simple: WACC = Cost of Equity * % Equity + Cost of Debt * (1 – Tax Rate) * % Debt + Cost of Preferred Stock * % Preferred Stock But it’s tricky to calculate because there are different methods to estimate these items: 1) Cost of Debt: Do you use the weighted average coupon rate on the company’s bonds? Or the Yield to Maturity (YTM)? Or the YTM of Debt from comparable companies? 2) Percentages of Debt, Equity, and Preferred Stock: Do you use the company’s current capital structure, “optimal” structure, or targeted structure? Or do you use the median percentages from the comparable public companies to approximate one of those? 3) Cost of Equity: There are different ways to calculate Beta, and no one agrees on the proper Equity Risk Premium.

Answer 64

Think of Unlevered FCF as “Free Cash Flow to Firm,” or FCFF, instead. Unlevered FCF, or FCFF, is available to ALL investors, and WACC represents ALL investors. Therefore, you pair WACC with Unlevered FCF. No Discount Rate can be “capital structure-neutral” since each part of a company’s capital structure affects the other parts. “Capital-structure neutrality” is a property of Free Cash Flow, not the Discount Rate.

Answer 65

A company’s “optimal” capital structure is the one that minimizes its WACC. But there’s no way to calculate it because you can’t tell in advance how the Costs of Equity, Debt, and Preferred Stock will change as the capital structure changes. So, in practice, you’ll often use the median capital structure percentages from the comparable public companies as a proxy for the “optimal” capital structure. It’s the same as the logic for un-levering and re-levering Beta: you want to capture what this company’s capital structure should be, not what it is right now. It’s better to use this expected capital structure because the company’s Implied Value in a DCF is based on its expected future cash flows.

Answer 66

Some textbooks claim that you should use Equity Value + Debt + Preferred Stock – Cash, rather than Equity Value + Debt + Preferred Stock, for the denominator of the capital structure percentages. We disagree with this approach for several reasons: 1) Cash Does Not “Offset” Debt – For example, many forms of Debt do not allow for early repayment or penalize the company for early repayment. So, a high Cash balance doesn’t necessarily reduce the risk of Debt on a 1:1 basis. 2) You May Get Nonsensical Results with High Cash Balances – For example, consider a company with an Equity Value of $1,000, Debt of $200, and Cash of $800. If you use Debt / (Equity Value + Debt – Cash), Debt represents 50% of the company’s capital structure! But that’s incorrect for this type of company; the ~17% Debt produced by the traditional method is much closer to reality.

Answer 67

Because it offers higher risk and higher potential returns. Expected stock market returns (plus dividends) exceed the yield to maturity on Debt in most cases, which, by itself, makes the Cost of Equity higher. But the interest on Debt is also tax-deductible, which further reduces the Cost of Debt and makes Equity more expensive. In developed markets, the average annualized stock market return is often in the 7-10% range, so a company with a Levered Beta of 1.0 will have a Cost of Equity in that range. For the Cost of Debt to be higher, the Pre-Tax Cost would have to be ~9-13% at a 25% tax rate. Outside of highly leveraged and distressed companies, corporate bond yields in that range are uncommon when government bond yields are close to 0% (or even below it).

Answer 68

Preferred Stock tends to be more expensive than Debt but less expensive than Equity: it offers higher risk and potential returns than Debt, but lower risk and potential returns than Equity. That’s because the coupon rates on Preferred Stock tend to be higher than the coupon rates on Debt (and the same with the YTMs), and Preferred Dividends are not tax-deductible. But these yields are still lower than expected stock market returns. The risk is also lower since the Preferred Stock investors have a higher claim to the company’s Assets than the common shareholders.

Answer 69

These Costs represent what the company would pay if it issued additional Debt or additional Preferred Stock. There is no way to observe these costs directly, but you can estimate them. For example, you could calculate the weighted average coupon rate on the company’s existing Debt or Preferred Stock or the median coupon rate on the outstanding issuances of comparable public companies. You could also use the Yield to Maturity (YTM), which reflects both the coupon rates on bonds and their market values (e.g., a bond with a coupon rate of 5% that’s trading at a discount to par value will have a YTM higher than 5%). Finally, you could also take the Risk-Free Rate and add a default spread based on the company’s expected credit rating if it issues more Debt or Preferred Stock. If you think its credit rating will fall from BB+ to BB after issuing Debt, you’d look up the average spread for BB-rated companies and add it to the Risk-Free Rate.

Answer 70

If the company’s current share price exceeds the conversion price of the bonds, you count the bonds as Equity and use a higher diluted share count, resulting in a higher Equity Value for the company and a greater Equity weighting in the WACC formula. But if the bonds are not currently convertible, you count them as Debt and use the YTM of equivalent, non-convertible bonds to calculate the Cost of Debt. You cannot use the stated coupon rate on convertible bonds or even their YTM because convertibles offer lower coupon rates than standard corporate bonds – due to the value of the conversion option. But if the bonds cannot convert into Equity, you must count them as traditional Debt. Convertible bonds usually reduce WACC when they count as Debt since the Cost of Debt is lower than the Cost of Equity (but this result may not hold for highly leveraged companies due to the “U-shaped curve” for WACC).

Answer 71

The Cost of Equity and the Cost of Debt always increase because more Debt increases the risk of bankruptcy, which affects all investors. As a company goes from no Debt to some Debt, WACC initially decreases because Debt is cheaper than Equity, but it starts increasing at higher levels of Debt as the risk of bankruptcy starts to outweigh the cost benefits of Debt. However, the exact impact depends on where the company is on that curve. If the company already has a very high level of Debt, WACC is likely to increase with more Debt; at lower levels of Debt, WACC is more likely to decrease with more Debt.

Answer 72

It depends on how you’re calculating WACC. If you’re using the company’s current capital structure, WACC will most likely increase because 20% Debt is a fairly low level. At that low level, the benefits of Debt tend to outweigh its risks, so less Debt will increase WACC. But if you’re using the targeted, optimal, or median capital structure from the comparable companies, this change won’t affect WACC because you’re not using the company’s current capital structure at all.

Answer 73

Yes, sometimes it makes sense to use different Discount Rates. For example, if a company is growing quickly right now but is expected to grow more slowly in the future, you might decrease the Discount Rate each year until the company reaches maturity. So, if the company’s current WACC is between 11% and 13%, and WACC for mature companies in the industry is between 8% and 9%, you might start it at 12% and then reduce it by 0.4% in each year of the explicit forecast period until it reaches 8.4% by the end. It makes less sense to do this if the company is already mature.

Answer 74

Most companies have small Finance Lease balances that they group with Debt; if that is the case, Finance Leases don’t affect much because they’re small and are already considered a form of Debt in the Discount Rate calculations. You could argue that Finance Leases are not “capital” and remove them from the Debt balances. If you do that, the Discount Rate would likely increase slightly (since Debt and Finance Leases are both cheaper than Equity), but the difference would be marginal. Operating Leases are more significant, and it’s easiest not to count them in in WACC at all and deduct the full Operating Lease Expense in the UFCF projections. If you want to count Operating Leases as capital, you need to look up the Cost of Leases in the company’s filings, add another term for Leases when un-levering and re-levering Beta, and add a term for Leases in the WACC formula (see below).

Answer 75

It’s fair to say that certain components of WACC, such as the Risk-Free Rate, Equity Risk Premium, and Cost of Debt, tend to be higher for the EM company. And if the Levered Beta numbers are similar or higher for the EM company, and the capital structure percentages are similar, yes, WACC should be higher as well. However, there are cases where differences in the capital structure or strange results for Levered Beta might result in a similar or lower WACC for the EM company. For example, if the government heavily controls the company’s industry in the emerging market, Levered Beta might be lower for the EM company due to the reduced volatility.

Answer 76

The company’s Free Cash Flow Growth Rate, and possibly its Discount Rate, change over time in the explicit forecast period since the company is still growing and changing. But in the Terminal Period, you assume that the company remains in a “steady state” forever: Its Free Cash Flow grows at the same rate each year, and its Discount Rate remains the same

Answer 77

The same as an integral in calculus = you have projected cash flows in a line, and you're summing the area under that line to give you a total value. That total value is worth less if the discount rate is higher, and worth more if the FCF growth rate is higher.

Answer 78

It’s better to start with the multiples from the Public Comps, ideally the ones from 1-2 years into the future, because you don’t want to reflect the control premium in the Precedent Transactions if you’re completing a standalone valuation of the company. If the selected multiples imply a reasonable Terminal FCF Growth Rate, you might stick with your initial guess; if not, adjust it up or down as necessary

Answer 79

This growth rate should be below the country’s long-term GDP growth rate and in-line with other macroeconomic variables like inflation. For example, if you’re in a developed country where the expected long-term GDP growth rate is 3.0%, you might use numbers ranging from 1.0% to 2.0% for the range of Terminal Growth Rates. You should NOT pick a rate above the country’s long-term GDP growth rate because the company will become bigger than the economy as a whole if you go far enough into the future. You can then check your work by calculating the Terminal Multiples implied by these growth rates.

Answer 80

Because the Terminal Value represents the Present Value of the company’s cash flows from the end of the explicit forecast period into perpetuity. In other words, it represents the company’s value AT a point in the future. Valuation tells you what a company is worth TODAY, so any “future value” must be discounted to its Present Value. If you did not discount the Terminal Value, you’d greatly overstate the company’s Implied Value because you’d be acting as if its Year 6, 11, or 16 cash flows arrived in Year 2 instead.

Answer 81

No. The Terminal Value does represent the Present Value of cash flows starting in Year 11, but it’s the Present Value as of the end of Year 10. You would use 11 for the discount period only if your explicit forecast period went to Year 11 and the Terminal Period started in Year 12.

Answer 82

If you’re building a Levered DCF analysis, you’re almost done because this summation gives you the company’s Implied Equity Value. The last step is to divide the company’s Implied Equity Value by its diluted share count to get its Implied Share Price (if the company is public). In an Unlevered DCF, the PV of Terminal Value + PV of Free Cash Flows equals the company’s Implied Enterprise Value, so you have to “back into” the Implied Equity Value and then calculate its Implied Share Price. You do this by adding non-operating Assets (Cash, Investments, etc.) and subtracting Liability and Equity items that represent other investor groups (Debt, Preferred Stock, Noncontrolling Interests, etc.). Then, you divide by the company’s diluted share count to get its Implied Share Price.

Answer 83

In theory, yes. Some academic sources use Black-Scholes to value these out-of-the-money options and then subtract them to determine the company’s Implied Equity Value. In practice, banks rarely include out-of-the-money options in a DCF. These options tend to make a small impact on most companies, and options valuation is tricky and requires inputs that you may or may not have. So, it is usually not worth the time and effort.

Answer 84

It’s an iterative process: you start by entering a range of assumptions for the Terminal Multiple or Terminal FCF Growth Rate, and then you cross-check your assumptions by calculating the Growth Rates or Multiples they imply. If it seems wrong, you adjust the range of Terminal Multiples or Terminal FCF Growth Rates until you get more reasonable results. Example: You start by picking 10x TEV / EBITDA for the Terminal Multiple. At a Discount Rate of 12%, this multiple implies a Terminal FCF Growth Rate of 5%, which is too high. So, you reduce it to 6x TEV / EBITDA, but now the Implied Terminal FCF Growth Rate drops to 1%, which is too low. So, you guess 8x TEV / EBITDA, which implies a Terminal FCF Growth Rate of 2.3%. That is more reasonable since it’s below the expected long-term GDP growth rate but slightly above the inflation rate. This 8x figure might be your “Baseline Terminal Multiple,” so you would start there and go slightly above and below it in the sensitivity tables.

Answer 85

The biggest issue is that EBITDA ignores CapEx. Two companies with similar TEV / EBITDA multiples might have very different Free Cash Flow and FCF growth figures. As a result, their Implied Values might differ significantly even if they have similar TEV / EBITDA multiples. You may get better results by using TEV / EBIT, TEV / NOPAT, or TEV / Unlevered FCF, but those multiples create other issues, such as less comparability across peer companies. This problem is one reason why the Gordon Growth Method is still the “real” way to calculate Terminal Value.

Answer 86

Yes. For example, if you’re valuing a biotech or pharmaceutical company and the patent on its key drug expires within the explicit forecast period, it might be reasonable to assume that the company never replaces the lost revenue from this drug, which results in declining cash flow. A negative Terminal FCF Growth Rate represents your expectation that the company will stop generating cash flow eventually (even if it happens decades into the future). It doesn’t make the company “worthless”; the company is just worth less.

Answer 87

The same assumptions make a big impact in any DCF: the Discount Rate, the Terminal FCF Growth Rate or Terminal Multiple, and the key operational drivers that affect the company’s revenue growth and margins. These drivers could be entire scenarios or specific numbers, such as the long-term price of steel, depending on the model setup. It doesn’t make sense to sensitize much else – the assumptions for CapEx and the Change in Working Capital, for example, tend to make a small difference. There may also be industry-specific assumptions that are worth sensitizing, such as the patent expiration dates for drugs in the biotech/pharmaceutical industry.

Answer 88

The Discount Rate and Terminal Value make the biggest impact on the DCF. That’s because the Discount Rate affects the PV of everything and because the PV of the Terminal Value often represents 50%+ of the company’s Implied Value. The assumptions for revenue growth and operating margins also make a significant impact, but less than the ones above. Other items, such as CapEx, Working Capital, and non-cash adjustments, make a smaller impact for most companies.

Answer 89

Assuming that both companies have the same capital structure percentages, the Cost of Equity and WACC should be higher for the $500 million company. All else being equal, smaller companies tend to offer higher potential returns and higher risk than larger companies, which explains why the Cost of Equity will be higher. Since smaller companies have a higher chance of defaulting on their Debt, their Cost of Debt (and Preferred) also tends to be higher. And since all these Costs tend to be higher for smaller companies, WACC should be higher as well, assuming the same capital structure percentages

Answer 90

The Discount Rate increase will make a bigger impact. Increasing the revenue growth from 9% to 10% will barely affect the FCF and Terminal Value, but the Discount Rate will affect the Present Value of everything, and 9% vs. 10% is a significant difference.

Answer 91

It’s harder to tell here. Doubling a company’s revenue growth could make a bigger impact than changing the Discount Rate by 1%, but when the changes are this different, you’d have to run the numbers to tell. These operational changes make a bigger impact in longer projection periods than in shorter ones, so you would see more of a difference in a 10-year DCF than a 5-year one.

Answer 92

This is a trick question because it depends on what you count toward the Implied Value. If it’s just this series of cash flows, Company A will have the higher Implied Value because of the time value of money: the cash flows arrive earlier, so they’re worth more. However, Company B will almost certainly have a much higher Terminal Value because it has a much higher FCF in Year 10. So, if the Implied Value = PV of FCFs + PV of Terminal Value, Company B will have the higher Implied Value.

Answer 93

The tax rate affects the Cost of Equity, Cost of Debt, and WACC only if the company has Debt. If the company does not have Debt, or its targeted/optimal capital structure does not include Debt, the tax rate doesn’t matter because there’s no tax benefit from Debt in that case. If the company has some Debt, a higher tax rate will reduce the Cost of Equity, Cost of Debt, and WACC. It’s easy to see why it reduces the Cost of Debt: since you multiply by (1 – Tax Rate), a higher tax rate reduces the after-tax cost. But it also reduces the Cost of Equity for the same reason: with a greater tax benefit, Debt is less risky even to Equity investors. If both of these Costs are lower, WACC will also be lower. However, the Implied Value from a DCF will also be lower because the higher tax rate reduces the FCF and the Terminal Value, and these changes outweigh a lower WACC. The opposite happens with a lower tax rate: the Cost of Equity, Cost of Debt, and WACC are all higher, and the Implied Value is also higher.

Answer 94

The discount rate represents the expected return on an investment based on its risk profile (meaning, the discount rate is a function of the riskiness of the cash flows). Put another way, the discount rate is the **minimum return threshold or "hurdle rate" of an investment** based on comparable investments with similar risks. A higher discount rate makes a company's cash flows less valuable, as it implies the investment carries a greater amount of risk, and therefore should be expected to yield a higher return (and vice versa).

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