DCF Flashcards
When calculating a terminal value in perpetuity, why would the growth rate of a company never exceed the discount rate?
The growth rate of a company can exceed the cost of capital for a short period, but in PERPETUITY a company whose growth rate exceeds the cost of capital would either be
1) riskless arbitrage
2) attract all the money in the world to invest in it, and would eventually become the whole economy
How does terminal value change when risk free rate increases / what is risk free rate?
Cost of Equity increases, so WACC increases, and TV decreases. The risk-free rate is the yield on risk-free government security, like the 10 year Treasury.
Companies at Beta of 1,0,-1
TBD
Beta of 1 = same as market risk, could be stocks like Industrials that oscillate with the market, but aren’t over 1 like Tech
Beta of 0 = companies whose equity returns are not sensitive to market return. Could be any company with a constant demand product: Tobacco, Insurance
Beta of -1 = counter-cyclical companies, companies that have greater returns when the market is doing poorly: Liquidation firms, Gold Mining (store of value)
How do you know if your terminal value assumption is reasonable from GGM?
If it’s a reasonable terminal growth rate for the economy you’re in. The US economy has an average growth rate of 2-3%.
You could also use the rate of inflation, or something similarly conservative.
For most developed countries, a long-term growth rate of over 4-5% would be too aggressive to use.
Why might two companies have a different cost of equity?
They have different betas. Higher beta = higher COE
Describe how to value a privately held company
Valuation for a private company is the same as the valuation of a public company with some complications, particularly as it relates to DCF (discounted cash flow). Because a private company has no publicly traded equity, a beta cannot be directly computed.
To find the cost of equity (COE)
- Estimate the total value of the private company based on comparables (use average EV/EBITDA)
- Deduct the value of the debt to get estimated “market” value of equity
- Get the average levered beta from the comparables and unlever it
- Re-lever the beta for the private company based on the target D/E (debt-to-equity) ratio
- Calculate COE based on CAPM (capital asset pricing model)
To find the cost of debt (COD)
- Some privately held companies have publicly traded debt – so look up trading yields to estimate COD
- Alternatively, estimate what the credit rating of the company would be based on comparables (look at credit statistics). For estimated credit ratings, use current market yields for similarly rated companies to determine COD
Then calculate WACC as normal and DCF as normal
Impact on WACC when
1) you increase Equity
2) you increase Debt
3) you increase Preferred Stock
COE > COPS > COD
The cost of equity is always the greatest.
1) An increase in Equity means an increase in WACC, because COE is the highest cost
2) An increase in Debt means an overall decrease in WACC, bc COD < COE. However, an increase in Debt increases the COE because as Debt increases investing in Equity becomes riskier = Debt increases the chances of the company defaulting and leaving the common shareholder with nothing.
3) An increase in Preferred Stock is more nebulous = has a lower cost than equity but higher than debt. (COPS < COD bc Preferred Stock dividends are not tax-deductible, unlike interest for Debt)
Impact on COE with
1) changes in risk-free rate
2) changes in Equity Risk Premium
3) change in Debt
1) Rf increase = COE increase, Rf decrease = COE decrease
2) ERP increase = COE increase, ERP decrease = COE decrease
3) COE increase
increases the COE because as Debt increases investing in Equity becomes riskier = Debt increases the chances of the company defaulting and leaving the common shareholder with nothing
Do you ever use Unlevered Beta when calculating the COE? Why/Why not?
No, because the Beta of a company should reflect both the inherent business risk (Unlevered Beta) and the risk of Debt (Levered Beta). Using just Unlevered Beta would be an incomplete measure of a company’s overall risk.
This is independent of Levered/Unlevered FCF = common conceptual trick question.
What’s the basic concept of a DCF?
The concept is that you value a company based on its present value of 1) future cash flows in the near future of 5-10 years and 2) terminal value in the far future.
You need to discount to present value because money today is worth more than money tomorrow.
Walk me through a DCF
A DCF values a company based on the present value of its future cash flows and terminal value.
1) you project a company’s financials using assumptions about revenue growth, operating margin, and change in operating assets & liabilities.
2) you calculate FCF for each year in near future, discounting to present value with a discount rate, usually WACC
3) determine the company’s Terminal Value via Perpetual Growth or Multiples, and discount back to present value also using the discount rate.
4) sum the PV of FCF and PV of Terminal Value for implied valuation
***IMPORTANT
Walk me through how you get from Revenue to FCF in the projections
Unlevered FCF
Revenue
- COGS
- Operating Expenses
= EBIT
EBIT(1 - TaxRate)
+ D&A, non-cash charges
+/- net change OWC (Assets larger, subtract. Liabilities larger, add)
- CapEx
Levered FCF (differences)
EBIT
- net interest expense
= EBT
EBT(1-Tax Rate)
at end, subtract Mandatory Debt Repayments
What’s the point of FCF? What are you trying to do?
You’re replicating the CF statement with only recurring, predictable items. UFCF you exclude Debt impact entirely.
That’s why whole CFI (except CapEx) and CFF (LFCF except Mandatory Debt Repayments) are excluded.
Why do you use 5 or 10 years for “near future” DCF projections?
Bc that’s about as far as you can predict for most companies. Less than 5 is too short to be useful, 10 is too long to have predictable patterns.
Is there a valid reason for why you might project 10 years or more anyway?
You might do this in a cyclical industry, such as chemicals, but it would be important to show an entire cycle from high to low.
What do you usually use for the Discount Rate?
UFCF = WACC
LFCF = Cost of Equity
If I’m working with a public company in a DCF, how do I move from implied Enterprise Value to Implied per Share Value?
You use the TEV/EqV bridge.
TEV
+ Cash (non-operating assets)
- Debt (equity & liability items due to other investor groups)
- Non-Controlling Interests
- Preferred Stock
Divide by diluted share count for implied per Share price.
If we find from a DCF that the Implied Price per Share value is $10, but the current market share price is $5, what does that mean?
By itself, it doesn’t mean much. You have to look for a range of outputs from a DCF rather than a single number via a sensitivity table that would show Implied Price per Share under different assumptions for Discount Rate, revenue growth, margins, etc.
If you consistently find that Implied Price per Share across that range is greater than the market price, the company might be undervalued. Vice versa for overvalued.
An alternative to the DCF is the Dividend Discount Model (DDM). How is it different in the general case (ie, for a normal company, not a commercial bank or insurance firm).
In this you still project revenue and expenses over a near term, and calculate Terminal Value.
However, you don’t calculate FCF. Instead, you stop at Net Income and assume the Dividends issued are a percentage of Net Income. You then discount those Dividends back to PV using COE as a discount rate.
You then add those up and add them to a PV of Terminal Value, which you might base on a P/E multiple instead.
Ending is Implied Equity Value, because you’re using metrics that include net interest expense.
When calculating FCF, is it always correct to leave out most of the CFI and CFF sections of the CF statement?
Yes, most of the time. Because items other than CapEx are generally not predictable/recurring.
If you can predict a change in CFF (buy/sell debt, sell/repurchase stock) or CFI (buy/sell securities) then you can factor that in. Extremely rare.
Why do you add back non-cash charges when calculating FCF?
Same as accounting: you want to reflect the fact they save the company in taxes, but they’re not an actual cash expense.
What are different methods for calculating UFCF?
Different methods result in different tax numbers (as a result of when you exclude the interest)
Method 1)
Revenue
- COGS
- OpEx
= EBIT
EBIT(1 - Tax Rate)
+ recurring non-cash expenses (D&A)
+/- changes in OWC
- CapEx
Method 2)
CFO
+ tax-adjusted net interest expense
- CapEx
Method 3)
Net Income
+ tax-adjusted net interest expense
+ non-cash charges
+/- changes in OWC
- CapEx
What are different methods for calculating LFCF?
Method 1)
EBIT
- net interest expense
= EBT
EBT(1 - TaxRate)
+ non-cash expenses
+/- change OWC
- CapEx
- Mandatory Debt Repayments
Method 2)
Net Income
+ non-cash charges
+/- changes in OWC
- CapEx
- Mandatory Debt Repayments
Method 3)
CFO
- CapEx
- Mandatory Debt Repayments
As an approximation, do you think it’s okay to use EBITDA - changes OWC - CapEx to estimate UFCF?
No bc this excludes taxes entirely.
If you add the impact of taxes that might work as a quick approximation.
What’s the point of “Changes in Operational Assets and Liabilities” section? What does it mean?
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.
What happens in a DCF if a cash flow is negative? What if EBIT is negative?
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.
If you use LFCF instead of UFCF, what changes in a DCF?
1) discount rate is COE
2) resulting valuation is Implied Equity Value
Let’s say that you use UFCF in a DCF to calculate TEV, then you use the company’s Cash, Debt, etc to calculate EqV.
Then you run an analysis using LFCF instead and calculate EqV. Will the results of both of these analyses be the same?
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
How do you calculate WACC?
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
How do you calculate the Cost of Equity?
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
COE tells you the return an equity investor might expect for investing in a given company, but what about dividends? Shouldn’t dividend yield be factored into the formula?
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.
How can we calculate COE without using CAPM?
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.
How do you calculate Beta?
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)]
Why do you have to unlever then relever Beta when using Comps?
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.
Would you still use Levered Beta with UFCF?
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.
How do you treat Preferred Stock in the formulas for Beta?
In calculating Beta, Preferred Stock is treated as Equity because Preferred Dividends are not tax-deductible, unlike interest paid on debt.
Can Beta ever be negative? What would that mean?
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.
Would you expect a technology or manufacturing company to have a higher Beta?
Technology companies are generally viewed as “riskier” industry than manufacturing, and therefore would have higher Betas.
Shouldn’t you use a company’s targeted capital structure rather than its current capital structure when calculating the Discount Rate?
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.
The Cost of Debt and Preferred Stock make intuitive sense because the company is paying interest or Preferred Dividends. What the company really paying?
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
What advantages does UFCF have over other types of FCF?
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
Do you include ALL non-cash expenses when projecting FCF?
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
For a DCF: what would be an appropriate forecast period, terminal growth rate, equity risk premium, beta and more importantly why?
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?
When would your cost of debt be higher than your cost of equity and give me an example.
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.
What happens to
1) Unlevered FCF
2) Terminal value
3) Kd
when Rf goes up?
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
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?
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.
How do you determine a firm’s Optimal Capital Structure? What does it mean?
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.
