3.8) DCF Analysis - Discount Rates and WACC

Question 1

In very concise terms complete: the Discount rate represents the [=] and the Debt and Equity levels affect [=].

Answer 1

The Discount rate represents the [opportunity cost] and the Debt and Equity levels affect [all investors].

Question 2

1. What does the Cost of Equity mean intuitively?

Answer 2

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.

Question 3

2. What does WACC mean intuitively?

Answer 3

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.

Question 4

3. How do you calculate the Cost of Equity?

Answer 4

Cost of Equity = Risk-Free Rate + Equity Risk Premium * Levered Beta

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.

And the 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.

Question 5

4. If a company operates in the EU, U.S., and U.K., what should you use for its Risk-Free Rate?

Answer 5

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.

Question 6

5. What should you use for the Risk-Free Rate if government bonds in the country are NOT risk-free (e.g., Greece)?

Answer 6

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.

Question 7

6. How do you calculate the Equity Risk Premium?

Answer 7

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.

Question 8

7. How do you calculate the Equity Risk Premium for a multinational company that operates in many different geographies?

Answer 8

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.

Question 9

8. What does Beta mean intuitively?

Answer 9

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.

Question 10

9. Could Beta ever be negative?

Answer 10

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.

Question 11

10. Why do you have to un-lever and re-lever Beta when calculating the Cost of Equity?

Answer 11

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.”

Question 12

11. What are the formulas for un-levering and re-levering Beta, and what do they mean?

Answer 12

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.

Question 13

12. The formulas for Beta do not factor in the interest rate on Debt. Isn’t that wrong? More expensive Debt should be riskier.

Answer 13

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.

Question 14

13. Do you still un-lever and re-lever Beta even when you’re using Unlevered FCF?

Answer 14

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 re-lever Beta regardless of the type of Free Cash Flow you’re using.

Question 15

14. What are some different ways to calculate Beta in the Cost of Equity calculation?

Answer 15

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.

Question 16

15. How would you estimate the Cost of Equity for a U.S.-based high-growth technology company?

Answer 16

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 1.3% for 10-year U.S. Treasuries. A high-growth tech company is more volatile than the market as a whole, with a likely Beta of around 1.5. So, if you assume an Equity Risk Premium of 6%, the Cost of Equity might be around 10.3%.” The specific numbers will change over time, but that’s the idea.

Question 17

16. How do you calculate WACC, and what makes it tricky?

Answer 17

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.

Question 18

17. WACC reflects the company’s entire capital structure, so why do you pair it with Unlevered FCF? WACC is not capital structure-neutral!

Answer 18

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.

Question 19

18. Should you use the company’s current capital structure or optimal capital structure to calculate WACC?

Answer 19

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.

Question 20

19. Should you use Total Debt or Net Debt to determine the capital structure percentages in the WACC calculation?

Answer 20

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.

Question 21

20. Why is Equity more expensive than Debt?

Answer 21

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).

Question 22

21. How does the Cost of Preferred Stock compare with the Cost of Debt and the Cost of Equity?

Answer 22

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.

Question 23

22. How do you determine the Cost of Debt and Cost of Preferred Stock in the WACC calculation, and what do they mean?

Answer 23

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.

Question 24

23. How do convertible bonds factor into the WACC calculation?

Answer 24

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).

Question 25

24. How do the Cost of Equity, Cost of Debt, and WACC change as a company uses more Debt?

Answer 25

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.

Question 26

25. If a company previously used 20% Debt and 80% Equity, but it just paid off all its Debt, how does that affect its WACC?

Answer 26

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.

Question 27

26. Should you ever use different Discount Rates for different years in a DCF?

Answer 27

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.

Question 28

27. How do Operating Leases and Finance Leases affect the Discount Rate?

Answer 28

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).

Question 29

28. If you count Operating Leases as a form of capital, how do the Cost of Equity and WACC calculations change?

Answer 29

If you calculate the Cost of Equity based on the company’s historical Beta, nothing changes.

If you un-lever Beta for each comparable company and then re-lever it, you add an extra term for the Leases:

Unlevered Beta = Levered Beta / (1 + Debt / Equity * (1 – Tax Rate) + Leases / Equity * (1 – Tax Rate) + Preferred Stock / Equity)

Levered Beta = Unlevered Beta * (1 + Debt / Equity * (1 – Tax Rate) + Leases / Equity * (1 – Tax Rate) + Preferred Stock / Equity)

And in the WACC formula, you do the same:

WACC = Cost of Equity * % Equity + Cost of Debt * (1 – Tax Rate) * % Debt + Cost of Leases * (1 – Tax Rate) * % Leases + Cost of Preferred Stock * % Preferred Stock

The Cost of Leases is based on the discount rate the company uses in its filings to calculate the Present Value of its Lease Liabilities.

Question 30

29. All else being equal, will counting all Leases as “capital” increase or decrease the Cost of Equity, Cost of Debt, and WACC?

Answer 30

If you treat Leases this way, the Cost of Debt should not change because Debt and Leases are now separate items, and the Cost of Debt is still based on the YTM of the company’s bonds (it might be slightly different if you remove Finance Leases from Total Debt). The Cost of Equity will stay the same or decrease slightly because the Unlevered Beta figures from the public comps will be lower if Leases are considered a form of leverage. But anything could happen when you re-lever Beta, so this change might be marginal.

WACC will usually decrease because Leases are, effectively, low-cost Debt, and Debt is already cheaper than Equity. Also, the entire Lease Expense, like interest on Debt, is tax-deductible. There may be exceptions for highly leveraged companies and ones with huge or expensive lease portfolios; past a certain point, the extra risk might outweigh the benefits.

Question 31

30. Suppose you’re calculating WACC for two similarly sized companies in the same industry, but one company is in a developed market (DM), and the other is in an emerging market (EM). Will the EM company always have a higher WACC?

Answer 31

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.