Part 2 – Lesson 7

### What are the different types of discount rates?

The discount rate we use in a valuation can be defined in different ways depending on the type of cash flow we are discounting.  If we are discounting payments on a debt security, we should use the cost of debt as the discount rate.  If we are discounting levered free cash flow (post-interest expense), we should use the cost of equity as the discount rate.  If we are discounting unlevered free cash flow (pre-interest expense), we should use a weighted average cost of capital (WACC) in our valuation.

1. Cash flow to debt holders → Discount using cost of debt
2. Cash flow to equity holders → Discount using cost of equity
3. Cash flow available to debt and equity holders → Discount using weighted average cost of capital (WACC)

The discount rate we have used in many of the prior lessons has been the cost of equity since we were referencing returns available to equity holders of an investment.

### Cost of equity vs. Cost of debt

In Part 1, Lesson 12, we discussed how to calculate free cash flow to equity holders.  Please review this lesson for detail on calculating free cash flow.  As a reminder, free cash flow to equity is the total amount of cash flow a company generates and is available for distribution to equity holders.  Therefore, this cash flow amount is after interest expense has been paid on debt.  If we’d like to value the equity using a discounted cash flow analysis, we’d have to project out future years of free cash flow, estimate our terminal value, and then discount these cash flows by our cost of equity.

Prior to learning how to calculate cost of equity, let’s discuss what exactly cost of equity means.  When a company is deciding how to fund a new project, there are really three ways it can fund this project: 1) use cash generated internally by the operations of the company, 2) use cash generated by issuing new equity, or 3) use cash generated by issuing new debt.  When a company uses cash that was generated by the business, this is really the cheapest form of financing it can use since the company does not need to issue new equity or debt.  Some may argue that using internally generated cash does have a cost since that cash could have been used to paydown debt or buyback equity, but in practice, most investors prefer the use of internally generated cash to fund investment priorities of the company.

Debt is typically the next cheapest form of financing.  This is because debt has higher priority in the capital structure, therefore, lenders generally offer a lower cost of financing relative to equity.  In other words, since debt holders will be paid back prior to any equity holders, debt holders are taking less risk than equity holders.  By taking less risk than equity holders, the cost of debt should generally be lower than the cost of equity.  Remember – the cost of debt to the company is the return on debt to the lender.  The cost of debt is also considered on an after-tax basis.  To calculate after-tax cost of debt, you’ll simply take the cost of debt and multiply it by (1 – tax rate):

After-Tax Cost of Debt = Pre-Tax Cost of Debt * (1 – tax rate)

Lastly, equity is considered the most expensive form of financing.  Equity holders are paid last in the capital structure stack and therefore take the most risk in the business.  For taking increased risk, the required return that an equity investor expects is typically high.  Remember – the cost of equity to the company is the return on equity to the investor.

The level of the required return that an equity investor or a lender will require is based on the inherent risk in the business.  In Part 2, Lesson 5, we outlined several factors that drive discount rate levels such as financial leverage, growth rates, quality of management team, quality of product, company margins, industry outlook, competitive dynamics, etc.  These are some of the many factors that equity and debt investors will consider when pricing what their equity or debt investment will cost the company.

### Illustration – John’s Pizzeria

Let’s assume that John starts John’s Pizzeria with \$100,000 of his own cash.  Initially, he owns 100% of the company’s equity.  For taking all the risk, John will earn 100% of the returns after paying all his costs.

Question – Let’s assume that John needs to borrow \$50,000 to fund his business.  If the lender charges 5% for this loan, what is John’s Pizzeria’s cost of debt on a pre-tax and post-tax basis?  Assume the tax rate is 40%

Answer – The pre-tax cost of debt is 5%.  The cost of debt is simply the interest expense that the lender will charge on the loan.  The post-tax cost of debt is 3%, which is calculated as 5% * (1 – 40%) = 3%.  Since John will take a deduction on interest expense, which will allow him to save 40 cents in taxes on every dollar of interest expense paid, the cost of debt is lowered to 3% on an after-tax basis.  This is, however, only possible if John has positive pre-tax income.

Question – John is unable to take on more debt, so he needs to find an equity partner to help him expand his business.  Let’s assume that John’s Pizzeria is currently generating \$20,000 in net income, John has thus far invested \$100,000 of equity into the business, and he needs to raise \$20,000 in equity from another partner.  What is John’s Pizzeria’s cost of equity?

Answer – The cost of equity is 20%, which is calculated as the net income of \$20,000 divided by the equity capital of \$100,000.  Remember, the cost of equity to the company is the return on equity earned by the investor.  Since the equity in John’s Pizzeria is currently earning a 20% return on equity, this is also the cost of equity if John needs to issue new equity to a new investor.  Another way to think of this is that if John raises \$20,000 in new equity, then, he will need to generate another 20% in net income on the new \$20,000 of equity to not dilute his prior earnings level.

Question – After taking on his first equity partner, John’s Pizzeria now has equity capital of \$120,000, but John’s Pizzeria’s net income has dropped to \$6,000.  What is John’s Pizzeria’s cost of equity?

Answer – The cost of equity is 5%, which is calculated as \$6,000 of net income divided by \$120,000 in equity capital.  In this example, if John can find a second equity investor at this level, he would be issuing equity at a cheaper cost of equity of 5% vs. 20% cost of equity in the prior question.  However, the big question mark in this scenario is if a new equity investor would accept a 5% return or if they would demand a lower valuation of the equity.

For example, if the new investor demanded a \$60,000 valuation of the equity capital, then, this would imply a 10% cost of equity to the company.  Remember – the \$120,000 of equity capital referenced is the book value of equity, but the market value of the equity can fluctuate based on how equity investors would value the company in the open market.

### Can cost of equity and cost of debt change year to year?

The answer to this question depends on the context.

When performing a DCF valuation, we must pick one cost of equity and one cost of debt.  It is too complicated to try to adjust the cost of equity and debt year to year.  Therefore, we project multiple years of cash flow, and then we discount those cash flows to today’s values based on our best view of the average cost of debt and cost of equity on a long-term basis.  If John’s Pizzeria is likely to pay 5% on debt long-term and if the minimum required equity return is likely 10% on a long-term basis, then, the cost of debt used in our DCF valuation should be 5% while the cost of equity should be 10%.

However, in practice, management teams, investors, and lenders must operate under the current conditions of the market.  If debt markets are very tight and financing is very hard to come by, John’s Pizzeria interest expense on new debt may explode to 10%.  This doesn’t mean that John’s Pizzeria’s cost of debt is likely to be 10% on a long-term basis.  Inversely, during very robust times, lenders may be willing to lend at 2%-3% interest rates to John’s Pizzeria.  If John is continually borrowing during both good times and bad times, then, the average cost of debt over the long-term is likely to end up somewhere in between.  Any DCF valuation of a company will implicitly make a simplifying assumption on the long-term cost of debt.

Likewise, the story is similar for equity.  During bad economic times, investors may feel more hesitant to provide equity investments into new businesses and therefore, will require a higher equity return to compensate for the increased perceived risk.  Similarly, when John’s Pizzeria is a new, early stage company, the perceived risk is higher, so investors are likely to require a higher equity return during the early stages of the company.

Inversely, equity investors during good economic times and/or when John’s Pizzeria has matured into a successful business will likely provide equity at lower required rates of return.  Therefore, John’s cost of equity will likely fluctuate over the life of the company, so any DCF valuation of the company will have to make a simplifying assumption on the long-term cost of equity for the business.

### Calculating Cost of Equity

As we’ve previously stated, the cost of equity to the company is the return on equity to the investor.  Therefore, the long-term cost of equity is essentially equal to the long-term return on equity of the business.  However, there are a few important points to consider.

When performing a valuation, such as a DCF valuation, the cost of equity should really be the required minimum return that a new equity investor in that business would need to earn in order to entice them to invest in that business today.  For example, when initially making an investment into John’s Pizzeria, an equity investor may judge that he/she needs a 10% equity return to satisfy the risks they would be taking.

However, if John’s Pizzeria subsequently ends up returning 40% to equity holders over the next few years, then, what is John’s cost of equity at that point?  It again depends on the context.

On a go forward basis, the cost of equity should still be 10% since this is still the minimum required level that new investors in the business will need.  However, previously issued equity did end up costing the company 40% due to how well the company did.  Had John issued debt instead of equity, then, in retrospect, John would have saved the company from sharing a lot of its profits.  However, on a go forward basis, John’s Pizzeria’s cost of equity is not 40%.  It should simply be the level at which new investors would be willing to invest in the company (which is 10% in this case).

In other words, the cost of equity is the minimum return equity investors require based on their perceived risk of the business at the time of the investmentOver the course of the investment, the equity return achieved may differ substantially than the initial cost of equity that was used in valuing the initial equity investment.

So how should we calculate cost of equity?

As you may have picked up, the cost of equity is subjective and based on the required return investors need to compensate for the risk of the investment.  There are various methods for calculating cost of equity, but when performing a DCF of a publicly traded company, investors may use the Capital Asset Pricing Model.

### Capital Asset Pricing Model

Risk of an Asset = Risk Free Rate + Beta * (Equity Market Premium)

In the above formula, the risk of the asset is the cost of equity that we are seeking to solve for.

The risk-free rate is the long-term expected return of a risk-free asset, which in the United States, we assume to be US federal debt.  Since we assume the federal government will never default on their debt, we can use the return of the 10-year treasury note as our risk-free rate.  This is the rate at which the federal government borrows from the public.

Beta is a measure of the risk of an asset relative to the risk of the market.  For a publicly traded stock, this is can be calculated as the statistical correlation of the past returns of the company relative to the returns of the market.  Most investors use the S&P 500 index to measure the returns of the market.  Let’s look at an example of calculating beta in Excel (Part 2 Excel Download): In the above example, we have downloaded the monthly returns of GOOGL vs. the S&P 500 index.  When calculating beta, there is no official standard as to the type of historical returns to use.  Generally, it is better to use a longer history.  Our recommendation would be to use monthly returns for 5 years at a minimum.  In this example, we have used monthly returns for 2.5 years just for illustration purposes.

After plotting monthly returns of the index vs. the company, you can use the SLOPE function in Excel to calculate Beta.  The slope function simply gives you the slope of the trendline between the x-axis values (the S&P 500 returns) vs. the y-axis values (GOOGL returns).

The trendline is a measure of the statistical relationship between these two data sets.  If the trendline had a slope of 1, this would imply that the market’s return correlates perfectly with the return of the company.  In other words, if GOOGL’s returns and the S&P 500 returns matched perfectly, then the slope of the trendline would be 1.  In practice, no company will ever have a slope of 1 since no company’s returns will ever match the S&P 500 returns perfectly.

Therefore, the market beta is said to be equal to 1 because the market correlates perfectly with itself.  Any stock beta is viewed relative to the market beta.  When we calculate the slope in the above example, it shows that GOOGL has a beta of 1.58.

Generally, investors will interpret a 1.58 beta to mean that for every 1% move in the market, GOOGL would be expected to move 1.58%.  Of course, this relationship doesn’t hold so nicely in practice, but beta gives an investor a sense for how volatile a stock has been historically.  When investors reference “high beta” stocks, they are referring to stocks with high volatility as measured by beta.  Although “high beta” is a subjective measure, we would call anything in the high 1s beta (or higher) as being “high beta.”  We would characterize stocks with a low 1s (or lower) as being “low beta.”

GOOGL seems to fall in the middle of the range with a 1.58 beta.  It is important to note that his beta could change depending on the time period and frequency (daily, weekly, or monthly) of historical returns used.  The final piece of the CAPM formula that we haven’t discussed yet is the Equity Market Premium.

Equity Market Premium is the excess return of the asset class over the risk-free rate.  Since we are calculating cost of equity, we are interested in measuring the equity market premium of the stock market.  To do this, we would take the long-term return of the S&P 500 and subtract out the 10-year treasury yield.  This gives us how much the market has returned above and beyond the risk-free rate.  In other words, this is the “premium” that an investor was rewarded by taking risk in the equity markets vs. what could have been achieved by simply investing in a risk-less asset such as the 10-year treasury note.

For simplicity, we will assume the long-term return of the S&P 500 is 9% and the 10-year treasury yield is 3.5%.  This implies an equity market premium of 5.5%.  Equity investors have been rewarded with a premium of 5.5% for having taken risk in the market vs. simply buying treasuries.

We can now complete the cost of equity formula for GOOGL:

GOOGL Cost of Equity = 3.5% + 1.58 * (5.5%)
GOOGL Cost of Equity = 12.2%

It is important to always sanity check calculations when building a model.  As an investor, you must ask yourself, does a 12.2% cost of equity make sense for GOOGL?  In our view, the 12.2% cost of equity seems a touch high for a company that has a virtual monopoly in search marketing and consistently high growth rates.  If we were performing a DCF of GOOGL, we would look to double check our inputs such as the historical data being used in determining beta and the equity risk premium being used.

### Calculating Cost of Debt

The cost of debt for a company is simply the rate at which it can borrow money.  It is important to understand that companies can borrow money through many different types of loan products and different maturities, which can have significant impacts on the interest rate.  For example, loans with short maturities will generally have interest rates that are lower than loans with longer maturities.  Loans with longer maturities and a fixed rate usually come at a higher interest cost since lenders need to be compensated for inflation risk.

Additionally, corporate debt can either be secured or unsecured.  Debt that is secured by certain physical assets generally comes with a lower interest rate vs. debt that is unsecured.  Lenders will offer a lower interest rate for secured debt due to the increased safety coming from having a lien on a specific asset.  In the event of default, the lender can fall back on taking ownership of the underlying asset and selling it to recoup what they are owed.  However, with unsecured debt, the lender must rely solely on the company’s ability to repay the loan from its cash flow.  The increased risk associated with unsecured debt generally leads to higher interest costs vs. secured debt.

Banks typically lend money to corporations based on a spread over a commonly used interest rate benchmark.

Cost of Debt = Spread + Interest Rate Benchmark

Commonly used interest rate benchmarks include LIBOR (London Inter-Bank Offer Rate), Federal Funds Rate, Prime, and the 10-Year Treasury to name a few.  Let’s look at each of these briefly:

LIBOR – The London Interbank Offer Rate is one of the most used benchmarks for short-term interest rates globally.  LIBOR represents the rate at which several large global banks are willing to lend to each other on a short-term basis.  These member banks include the likes of Citigroup, Bank of America, HSBC, Deutsche Bank, Royal Bank of Canada, Barclays, UBS, and several others.  LIBOR is quoted for several short-term maturities including 1-day, 1-week, 1-month, 2-month, 3-month, 6-month, and 12-month.  However, the most commonly used reference rate is the 3-month LIBOR.

Corporate short-term debt is very commonly priced off LIBOR.  Since LIBOR changes continuously, the interest rate charged to corporate borrowers will periodically re-adjust based on the then current LIBOR rate.  For example, if Verizon borrows short-term debt at L + 200, this would imply a 4.34% interest rate today.  L is short for LIBOR, which as of July 2018 is 2.34%.  Spreads are usually quoted in “basis points.”  One basis point is equal to .01%, so 200 basis points (bps) is equal to 2.0%.  Adding the 2% spread to the 2.34% benchmark gets us to 4.34%.  If LIBOR increases by 50 bps in the next 3 months to 2.84%, then Verizon’s cost of debt on this borrowing will also increase to 4.84%.  When the cost of debt can change during the loan term based on changes in the underlying benchmark, this is referred to as “floating-rate” or “variable-rate” debt.

Federal Funds Rate – the Federal Funds rate is the rate at which depository institutions in the United States (banks and credit unions) will lend reserves to each other on an over-night basis.  In the United States, the Federal Reserve requires banks to maintain a minimum amount of “reserves” to be held at the Federal Reserve.  These required reserves are federally mandated and typically set at 10% of the value of the deposits that the bank has on its own balance sheet.  The required reserves are seen as a backstop to meet liquidity needs of the bank and to prevent banking crises (such as a run on the bank).  If a bank was running below its required reserve level, it could borrow reserves from another bank that has excess reserves.  The rate at which the bank with excess reserves would lend to the other bank is the Federal Funds rate.

The Federal Funds rate is not officially set by the Federal Reserve, but rather, the Federal Reserve sets a “target range” for the Fed Funds.  As of July 2018, the Fed Funds target range is 1.75%-2.00%.  The Fed Funds rate is an extremely important short-term interest rate in the United States since so much of the short-term debt in the United States is priced off the Fed Funds.  The Fed Funds rate is also one of the primary tools that the Federal Reserve uses in trying to stimulate an economy during bad times (by lowering the Fed Funds rate target) or keep an economy from over-heating in good times (by raising the Fed Funds rate target).

Prime – The prime rate is a short-term interest rate benchmark set by the leading banks in the United States, and it typically follows the federal reserve rate.  As of July 2018, the prime rate is 5.0%, while the federal funds rate target is 1.75%-2.00%.  If the Federal Reserve were to raise the fed funds rate by 25 basis points to 2.00%-2.25%, history would suggest that banks would immediately raise the Prime rate to 5.25%.  The Prime rate is the rate that banks would offer to the highest credit quality borrowers.  For anyone not considered very high credit quality, banks will add a spread to the Prime rate.  Many credit cards and small business loans are priced off the Prime rate.

10-Year Treasury – The 10-year treasury note is the rate at which the federal government can borrow money for 10 years (this is our “risk free rate” that we’ve referenced previously).  Many forms of long-term, fixed rate debt is priced based on a spread to the 10-year treasury.  For example, many commercial real estate loans have a 10-year term, so banks will price these 10-year loans off a spread to the current 10-year treasury rate.  As of July 2018, the 10-year treasury is currently yielding 2.83%.  If a commercial real estate loan were priced at 250 bps over the 10-year treasury, then, this borrower would take out a loan at a 5.33%.  Many commercial real estate loans are fixed-rate, so depending on the terms of the loan, this borrower may be able to borrow at a fixed 5.33% for the full 10 years of the loan.

Cost of Debt = Spread + Interest Rate Benchmark

Let’s assume that Verizon wishes to borrow debt at a fixed rate for 10-years and approaches the large investment banks for a loan.  Verizon may solicit quotes from multiple banks, who may price the loan based on a spread to the 10-year treasury.  Let’s assume Bank A offers a spread of 350 bps, Bank B offers a spread of 325 bps, and Bank C offers a spread of 300 bps.

While the interest rate benchmark is determined based on the benchmark, the spread is determined based on the perceived risk of Verizon’s business.  Banks will analyze the financial health of Verizon, their growth prospects, and the current debt profile of Verizon (amongst other factors) to determine Verizon’s ability to repay and its credit worthiness.  Based on the bank’s assessment of Verizon’s credit worthiness, they will offer pricing accordingly.

To assist banks in the evaluation of large corporate borrowers, credit ratings agencies have formed, which publish research on the credit worthiness of corporate borrowers.  The primary credit rating agencies in the United States are Moody’s, S&P, and Fitch.  These rating agencies will assign “credit ratings” to many large companies who regularly issue debt.  The S&P ratings scale goes from AAA (very high credit quality) all the way down to D (in default).  Many of the banks will use the credit ratings assigned from the rating agencies to assist them with the pricing of the loan they are willing to offer to corporate borrowers.

In this example, Verizon will likely choose to borrow from Bank C at a spread of 300 bps.  With the 10-year currently at 2.83%, this would imply a 5.83% interest rate on this loan.

### How do we pick one cost of debt to use in a DCF analysis?

Similar to the cost of equity, we must make a simplifying assumption when picking our cost of debt in the DCF analysis.  A company’s cost of debt will change continuously over its life based on its credit rating, growth outlook, industry outlook, and other market or macroeconomic factors.  However, predicting how this will change in the future is impossible, so for the cost of debt, we will use the rate at which the company is able to borrow on average over the long-term.

The cost of debt should also reflect the likely mix of short-term vs. long-term debt that a company is likely to use.  For instance, if we were performing a DCF analysis on a company that has all long-term debt, it would be improper to use a cost of debt based on a short-term interest rate.  However, for a company that issues exclusively short-term debt, it may make more sense in this instance to calculate the cost of debt using a short-term rate.

### Weighted Average Cost of Capital (WACC)

Now that we know how to calculate both cost of equity and cost of debt, we will combine these two discount rates into our Weighted Average Cost of Capital (WACC).  The WACC is essentially the combined discount rate to use when valuing the unlevered (pre-interest expense) cash flows of a company.  It uses the relative weighting of equity capital vs. debt capital to calculate a blended discount rate.

Let’s assume the following:

Cost of Equity = 12%
Cost of Debt = 5%
Tax Rate = 40%

Market Value of Equity = \$750 million
Market Value of Debt = \$250 million

What is our WACC?

WACC = Equity / Total Capital * Cost of Equity + Debt / Total Capital * After-Tax Cost of Debt
WACC = (\$750mm / \$1,000mm) * 12% + (\$250mm / \$1,000mm) * (1 – 40%) * (5%)
WACC = 75% * 12% + 25% * 3%
WACC = 9.75%

When calculating WACC, it is important to note the following:

1. We will always use the market value of equity (the market cap) by multiplying the share price by the total shares outstanding
2. We should also use the market value of debt, but in most instances, investors will just use the book value as shown on the balance sheet for simplicity
3. The cost of debt should be after-tax since we are discounting after-tax cash flows

In the next lesson, we will perform a simple DCF analysis of a public company, Verizon.