by elmads

Introduction

The rate of the current US Treasury bond, also known as the US Government bond, is an integral part used by most investors worldwide in their discounted cash flow model—projecting an asset’s cash flow in the future and discounting it in today’s value—which is to know the possible intrinsic value of an asset (businesses, real estate, and stocks).

There is this one fact about businesses: all of them want to live and operate forever, but that is unrealistic. Businesses, like humans, have their own lives. They grow mature and eventually die; it’s exactly the same, but the duration of life differs. Some can live for centuries, others for decades, while the majority operate only for days.

Businesses usually die in three ways: either through bankruptcy, are acquired by a larger business, or are merged with another business.

You might argue that the longest-operating business in the world is Kongo Gumi, a construction company in Osaka, Japan.

You have a valid point because Kongo Gumi was established in 578 AD, making it the longest-standing business to date. Operating its business for 1,445 years with thousands of generations of managers who’ve handled it through good and bad times. That’s indeed an impressive feat; there are many more. See the image below, which was taken from VisualCapitalist.

https://www.visualcapitalist.com/oldest-companies/

The century-old operating companies are indeed impressive, but when compared to the hundreds of thousands to millions of businesses that’ve started, these successful, long-standing companies are only miniscule in amount compared to them.

There are a lot of businesses that have failed than survived. They’re not just being written about and talked about that much, unlike the success stories. The same can be said with the lives of people; there are a lot more extraordinary and successful biographies than just the memoirs of an average person.

It’s understandable why this happens because what is extraordinary is usually sought after by everyone, while what is common is, to use a better word, boring.

So, what’s my point here? No one in this world can predict how long a company will continue to do business. Even the century-old, long-standing companies in this world can go into bankruptcy or be acquired or merged by or with another company tomorrow, next week, or next year. If this is the case, then we can somehow surmise that no one can accurately predict for how long a business will be able to generate cash flows for its owners.

In the world of financial analysis, investors often employ a practical but simplified assumption: they project that a company will generate cash flows indefinitely into the future. This doesn’t mean they believe a company will literally operate forever; rather, it’s a way to assess the long-term value of an investment.

While it’s true that no one can predict precisely how long a company will continue to operate, most businesses aspire to thrive and endure. They make strategic decisions aimed at long-term growth and sustainability. When investors analyse a company, they typically consider the potential for ongoing cash flows over an extended horizon.

This assumption of indefinite cash flows is especially relevant when estimating the terminal value in a discounted cash flow (DCF) analysis. It allows investors to evaluate an investment’s potential over a longer timeframe, aligning with the expectation that successful companies will continue to operate and generate returns well into the future. In essence, investors prefer to envision a company’s cash flows as enduring, even if the reality is more complex. This perspective offers a more extended runway for assessing growth-oriented investments, which aligns with the goals of many investors.

And making a terminal-value cash flow is also sensible, as who would first want to invest in a company that would die in 10 or 20 years? Most of us would assume that we invest our hard-earned money because a specific company that we want to become part owners of will continue to operate for a long, extended period of time in the future. Though there are ways to make money on a dying company, most investors still prefer the long runway of growth-oriented companies.

Now, we come back to the risk-free rate, which I wrote about in my previous blog as the rate that most investors use for their terminal value rate.

📣 https://elmads.com/?p=11555 – Investor’s Toolkit: How to Identify and Utilize Risk-Free Assets

Recall that investors usually project 3–10 years’ worth of a business’s cash flow into the future, and then after the end of their projected year, they do a terminal cash flow model built on the terminal value rate (usually based on the risk-free rate).

Terminal value cash flow does represent the cash flows that are expected to continue indefinitely at a stable rate after the explicit forecast period. It’s a practical way to capture the long-term value of an investment while avoiding the complexity and uncertainty of projecting cash flows indefinitely into the future.

How To Use The Risk-Free Rate In A DCF Analysis

In doing a financial valuation of a business, we project its cash flows into the future for 3–10 years, and then, after the end of our projection, we use the terminal value rate, which is usually based on the risk-free rate of an asset.

In my previous blog, “Investor’s Toolkit: How to Identify and Utilize Risk-Free Assets” I wrote that the US government bond rate is considered risk-free, and the current rate is its risk-free rate.

📝 NOTE: The US government bond rate that you’ll use for your risk-free rate is dependent on the number of years of your cash flow projection for a company. If you project 3 years, then you should be using the current 3-year US government bond rate. If you’ll be projecting 5 years, then use the current 5-year US bond rate, and so on and so forth.

This forms a system for doing our own valuation.

Let’s say you’ve done a 10-year cash flow project for company XYZ. Therefore, you need to find out what the current 10-year US government bond rate is, which you’ll be using as your terminal rate.

It’s easy to find the current 10-year US government bond rate; just do a quick Google search.

As of this writing, September 10, 2023, the 10-year US government bond rate is at 4.26%.

The percentage here would then be used for the terminal rate beyond year 10 of our projected cash flows.

In my blog titled “DCF Valuation: Unveiling the Secrets of Intrinsic Value Calculation”, I used Alphabet Inc.’s (a parent company of Google) past 10-year cash flow and a DCF model. In my example, we assumed that it was 2013 and that we were so good that we were able to accurately project the 10-year FCF of Alphabet Inc. from 2013 to 2022. With that, we arrived at its approximate intrinsic value of $31.29 per share in 2013.

Back then, I used a 2% terminal rate for it, but now I’ll be utilising the current 10-year yield of 4.26%. Let’s see what happens to its value after changing it from 2% to 4.26%, shall we? (See images below.)

By changing the terminal Free Cash Flow Rate from 2% (left image) to 4.26$ (right image and current 10-year bond yield), our estimated value per share increased from $31.29 to $38.58.

Every time we do a discounted cash flow or update our information in an asset valuation, we have to use the current Risk-Free rate. This is to take into account our present financial environment.

📝 NOTE: Our focus is still on the terminal free cash flow rate; don’t mind the other variables, as we’ve not talked about them yet.

It seems easy, isn’t it? But what if we’re valuing a company that is not in the US and doesn’t use US dollars? For example, a company domiciled and operating exclusively in the Philippines, and only uses the Philippine peso currency. Can we still use the 10-year US government bond rate for the terminal rate?

My quick answer to you is no.

Risk-Free Rate in a Global View

Consistency Principle

“The risk-free rate used to come up with expected returns should be measured consistently with how the cash flows are measured”.

—Aswath Damodaran, Investment Valuation

When using a risk-free rate for our terminal rate, we must first and foremost be aware of the currency we are using in our free cash flow projection. If we’re projecting the cash flows in US dollars, then we must use the U.S. government bond rate as the risk-free rate.

“This also implies that it is NOT where the firm is domiciled that determines the choice of risk-free rate, but the CURRENCY in which the cash flows of the firm are estimated”.

—Aswath Damodaran, Investment Valuation

For example, the global company Louis Vuitton Moët Hennessy (ticker symbol: LVMH) can be valued using cash flows in USD despite the firm being domiciled in France. If we do it via the USD currency, then we need to use a U.S. long-term government bond rate as the risk-free rate for our valuation, or the cash flows can be projected and valued in euros with a French long-term government bond rate.

The key here is the currency. Your currency used for your cash flow projection of a company should have a risk-free rate in the same currency as its own government bond rate.

A Government Bond that Has a Default Risk

“In theory, the US government doesn’t have default risks, not because their government is better run than corporations, but because they usually control the printing of currency and can continue to borrow large amounts of money”.

—Investor’s Toolkit: How to Identify and Utilize Risk-Free Assets https://elmads.com/?p=11555

The concept of the US government bond as a default-free asset still holds true to this day, which is wonderful because it would be nice to invest a portion of your hard-earned money in an asset that would pay you the promised coupon amount with 100% certainty, theoretically, over the lifetime of that asset. Well, that’s nice if we live in the US and if we value the cash flows of a company in USD.

But what if we’re valuing a company in a different country and in a different currency?

Evan That’s easy; you just told us to have consistency. Thus, let’s say, for example, we’re valuing a company whose operations are domestically in the Philippines and uses the Philippine Peso. Then we’ll use the Philippine government bond as our risk-free rate.

You got that right! But the Philippines has a default risk, unlike the US, which has a government that is considered default-free.

It’s not just the Philippine government that has a default risk on their debts, but also most countries around the world, especially emerging market economies. Yes, you read it right. Most countries, even the top economies of our world as of 2023, which are China, Japan, India, the UK, France, Italy, Canada, and Brazil, all have default risk.

“This is predicated on the assumption that governments do not default, at least on local borrowing (on their own currency). There are many emerging market economies and quite a few developed markets where this assumption might not be viewed as reasonable. “

—Aswath Damodaran, Investment Valuation

With that said, how could we then approach this problem? How can we have the consistency principle of cash flows and risk-free rates in a currency that has a government that has a default risk?

Don’t fret because we can still use the government bond rate of the currency we’re using in our cash flow projections, and then we’ll take into account the default risk of the government by subtracting it from their current government bond rate.

To put it simply, “if the government issues long-term bonds denominated in the local currency and these bonds are traded, we can use the interest rates on these bonds as a starting point for estimating the risk-free rate in that currency”. 

—Aswath Damodaran, Investment Valuation

I’m currently valuing a utility company in the Philippines, and let’s call this company ABC. The image below is only a hypothetical free cash flow projection for company ABC, meaning I didn’t specifically put my own projections here and just made up the free cash flow numbers for example purposes only.

In the Terminal Free Cash Flow rate, I put a risk-free rate of 4.53%.

As per the duration matching strategy, I need to use a 10-year government bond rate because I did a 10-year cash flow projection for company ABC.

Then, for the consistency principle, I need to use the 10-year Philippine government bond rate as my risk-free rate. As of September 11, 2023, the current 10-year Philippine government bond rate is 6.57%.

But that doesn’t end there because the Philippine government has a default risk, and its default risk is translated to 2.04%. That percentage is called the default spread.

To determine the risk-free rate of a government and its currency, which has a default risk, we need to use this formula.

Risk-free rate in currency = government bond rate minus default spread

Risk-free rate in PHP as of September 11, 2023 = 6.57% – 2.04%

As of 11/09/2023, the risk-free rate in PHP is 4.53%.

Done and dusted, but we still have some information loopholes in what we did here, namely, where did we even get that default spread of 2.04%? Where is it even based?

The Credit Rating Agencies

A credit rating is an independent assessment of a company or government entity’s creditworthiness. Think of it as like an individual’s credit score, but for companies and governments.

As defined by Investopedia, “countries are issued sovereign credit ratings. This rating analyses the general creditworthiness of a country or foreign government. Sovereign credit ratings measure the overall economic conditions of a country, including the volume of foreign, public, and private investment, capital market transparency, and foreign currency reserves.

Ratings also assess conditions such as overall political stability and the level of economic stability a country will maintain during a political transition. Institutional investors rely on sovereign ratings to qualify and quantify the general investment atmosphere of a particular country.”

—Investopedia

Credit rating agencies were formed around the 19^th century, when the earliest agencies primarily focused on providing credit information to subscribers, typically merchants and banks. These agencies gathered data on the creditworthiness of individuals and businesses and shared it with their subscribers.

Then it began to grow and expand further in the 20^th century. They evolved from being primarily data providers to agencies that assigned credit ratings. Agencies like Moody’s and Standard & Poor’s (S&P) became well-established during this period. These agencies played a significant role in providing investors with information about the credit quality of bonds.

Today, we have three major credit rating agencies, which are Fitch Ratings, Moody’s Investor Service, and S&P Global Ratings.

Each rating of the top three rating agencies is expressed via three letters, except for Moody’s, where it uses two letters and a number.

These three credit rating companies are the basis of our default spread.

Read also my blog titled “Credit Ratings” to understand the significance of each rating to a bond investment. See link below.

📣 https://elmads.com/?p=1392 – What is a credit rating?

The credit rating of a government has a corresponding default spread percentage. That default spread would then be used as our subtrahend while the minuend is the current government bond yield, giving us the risk-free rate for a certain currency. This is what we did previously with our company ABC example.

📝 NOTE: “The default spread for a rating is computed by looking at dollar-denominated bonds issued by the governments with a Ba2 rating and comparing the rates on these bonds to the US Treasury bond rate.” —Aswath Damodaran, Investment Valuation

How Professor Damodaran gets the default spread is still complex and a daunting task, especially if you lack resources to find the required information. This is where he made everything simple for his students and some of the investment analysts who follow his work.

He made a table of the country’s default spreads and risk premiums, which he updates more than twice every year. A link is provided below.

https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/ctryprem.html

As you can see from the images above, Professor Damodaran’s table summarises the information needed to come up with the default spread of a certain country based on Moody’s rating. He also shows the date when he took that information.

The downside of using the default spread is that it assumes the rating agency is correct in its assessment of sovereign risk and that the default spread based on the rating is correct.

In Professor Damodaran’s Valuation textbook, he also stated other approaches to getting the risk-free rate of currency of a government that has a default risk, but I will not share that anymore as I prefer to use this approach than the others.

He did state that there are other approaches to getting the risk-free rate of a government that has default risk, but he did encourage us to find just one that we prefer and that we could use easily with our valuation process.

Additional Content – Sovereign Bonds

The terms, sovereign bonds and government bonds, are the same. Don’t confuse these two.

It is one of the means for a government to raise additional capital to fund their programmes, pay down old debts, pay interest on their debts, and meet other government spending needs.

A government can do this both domestically and internationally.

◾Domestically, they entice people to purchase government bonds using their own currency. They’ll be taking on debt, paying the interest on the debt, and paying the principal after the debt matures in their own currency.

For example, the UK government offered the public a 5-year government bond. Interested persons or institutions will be loaning them money in GBP, while the UK government will pay the coupon payments in GBP, the same for the principal amount on their owed debt once the bond matures.

◾Internationally, the riskier the government that will be borrowing money from foreign international investors, governments, and institutions, the more likely it is that they’ll give them a better deal by increasing the coupon rate. Why? Well, in the first place, why would foreign investors, governments, and institutions loan money to a government that has a high risk of default without giving them a better deal? To offset that risk, risky governments usually increase the coupon rate of their bond offerings. If they don’t do this, no one on the international stage will be willing to loan them the required amount of money.

For example, you have two bond assets offered to you. The first one is a 10-year US government bond that would give 4.5% per year, and the second one is a 10-year Egyptian government bond that would also give 4.5% per year. What would you choose?

The first thing that you should consider is the certainty of the investment. Which one would give the guaranteed interest payment, considering both of them give around 4.5%? Obviously, the US government is almost a risk-free entity compared to the Egyptian government. And that reflects on the credit rating agencies.

As of September 2023, Moody’s rating for the US government is Aaa, while the Egyptian government is only at B3.

To put that into context, see the graph below and/or read my blog regarding “What is a credit rating?”.

As shown above, with the help of rating agencies, we can be informed about the approximate risk level of the government bonds offered both locally and internationally, which would give us more certainty on our returns. Thus, going back to our example, it is obvious that taking the US government bond over the Egyptian government bond is a sensible investment decision based on the certainty of cash flows.

For risky governments to raise capital internationally, they would need to increase the coupon rates on their offerings.

That’s just one side of the story, because when governments borrow money internationally, there is a risk of foreign exchange fluctuations. This can either make the interest payment on debt cheap or expensive in terms of currency exchanges.

Surely, if you are a risky government and need international capital, you don’t have the leverage to say to foreign investors that I’ll be paying you in our own currency, because what you’re saying here is this: You foreign investors, you’ll be the ones taking on the currency fluctuation risks.

If that’s the case, then these risky governments may struggle to find willing lenders on the international stage. Thus, risky governments are the ones who always take the currency rate fluctuation risks.

For a better understanding of my point here, see the infographic images and scenarios below.

📝 NOTE: The forex exchange rate I used in this example is based on the yearly average USD/PHP exchange rate from 2013-2022).

In this scenario, the US government will be buying a Philippine government bond that will pay them coupons in USD every year.

As you can see from the image above, the US government would receive a steady coupon payment worth 65 thousand USD every year, which is 6.5% of their loaned capital of 1 million USD.

On the flip side, the Philippine government took the currency fluctuation risks because, as you can see, they paid an amount in USD, which substantially impacted the amount in PHP as it was dependent on the USD/PHP rate at the time they paid their interest on their debt. In this example, the Philippine government paid more in pesos due to the increase in the USD/PHP rate over time. The case would be different if the USD/PHP rate went down, as they would just pay less in their PHP local currency for every USD.

Now, let’s see what would happen if the US government instead took on the foreign exchange risk by exchanging their loaned money in Philippine pesos and also accepting a constant coupon amount in Philippine pesos.

As expected, the US government would only receive less in USD terms due to the currency fluctuation and strengthening of the USD against the PHP over this period of time.

It is unfortunate, but for risky governments and economies to be able to raise capital internationally, they would, for most of the time, need to have a higher coupon payment offer on their loaned money and take on the currency risk. That’s the only way to borrow money from the world stage.

To Sum It Up

• The risk-free rate is usually used for the terminal rate to get the terminal value at the end of the projected cash flow valuation in a discounted cash flow analysis.
• The risk-free rate is taken from a risk-free asset.
• A risk-free asset should not have default risk or reinvestment risk. The U.S. government bond is considered a risk-free asset.
• The consistency principle: The risk-free rate used to come up with expected returns should be measured consistently with how the cash flows are measured. 10-year cash flow projections, use a 10-year government bond rate as your risk-free rate.
• If a government has a default risk on its debt, you can still use its government bond rate as the risk-free rate, but you’ll need to adjust the rate based on its default risk. The default risk is based on the ratings given by international rating agencies such as Moody’s, S&P Global, and Fitch.

“The value of a firm is the present value of its expected cash flows over its life. Since firms have infinite lives, you apply closure to a valuation by estimating cash flows for a period and then estimating a value for the firm at the end of the period—a terminal value”.

—Aswath Damodaran, Investment Valuation

That summarises basic information about the risk-free rate. “What is a risk-free rate?, how is it used, when to use it, and why?”

I hope this somehow sheds light on the importance of bonds in asset valuation.

To know more in depth about valuations, I highly recommend that you watch the free online classes posted by Professor Aswath Damodaran on Youtube. He posts all of the recorded sessions of his valuation class online for free, or you could just buy his textbooks, one of which is “Investment Valuation: Tools and Techniques for Determining the Value of Any Asset, University Edition.”.

Happy Investing, Everyone!! Never Stop Following your Passions and Curiosities. 

CHEERS TO A BRIGHTER FINANCIAL LIFE

Knowledge is my Sword and Patience is my Shield

elmads

This blog is for informational purposes only and not a Financial Recommendation. Not all information will be accurate. Consult an independent financial professional before making any major financial decisions.