I plan to write this note as a concept note with an intent to serve two purposes — a) to sharpen my own understanding of this subject; b) to preserve it as a reference for the future. The note is a synthesis of my learnings from the lectures of professor Aswath Damodaran. While writing I have removed details that you can access directly from his page. Hope you will also find this effort useful.
Valuation
In order to arrive at the valuation of an asset, we need to undertake the following steps — a) Estimate future cash flows based on some key assumptions; b) Aggregrate these cash flows using an appropriate discounting rate (reflecting the return that we need to make to justify the risk).
Assumptions that we make to estimate future cash flows are as follows — a) Estimate revenues generated by the sale of goods and services by leveraging the assets which we are trying to value; b) Estimate the cost of operating these assets (like daily maintenance and paying salaries etc); c) Estimate the spend on incremental Capex in order to sustain a certain rate of growth in revenues; d) Estimate the cash outflow on payment of debt obligations (interest and principal).
Note — All flows used to estimate valuations are actual cash and not accounting earnings (like those which include notional items like depreciation, accrual revenues, etc).
Price vs Valuation
The price of an asset emanates from its demand and supply equation at any particular point in time. The higher the demand (compared to its supply), the greater will be its price. Normally we must expect some correlation between price and valuation. Why? As a higher-value asset is expected to have more demand compared to one with a lower value. But many times this correlation is lost due to the play of sentiments (strategic), opportunism (trading), or incorrect valuation (suboptimal assumptions).
Cash vs Earnings
Cash is real money exchanging hands at a chosen reference in time, whereas the earnings are an estimate of incremental loss/gain in the value of the asset (business) for the targeted quarter. By looking at this (earnings) number one can tell the direction in which the business is heading (gain/loss). That is why while calculating earnings, the notional (non-cash items) like depreciation (loss of value of an asset due to wear and tear, etc), and revenue accrual (revenue booked even when the payment is pending) are added seamlessly to the cash items. The whole idea is that the value of the asset should reflect all the cash that is legally due as soon as the accounting obligations are met. Therefore, the price that we can hope to make by making a sale of the asset at that time when its earnings got estimated must include the value of all the unclaimed cash flows.
Extracting Cash from Earnings
Free Cash flow can be extracted from the earnings by adding depreciation/amortization, and spending on incremental Capex back to operating income. The reason “earnings” do not include “incremental Capex” is that by making such an expense you do not alter the value of your asset, as any cash tagged with it just got exchanged by something material which ideally can be exchanged back at the time of sale. The reason for subtracting depreciation is to account for the loss of value of an asset with time due to wear and tear. And any attempt of making a sale of a depreciated asset will never unlock its full value. Though the quantum of that “value lost” can differ on a case-by-case basis, however, by attaching a pre-determined “rate of depreciation” the accountants are just trying to bring some order to the process of estimating value — which otherwise can get quite chaotic (due to different flavors of maintenance, and demand at the time of sale).
Discounting Rate
What is it?
This is nothing but the minimum return that one needs to make to cover up for the risk of making the investment. We all know that one cannot be absolutely certain about the returns he/she might end up making on a risky investment. Why? As risky investments are always laced with uncertainty on returns— driven by macro and micro economic factors. Some such investments might throw up losses, and others might returns gains more than what was estimated initially. Hence, to stay afloat as an entity, one needs to diversify and aim to make higher returns on investments that are risky, so that the gains in some are sufficiently large to cover up for the losses in others.
Whose risk matters the most?
Since the risk-taking capabilities of all individuals/entities are different then why do we use a specific discounting rate (anchored on some well-defined process) while evaluating publicly traded stocks? The reason is simple —the individual who isn’t diversified or not trading adequately does not influence the prices of stocks. The prices are actually influenced by institutional investors, who not only trade in them actively but also are deeply entrenched. Hence, the risk that the institutional investors see in the asset matters more than the retail investors (who are less exposed and will have negligible volumes). Therefore we pick the same discounting factor the institutional investors use to measure risk to value stocks.
How is it calculated?
The discount rate of any asset can be calculated using the following items — a) risk-free rate; b) risk premium rate; c) beta; d) net debt; e) default risk (country & company).
a) Risk-Free Rate
The risk-free rate is the return that we earn on investments that are safe and guaranteed. For example, bonds issued by the government of sovereign states with AAA ratings. These bonds do not attract any default risk as they have the state’s blessing who we all trust. But since bonds of different time periods attract different rates, which one we should choose as a risk-free rate? It all depends on the time period for which the valuation is done. Why? Because of the need to match durations (of bond maturity and valuation period) else, we will have an issue of dealing with an additional risk of managing “reinvestment”.
But what if the state issuing the bond has a default risk, i.e its rating is lower than AAA? In this case, the risk-free rate will be the difference between the bond yield rate and the default spread — the number, one needs to estimate based on the country rating assigned by the rating agency. For example, if the 10-year bond rate for India is 7.5% and India’s default spread is 2.5%, the risk-free rate for the Indian market = 7.5% — 2.5% = 5%.
b) Risk Premium
Now risk premium is the additional return the entity needs to make (on top of the risk-free rate) to stay afloat. Sometimes the risk premium can be driven more by the sentiments of the investors (or their perception of the market in the future) than by fundamentals. The more scared the investor is about the market conditions, the higher the premium he will demand. And if he thinks that the expected premium is not in sight he will exit the market by making a sale — resulting fall in the asset price due to increased supply and decreased demand. This fall in asset price will in turn jack up the discount rates, thereby bumping up the risk premium. This constantly changing perception of “Risk Premium” is the fundamental reason for “market volatility” at the time of a catastrophic event like Covid19. We all know that as soon as the fear got extinguished the market corrected and even surpassed all expectations with any inherent alteration in fundamentals.
Risk Premium (Mature Market)
There are many ways of estimating risk premiums — both based on historic numbers or using a forward-looking approach. Since ERP (equity risk premium) is an estimate of the market sentiment (that changes dynamically), historic numbers are useless and serve very little purpose. Calculating ERP based on a forward-looking approach entails calculating cash flows for an index that is sufficiently large and diversified so that the index’s value (at a particular point in time) can be seen as a reflection of that of the market. Knowing the index’s value and the estimated cash flows (dividends and buybacks) of all companies one can estimate the applicable discount rate. Then subtracting this discount rate from the Risk-Free rate will give us the Risk Premium the market sees at that point in time.
However, a question that can come to the mind of an attentive reader is what if the future cash flows are estimated incorrectly, or change due to the perception of recession or boom? The risk premium will also change and that will get reflected in the price of the index.
Risk Premium (Emerging Market)
Now, what if the data of cash flows and buybacks are not available for the emerging market for which we intend to estimate the ERP? In that case, we have no other options but to switch currencies and use the ERP for the mature market for which we have this information for estimating the ERP of the emerging market. For this purpose, the data on the default risk of the mature market country comes in handy. This number on the default risk is proportionately scaled up for equities (equities will have higher default risks than bonds) and added to the ERP for the mature market to arrive at the ERP of the emerging market.
The factor used to scale up for equities can be estimated by calculating the ratio of the Std dev of the emerging market equity index / Std of emerging market bond index =1.16 (estimated by Ashwad D in 1st July 2022)
ERP of Emerging Market = ERP of Mature Market + Default Spread x (STDV of Equities / STDV of Bonds)
c) Beta
Beta is a measure of the price volatility of an asset compared to the market. It is indicative of the type of business that the company is in practice. Some businesses have higher price volatility compared to others due to the discretionary nature of their products which in difficult times sell less compared to their peers — resulting in a fall in revenues and shrinkage in earnings at times of distress. The beta also is highly influenced by leverage. More the leverage, the higher the price volatility as the obligation to pay interest cannot be avoided even in difficult times.
The beta of a type of business can be estimated by running a regression of all businesses of a similar type against an index that is sufficiently large and then taking the weighted average of their respective standard deviations. The law of large numbers plays out and all distortions due to smaller sample sizes get ironed out. Why regression against an index that is sufficiently large? As the index should mimic the market in which we want to measure price volatility.
The Beta of any business without any leverage needs to be appropriately scaled up using the Debt/Equity Ratio to arrive at the levered Beta for the purpose of estimating the huddle rate.
Influence of Currency
The cost of equity (discounting rate) is dependent on the currencies in which it is calculated. But it won’t affect the estimated valuation number as long as one stays consistent in estimating all the numbers (revenues, earnings, etc) in the same currency. Why? the revenues will get scaled down accordingly reflecting the lower inflation in the mature market compared to that of the emerging.
Let’s say one is trying to estimate the valuation of an Indian company operating in India in US dollars. To estimate the risk-free rate one has to start with the 10-year bond rate of the US. Now for estimating the ERP for India we have to add to the US ERP an additional number which is the default risk (based on India’s rating) scaled up for equities.
Hence, the ERP for India = ERP of US+ India’s Default Spread x (Std deviation of equities/Std deviation of bonds).
Now to estimate the huddle rate (cost of equity) we have two options —
a) Use USD, then huddle rate = US 10-Year TBond Rate +(ERP of India) x Levered Beta. Note in order to stay consistent, the revenues also have to be estimated in USD;
b) Use INR, then huddle rate = Indian 10-Year Bond Rate — India’s Country Default Risk + ERP of US x Levered Beta. Here the revenues also have to be estimated in INR.
Influence of Expected Inflation
A question might come to the reader’s mind as to how inflation might have an impact on huddle rates (cost of equity). The rise of expected inflation will increase the yield of the 10-year bond rate. Why? No one will like to buy a bond at a lower yield if he/she is expecting inflation down the line at a high value compared to the yield the bond ends up promising. Hence, the rising of “expected inflation” for the long term will also increase the risk-free rate. This will have a bearing on the huddle rate, as the risk-free rate gets added to the ERP for the purpose of discounting future cash flows. Now, what about the impact on future cash flows on account of rising inflation? It all depends on the discretionary nature of the products that the business is trying to sell. If the product is non-discretionary then the pricing power lies in the hands of the business and therefore whatever value is lost due to the increased huddle rate is made by increased revenue due to a rise in price on account of inflation.
Hence, the business with pricing power stays relatively protected at a time when expected long-term inflation is on the rise, compared to the one that has none.
Valuing Debt
Debt is something that entails payment of interest at a predetermined rate which cannot be avoided at the time of distress. For estimating its market value we need the cost of debt. This is an important part of the exercise for estimating the cost of capital. This can be calculated as under.
The pre-tax cost of debt = Risk-Free Rate + Default Spread of the Company + Default Spread of the Country
Now, the default Spread of the company can be estimated based on the rating assigned by the rating agencies. If the company rating is not available then the default spread can be estimated using the interest coverage ratio (Earning Before Interest & Taxes / Interest Expenses). The interest coverage ratio gives measures how much cushion the company has built into its finances for enabling interest payments. The higher the number the better.
To calculate the post-tax cost of debt we need the tax rate, as interest payments save taxes on the marginal value of the currency.
The post-tax cost of debt = The pre-tax cost of debt X (1-tax rate)
To value the market value of debt at any point in time, we need to know the outstanding book value of debt, the average payout period, and the yearly interest payment obligation. Then the market value of debt can be estimated as follows.
Market Value of Debt = PV of interest payment discounted by post-tax cost of debt + PV of book value of debt discounted by post-tax cost of debt to be paid at the end of the maturity period.
Note — In order to calculate the true aggregated value of debt all interest-bearing items (like leases, and vendor financing) need to be valued separately and added to the above number to calculate the total “Market Value” of Debt.
Cost of Capital
Now the cost of capital is simply the weighted average of the cost of equity + the cost of debt.
Cost of Capital = Market Cap of Equity x Cost of Equity + Market Value of Debt x Cost of Debt
Using this cost of capital we can calculate the Enterprise Value of the company that we intend to value.
Finally
The huddle rate (discounting rate) used to estimate the valuation of any asset/company is directly linked to the jurisdiction in which the business operates (where all risk resides). It has nothing to do with the currency used to value the asset. Hence, even when a different currency is used to value companies, the valuation stays consistent as long as the huddle rates are modulated to reflect the changes in default risks, and the revenues are estimated in the same currency in which the huddle rate is calculated. If a company is operating in different jurisdictions laced with different default risks then huddle rates for each jurisdiction have to be calculated separately and the revenues emanating from these jurisdictions have to be discounted using their respective huddle rate for calculating the overall valuation of the company. A similar strategy shall apply to debt as well. The total value of the company (enterprise value) is the sum of two.
(This is only a concept note, and for simplicity, I have deliberately kept the hard numbers out to prevent unnecessary distractions)
