Capital Asset pricing model has a very important place in valuation, it helps us to find cost of equity for the valuation. The model has 3 inputs risk free rate, equity risk premium and beta, in this article we will talk about beta, its importance and how its calculated.

Risk is deviation of returns from expectations, financial theories have long taught us that high risk is always equals to high returns, but are all risk compensated? In fact, its only systematic risk that cannot be diversified is what is compensated.

Risk & Return models

There are several accepted risk return models in finance and they all share some common views about risk:

1. They all determine risk in terms of variance in actual returns around expectations, thus risk free investment is one that has equal expected and actual return

2. They measure risk from the perspective of marginal investors that are well diversified.

This makes risk models to break into 2 components: firm specific risk that are related only to a particular company or sector, and market component contain risk that cannot be diversified and this market risk should be rewarded.

The beta is one of the most important but elusive parameters in finance. According to the CAPM, it is a measure of the so-called systematic risk.

CAPM with assumptions about no transaction cost or private information, concludes that marginal investors hold a portfolio that include every traded asset in the market and the risk of any investment is the risk it adds on this “ market portfolio”. Expected return model under CAPM:

Expected return = RF + ERP(Beta)

APM which is built on assumption that asset should be priced to prevent any arbitrage opportunity, concludes there can be multiple source of market risk and beta’s relative to each of these sources measure expected return.

Expected return = Rf + ∑B(Risk premium)

What is beta?

Beta as a measure of systematic risk has 2 basic characterstics:

1. It measures the risk added on to a diversified portfolio, rather than total risk. thus, its possible for a instrument to have high risk individually but low risk when analysed in terms of market risk.

2. Beta is a relative measure of risk and it is standardized to be around 1.

Beta of an asset can be calculated using regression of returns of any asset against the returns of index, representing the market portfolio over a reasonable time period. Where returns of asset represents Y variable and returns on market represents X variale.

Equation we get is : R = a + b*RM

The slope of regression “B” is beta, because it measure the risk added by the investment to index used as proxy to the market portfolio.

Problem with regression beta:

1. Index Problem: Regression beta depend heavenly on the index used to regress the beta but which index shall we use? , A local equity index can be used as proxy for market portfolio but it can raise problem of large company in a small equity market, example Nokia in Finland’s equity market. where Nokia accounted for around 90% of Finnish equity market, which meant that we were regressing Nokia with 90% of Nokia only.

   Result, high beta close to 1 or high for Nokia and beta less than 1 for smaller riskier companies. This problem can be solved by looking at who the marginal investor are? A good idea is to look at the marginal investors stock holding in the company and where are they based. If marginal investor is domestic then we can use domestic index but if marginal investor is from US then use S&P500 and if marginal investor is global then use global index like MSCI global index.

2. Noise problem: Using MSCI or S&P500 we can solve problem of dominating companies in small index but their is a second issue is how far shall we go back?

   The regression beta is noisy and the range we get is quite large, for eg - let say you got regression beta as 1.2 with a standard error of 0.5, beta can practically be 0.7 to 1.7 which is practically of no use in valuation. To reduce standard error we need to increase the number of observation.

   Standard error = Standard deviation/√no. of observation.

3. Problem of firm changing overtime: Even if stock do not dominate the index and beta we got has low standard error, their is another problem with regression beta i.e they are based on historical data & firm change over time.

   The regression beta reflect the firms character on average given the period of estimate rather than firm as it exist today.

   Firms have 3 reasons to change:

   a. They divest in existing business, invest in new business or acquire new firm. In this situation it changes the business mix and which change their beta.

   b. They can change the financial leverage by adding or paying off debt, in addition such as payment of dividend and buyback can effect financial leverage.

   c. Even if financial leverage or business mix don’t change they tend to grow overtime as they grow their operating structure change which change their beta.

Adjusted beta

As result of difference in period, return interval and index etc. different service often end up with different beta, most service adjust their beta towards 1. A similar model developed by bloomberg is:

Adjusted beta = Regression beta (0.67) + 1(0.33)

Effectively pushing beta towards 1

but why adjust beta towards 1? The rationale is that overtime their is a tendency on part of beta of all companies to move towards one, Practically this should not come as a surprise as firms that survive in the market tend to grow and increase in size, overtime becoming more diversified and have more assets in place to produce cash flows. All this pushes the beta towards 1.

I have shared my own work on how to calculate regression beta on excel:

Beta Regression

27.5KB ∙ XLSX file

Download

Here I have calculated 2 year weekly and 5 year monthly beta of Apollo tyres ltd. regressed on Nifty

Download

Bottom up Beta

Beta of a firm is determined by the fundamental decisions that firm takes on where to invest, what type of cost structure it plans to maintain and how much debt it takes on. Bottom up beta considers this factors in estimate of companies equity beta.

Lets first understand the fundamental that determine beta.

• Type of business

• Degree of operating leverage

• Degree of financial leverage

1. Type of business: Since beta measure risk of firm relative to market index, the more sensitive a business is to market condition, higher the beta. Thus other things being equal a cyclical company will be expected to have a higher beta than non cyclical.

   Building upon this point, we will also point that the degree to which firm’s products are discretionary or not will effect its beta. thus we can say beta of a cereal manufacturer will be low than beta of car manufacturer.

   Firms generally have limited control over how discretionary their product or service that they provide to customer. Their are firms that have used this limited control to position their products as less discretionary to buyer and lower business risk. One approach is to make product integral and necessary to part of everyday life, thus making its purchase more a requirement. eg, blinkit e-commerce business positioning. Second approach is to effectively use advertisement and marketing to build brand loyalty.

2. Degree of operating leverage: Degree of operating leverage is function of cost structure of a firm and its usually defined in terms of relations between fix cost and total cost.

   Generally firms with higher operating leverage will have a higher variability in earnings than a similar firm with lower operating leverage. thus, higher operating leverage will lead to a higher beta.

   While operating leverage do affect a companies beta, it is difficult to measure operating leverage of a firm from outside since fix cost and variable cost bifurcation is not provided by companies.

   An approximate approach to measure operating leverage is :

   % change in operating income/%change in sales

3. Degree of financial leverage: Other things being equal increase in financial leverage lead to increase in equity beta. As obligated payment on debt increase the volatility in net income, with higher leverage increasing income in good times and reduce at bad times.

   BL = Bu ( 1+(1-T)*(D/E))

   Unlevered beta is determined by the type of business it operate and operating leverage, then equity beta is determined by riskiness of business, operating leverage and financial leverage.

   Breaking bottom up beta into business risk, operating leverage and financial leverage help us with an alternative way of estimating beta.

#Steps in calculating bottom up beta:

1. Identify the business or businesses that make up the firm.

2. Estimate the unlevered beta for the business or businesses that firm is involved, the simplest approach uses those unlevered beta directly without adjusting for any difference between the firm being analyse and average firm in the sector.

3. Calculate unlevered beta for firm, take average of unlevered beta of firms being analysed

4. Calculate the leverage of the firm using market value if available, if not use target leverage specified by management or industries typically debt ratios

5. Estimate levered beta for the firm. using unlevered beta of firm from step 3 and leverage of firm from step 4.

Their are 3 reasons this beta is better estimate than regression.

1. We calculate unlevered beta by sector with average across regression beta, while regression beta can be noisy & have higher standard error, average across regression beta can reduce the noise in estimation.

2. Beta reflects the firm as it exist today, since it is computed based upon current weights for different business. In fact changes in business mix is easily reflected in bottom up beta.

3. Finally levered beta is calculated using current leverage of the firm, rather than average leverage over the period of time.

I have provided my own bottom up beta calculation below, do check out.

Apollo Bottomup Beta

21.5KB ∙ XLSX file

Download

Download

Precedent transaction analysis is just like comparable company analysis, employs a multiple based approach to derive implied valuation of company. Its premised on multiple paid for comparable companies on prior M&A transactions.

Most appropriate application for precedent transaction analysis is to determine sale price of company in M&A transaction or restructuring.selection of most appropriate universe of comparable acquisition is foundation for performing precedent transaction analysis.

Best comparable acquisition typically involve companies similar to target on fundamental level ( size, growth , return, credit etc.) , as with trading company analysis its is often challenging to obtain universe of truly comparable acquisitions and in most part require bankers discretion.

It is common to include transaction involving companies from different but related sector that may share similar end market, distribution channel or financial profile. As a general rule, most recent transaction within 2 to 3 years are preferred most relevant as they most likely took place under similar conditions.

In some cases older transactions can be relevant if they occurred during similar point in the targets business cycle or macro environment.

Under normal business conditions precedent transaction analysis provide higher multiple range than trading company for 2 reasons:

1. Buyer generally pay a “Control Premium” when purchasing another company. In return they acquire company and get right to control decisions regarding targets business.

2. Strategic buyer often pay higher value for opportunity to realize a synergy, synergy refer to expected cost saving or growth opportunity that occur due to combination of 2 business.

Step by step process of precedent transaction analysis:

1. Select Universe of Comparable Acquisitions

2. Locate necessary deal related & financial informations

3. Spread key stats, ratios and transaction multiples

4. Benchmark comparable acquisition.

5. Determine valuation.

Lets understand each step one by one :

#Select Universe of comparable Acquisitions:

Identification of universe of comparable acquisition is the first step in performing transaction company analysis, its very similar to determining universe of comparable companies for trading company analysis, can be often challenging and require strong understanding of target and its sector.

Screen for comparable acquisitions:

Initial goal when screening comparable acquisition is to locate for as many as potential transaction as possible for relevant potential time period and then further refine the universe/

Below is how to create a initial list:

1. Search M&A database, which allow for screening of M&A transactions through multiple search criteria, such as multiple search criteria such as size, form consideration, time period and geography etc.

2. Examine the target M&A history & determine multiple it has paid and received for purchase and sale.

3. Revisiting targets universe of comparable company and examine M&A history of each company

4. Search merger proxy for comparable acquisition as they contain excerpts from fairness opinion.

5. Review equity research report of target and its comparable and sector as it might contain list of comparable acquisition including relevant financial data.

Examine other consideration:

Once initial set of comparable acquisition is selected the banker then try to gain better understanding of specific understanding for each transaction. Although this does not change the list of comparable acquisition to be examined, understanding of “story” behind the transaction help the banker better interpret the multiple paid and its relevance to target being valued, this involve examining the factor such as market condition and deal dynamics.

Market Conditions: Market condition refer to business and economic environment as well as prevailing state of capital market at time of given transaction. They must be reviewed in context of specific sector and cycles. This conditions directly affected the availability and cost of acquisition financing and therefore effect the price paid.

Deal Dynamics: Deal dynamics refer to specific circumstance surrounding transaction.

• Was the acquirer a strategic buyer or financial sponsor?

• What were the buyer and seller motivation for transaction ?

• Was the target sold through an auction process or negotiated sale?

• What was the nature of the deal - Hostile or friendly?

• What was the purchase consideration?

lets talk about each one by one:

Strategic buyer V/S financial sponsor: Traditionally strategic buyers were able to place higher purchase price than financial sponsor due to their potential ability to realize synergy.

During the robust credit markets such as mid 2000’s financial sponsors were able to compete with strategic buyers due to use of leverage. After credit crunch advantage shifted back to strategic buyer as the strongest companies to source acquisitions.

Motivation: Buyer & seller motivation play a crucial role in interpreting purchase price.

For eg: strategic buyer pay higher price for synergy or security. financial sponsor may pay aggressively for possible of synergy of target with portfolio company.

selling companies motivation also matters. For eg: they might prioritize speed of transaction if part of business is non core, This might lead to lower purchase consideration.

Sale process and nature of deal: For eg auction is designed to maximize competition dynamic with goal of producing best offer at highest price possible.

Hostile takeover where target seek alternative to proposed takeover may pay higher price. Mergers of equal is situation where both parties forego premium & work collectively upside.

Purchase consideration: In general use of stock used to lower the valuation than all cash deal a stocks give target a potential to participate in upward move.

#Locate necessary deal related & financial information:

This section focus on sourcing key deal related & financial information for M&A transaction involving public & private target. Getting deal related information for comparable acquisition are variably easier for public companies than for private.

Some relevant sources to get such information for public targets:

• Proxy statement: In one step merger transaction the target company obtain approval from shareholders and provide them with detailed disclosure about the terms of transaction, fairness opinion of advisor, definitive purchase agreement, performance financial data etc. Proxy is primary source of data relevant to precedent transaction.

• Tender offer: In tender offer, acquirer offer to buy share directly from targets shareholder, as part of process, acquirer mail a offer to purchase targets shareholder and file documents with regulatory authorities. for eg, Schedule TO in SEC filings.

• Prospectus: When public acquirer issue shares as part of purchase consideration for public target, acquirer is typically required to file a registration statement/prospectus in order for those shares to trade freely by target’s shareholder.

• Other sources include Equity research reports, industry reports, annual reports etc.

Some relevant sources to get such information for private targets:

Private companies are not required to make detailed documentations like public companies, thus finding relevant information is harder task and type of information depend on type of transaction.

When public acquirer buy private company it may require documentations ,For eg, public company will need to file a prospectus if its using public security as part of purchase consideration. further if acquirer issue more than 20% of pre-deal shares it need to file proxy statement. For LBO private target availability of information might depend on what a public debt security was issued as purchase consideration.

Private target transaction involving non public financing are most difficult transactions to obtain information, their a banker may rely on use of sourced like press releases, news etc.

#Spread key statistics, Ratio and transaction multiples.

Once relevant deal related data has been located banker spread each selected transaction, This step includes:

Calculation of key financial statistics & ratios:

Process of spreading key financial ratios & stats for precedent transaction is similar to that outlined in comparable company analysis, therefore here we will focus on calculation of Equity value & Enterprise value for precedent transaction depending on different purchase consideration, we will also analyse premium paid and synergy.

#Equity Value: equity value calculation is done similar to comparable company analysis, however here it is based on announced offer price per share as opposed to closing price per share on given day.

To calculate equity value for public M&A target, offer price is multiplied to target’s fully diluted share outstanding. In calculation of fully diluted share outstanding for preceding transaction all outstanding share in the money options & warrants are converted to average strike price regardless of whether they are exercised or not. As with comparable company analysis out of money option are not considered in calculation.

For convertibles also the treatment is similar to comparable company analysis.

For M&A transactions in which target is private, equity value is simply enterprise value less any assumed net debt.

Purchase consideration: Purchase consideration refer to mix of cash, stocks and other securities that acquirer offer to targets share holders.

In some cases the form can effect targets perception of value. For eg, some might prefer all cash over stock due to its guaranteed value and other might prefer stock over cash due to upside potential.

3 type are - all cash, stock for stock, mix of both cash/stock.

1. All cash transaction: As name suggest in all cash transaction acquirer make and offer to purchase all or portion of targets share outstanding for cash only. This make a simple equity value calculation multiplying cash offer per share by fully diluted share outstanding.

[Equity value = Cash offer price x Diluted share outstanding].

However cash deal can lead to taxable event as opposed to exchange or receipt of stock, which if structured properly is not taxable until they are sold eventually.

2. Stock for stock transaction: In stock for stock transaction calculation of equity value is based on fixed exchange ratio or floating exchange ratio.

[ Exchange Ratio = Offer price per share/ acquirer share price ].

• Fixed exchange ratio: Fix exchange ratio id defined as a ratio of how many shares of acquirer are exchanged for each shares of target. for eg, acquire exchange half of stock for each share of target the fix exchange ratio is 0.5,

  Calculation of equity value -

  [ Offer price per share = exchange ratio x Acquirer share price ].

  [ Equity value = offer price per share x targets fully diluted share o/s]

  In fix exchange ratio structure, offer price per share move in line with underlying share price of acquirer, the amount of share received however remain constant. following a deal announcement, market immediately start to assimilate the publicly disclosed information. In respond target & acquirers share price start reacting in line with those perception. Therefore, target assumes risk of decline in acquirer share price but retain potential for upside.

  

  Fixed is generally used more than floating to link both parties to share risk together.

• Floating exchange ratio: It set the dollar amount that acquirer has agreed to pay for each share or target’s stock. For eg, targets shareholder will get $20 worth of acquirer share for each share. In floating exchange rare as opposed to fixed has fixed dollar price per share & no. of share exchange fluctuate in accordance to share price movement. Number of shares depend on average share price of acquirer for time prior to transaction close.

  This structure provide target’s shareholders with good degree of precision on value received as acquirer assume risk of decline of share price.

  

  3. Mix of cash and stock transactions: Under this transaction acquirer offer a mix of cash and stock as a purchase consideration. Cash portion represent a fix value per share for target share holder and then stock can be either fix exchange rate or floating exchange rate.

Offer Price = Cash offer price per share + [ Exchange ratio x acquirer share price]

Equity value = Offer price x targets fully diluted share o/s

Enterprise value: EV is total value offered by acquirer for targets equity interest, as well as assumption of targets net debt.

Its calculation is same as its done in comparable company analysis

EV = Equity value + debt value + preference share + non controlling interest - cash

Calculation of key transaction multiples:

Key transaction multiples in precedent transaction mirror those used in comparable company analysis

Equity value as represented by offer price of target’s equity is used a multiple of net income. Enterprise value is used as multiple of EBIT, EBITDA and sales.

multiples in precedent transaction analysis is calculated basis of LTM available at time of announcement.

Equity multiple: Offer price/LTM diluted EPS

EV multiple : EV/ LTM EBITDA, EV/LTM EBIT, EV/LTM sales

Premium paid: Premium paid refer to incremental dollar amount per share that the acquirer offer relative to targets unaffected share price expressed in percentage, Its only relevant for public target companies.

Closing share price on day prior to official transaction announced typically serves as good proxy for unaffected share price.

In event that target has publicly announced its intentions to pursue “strategic alternative” or there is a major leak prior to announcement, targets share price might increase in anticipation of potential takeover.

In that case targets share price before transaction announcement is not truly unaffected therefore here we will examine price paid at share price before leak or announcement.

Calculation of premium = Offer price per share/unaffected share price - 1

Synergy: synergy refer to expected cost saving, growth opportunity and other financial benefit that own due to control of 2 business, it become important to analyse it when strategic buyer is purchase target. synergy represent opportunity to increase future cash flow & earnings above and higher than what could be earned in standalone basis. Therefore, higher benefit synergy lead to higher purchase price paid by acquirer. upon announcement public acquirer give information about guidance on nature and amount of expected synergy. synergy provides a great perception on price paid and multiple.

In precedent transaction analysis it is important to note the announced expected synergies for each transaction when such information is available, however transaction multiple are shown on basis of target reported LTM information without synergy. For a deep understanding of particular multiple paid banker shows a adjusted multiple that reflect expected synergy.

Typically involving adding full effect of expected annual run rate cost saving synergy to earning metric in denominator.

Synergy adjusted multiple : EV/(LTM EBITDA + Synergy)

# Bench marking comparable acquisitions:

As with trading companies, next step here is to analyse involving a in depth study of selected comparable acquisition so as to determine those most relevant for valuing target. As a part of process banker re examine business profile & benchmark the key stats & ratio’s to find the most appropriate acquisition. Each acquisition is closely examined as part of final refining with best comparable acquisition is identified & outlier is eliminated. As would be expected recent deal involving a direct competition with similar financial information is more relevant than older transaction from different point in business cycle and credit cycle.

#Determine Valuation:

The multiplier of selected comparable acquisition are used to find out implied valuation of target. while multiple used vary by sector key multiples used is EV/EBITDA and Equity multiple. banker generally use mean and median for universe to set preliminary valuation range, with high & low also serve as references.

As noted valuation is a art in addition to a science therefore, while mean and median can be used to find the initial value banker use multiple of closest 2 or 3 best transaction. The chosen multiple is then applied to targets LTM financials to determine implied valuation of target.

"Valuing a company is part science, part judgment — and comparable company analysis is where the two meet."

"This article draws heavily from Investment Banking by Joshua Rosenbaum and Joshua Pearl — an essential read for anyone serious about corporate finance." Lets begin.

Comparable company analysis is one of the primary methods of used to value companies along with DCF (discounted cash flow), asset based valuation, precedent transaction analysis etc. It help us to value a private company & to help analyze value for public company. The foundation of comparable company analysis is that similar companies should trade at similar multiples due to the fact that they share similar business, financial characteristics, performance drivers and risk factors. The core of the analysis if to find out appropriate peers of the target company, peers are then bench-marked against one another based on financial ratios & statistics. The valuation range is then calculated by applying selected multiples to target relevant financial ratios/stats.

2 most common multiples used for bench marking are - P/E multiple and EV multiples

P/E multiples are most popular among retailers, within banking sphere EV multiples are widely used as they are unrelated to business operations.

Step by step approach to comparable company analysis:

1. Selecting the universe of comparable companies

2. Locate the necessary financial information

3. Spread key stats, ratio and trading multiples

4. benchmark comparable companies

5. Determine valuation.

lets dive into each step one by one:

#Selecting the universe of comparable companies:

The foundation of comparable companies analysis is to find out appropriate comparable company, to find out appropriate comparable we need to understand the target company very well. This could be easy for certain sectors and difficult for others.

For companies with no clear publicly traded comparable banker seek companies outside the target’s core sector that share business & financial characteristics on fundamental level.

For eg, Publicly trading window manufacturing company has no publicly trading peer, If universe could be expanded to include companies that manufacture building products, serve home builders or have exposure to housing cycles the probability of locating company with similar business drivers is increased. In this case we can include related building products manufacturer such as decking, roofing, doors & cabinets etc.

Study the target first: Studying the target is essential to determine appropriate comparable at this stage banker is encouraged to read & study as much as possible about the company and the sector as a whole through sector specific material. selection of comparable happen only after understanding of target companies business model.

Screen target: Once the target company business is well understood banker use various resources to screen for potential comparable companies, At this stage focus is on identifying companies with similar business profile. Best is to start with examining competition of the target company. competition share business risk and character and we can find them in equity research reports especially initial coverage reports, investment presentations or in sector reports.

# Locate the necessary financial information:

The section provide overview of various sources for necessary information to calculate ratios and multiples of selected companies.

Common sources include: SEC filings (US companies), earning announcements, investment presentations, equity research reports, consensus estimates, press releases etc. Company analysis can be done historically & forward looking, for future years financial performances are typically sourced from consensus estimates as well as equity research reports.

#Spread key statistics, ratios & Trading multiples:

Calculation of key statistics & ratios: Here we will calculate key stats & ratios of the target and comparable companies based on certain metrics such as:

• Size ( Market value, equity value, enterprise value, key financial data such as sales, gross profit, EBITDA, EBIT & net income).

• Profit ( Gross profit, EBITDA, EBIT & net income margin)

• Growth profile ( historical & estimate)

• Return on investment ( ROIC, ROE, ROA & dividend yield)

• Credit profile ( leverage ratio, coverage ratios, credit rating)

Lets understand some important concepts being discussed in the list.

#Equity value: Popularly known as market value or market capitalization is calculated by multiplying market price and fully diluted out standing shares.

Calculation of fully diluted share outstanding: Its calculated by adding no. of shares represented by in the money options, warrants & convertible securities to basic share outstanding.

A) Options and warrants- Treasury stock method (TSM):

TSM assume that in the money options & warrants exercised at strike price with resulting option proceed used to repurchase outstanding shares of stock at company current price. As the option strike price is less than current market price the no. of share repurchased is less than additional share outstanding from exercise of option resulting in net issuance.

B) Convertible & equity linked securities- If convertible method:

It include broad range of instrument such as convertible bond, convertible preference stock etc. under if convertible method if convertible are in the money they are converted to additional shares. convertible debt also leads to upward adjustment of net income to account for foregone interest expense adjusted for tax associated with coupon on convertible.

# Enterprise Value (EV): EV is sum of all ownership interest in company & claim on its assets from both debt & equity holders.

EV= Equity value+ debt value+ preference share + non controlling interest - cash & cash equivalent.

EV is considered to be independent of capital structure, lets understand this with an example,

Eg 1: If unlevered company issue debt then debt increase and cash increase overall EV remains stable.

Eg 2: If company issue equity to payoff debt, then equity value increase is offset by decrease in debt value.

Supplementary financial concepts to know:

1. Calculation of LTM: companies report performance quarterly, therefore in order to measure financial performance for LTM period. company result of previous 4 quarters are summed.

   LTM = prior fiscal year + current quarter - same period quarter last year

2. Calenderization: US companies report data as on 31 December while other companies report data as on 31 march. variation in fiscal year end among comparable can distort comparison.

   To account for variation each country’s financial is adjusted to common period for clear comparison, this is known as calenderization.

3. Adjustment of non recurring items: To assess company’s financial performance on “normalized” basis, it is standard practice to adjust reported financial data for non recurring items a process called normalized earnings.

   These include: Adding back one time charges or removing one time gains, in many cases banker have to use discretion to determine whether certain expenses are recurring or non recurring.

   For eg, large pharma companies may find themselves in courts regularly due to lawsuits by drug manufacturers related to patents.

   When adjusting for non recurring items its important to keep in mind pre tax and post tax adjustments

   Pre-tax restructuring cost is added back to calculate adjusted EBIT & EBITDA, to calculate net income pre tax charges need to be tax adjusted before adding back

   Post tax could be added back directly to net income but need to be grossed up for EBIT and EBITDA.

#Calculation of key multiples:

While companies can have different multiples according to their sector the generic structure include a measure of market valuation in numerator ( EV or equity value) and company’s financial performance metric in denominator ( EBIT, EBITDA or net income)

For EV multiple denominator has profit metric that flow to both debt and equity such as EBIT and EBITDA.

For equity value multiples the denominator must have financial metric that is only for equity shareholders like net income.

1. Equity value multiples (P/E): Current market price divided by EPS, this ratio can be viewed as measure of how much an investor are willing to pay for a dollar of company’s current or future earning.

   P/E can be based on forward outlook using forward EPS, high P/E shoe high investor earning growth expectations.

   P/E is relevant for mature companies and that have shown ability to show consistent growth.

   Limitations of P/E - not relevant for company’s with no positive earnings, net income is net of interest this means it depend on capital structure of the company as a result two comparable companies can have different net income due to difference in capital structure leading to different P/E.

2. Enterprise value multiples: EV is for both debt and equity, most popular EV multiple are EV/EBIT, EV/EBITDA, and EV/sales.

   A.) EV/EBITDA or EBIT: EV/EBITDA is independent of capital structure and taxes as well as distortion that may arise from differences in depreciation and amortization.

   If one company did capex recently and other didn’t then company who did capex will have a larger value of depreciation and amortization for current period, this will effect its EBIT margins but not EBITDA margin.

   For this reason to prevent probability of discrepancy in multiples of company with recent acquisition or capex, EV/EBITDA is used not EV/EBIT.

   B.) EV/Sales: Sales give indication of size but not necessary converts to profits or cash flows, In certain sectors & company with little to no profits EV/Sales can be relied upon as measure of valuation multiple.

{ We have discussed sector specific ratios at the end do read them }

# Bench marking the comparable companies:

Once initial comparable companies are known is selected & key financial statistics, ratio are spread the banker is set to perform bench marking analysis.

Ultimate objective of bench marking is to derive target’s relative ranking so as to frame valuation accordingly.

We have broken bench marking into 2 parts:

1. We benchmark key financial ratios & stats for target and its comparable in order to establish relative positions, with focus on finding the closest or the “Best” comparable and noting the outliers.

2. We analyze and compare trading multiple of peer group, placing particular emphasis on best comparable.

A.) Bench marking financial ratios and stats: The first stage of bench marking involve comparison of target & comparable universe on basis of key financial performance metric, this metric can involve size, profit, growth, return and credit.

Bench marking goes beyond qualitative comparison of comparable financial metric, in order to access target relative strength banker need to have a strong understanding of each comparison company’s story. Eg: reason for such high growth? why margins are greater or lower for a company? Is company a market leader? Is company gaining or losing market share? etc.

The ability of a banker to interpret such issues are critical to develop targets relative position.

B.) Bench marking trading multiples: This enable analyst to look at range of multiples and access relative valuation for each companies comparables.

As with ratio, analyst calculate mean, median, high and low for range of multiples providing a reference point of target range. Once trading multiples are analyzed the banker conduct further refining of comparable depending on resulting output, it may become apparent that certain outliers need to be removed.

# Determining Valuation:

Trading multiple of comparable companies serve as basis for deriving appropriate valuation range. banker typically use mean or median of most relevant multiple of sector to extrapolate highest range.

Multiple of best comparable resource are typically relied upon as guide post for selecting highest range.

As part of exercise banker must also determine which financial period data is most relevant for calculating multiples.

Depending on sector, point in business cycle, comfort with consensus estimate comparable companies may be trading on basis of LTM, 1Y forward or 2 years forward.

Selected multiple are then applied to target company to finally calculate our implied value.

As closing its important to understand areas where bankers can make mistakes, most common among them are:

1. Inclusion or over emphasis of inappropriate comparable companies.

2. Incorrect calculation of LTM, EV, diluted share oustanding, equity value etc.

3. Failure to incorrectly remove non recurring items.

Some sector specific ratios:

{Thank you for reading till end to share your opinion on the topic}

Returns in finance is measured as sum of Risk free rate and Risk premiums to compensate for the additional risk, the additional risk investors bear for investing in equity markets is known as Equity risk premium

What is Equity risk premium (ERP)?

Equity risk premium is the extra premium that an investor will ask for investing in a countries equity market over and above the risk free rate of the countries currency to be compensated for the extra risk associated with the equity markets.

The core concept that explains a risk premium is extra return for extra risk.

We know bonds have fixed payment obligation but equity returns are implicit that is when you buy the share it is not written on it that it will give you a specific return, in fact the returns of equity is far more volatile than bonds thus making equity riskier than bond. Not saying bonds are risk free their returns are volatile to changes in interest rates but compared to equity bonds are less risky.

Risk from prospective of whom?

Earlier we said that ERP is the extra return an investor expects for investing in equity markets of a country over and above the risk free rate,

But who is that investor? Should we consider any random investor and ask them their perspective of risk in a equity market?

When talking about risk premium we are presumably talking about risk from the perspective of Marginal investors, But who are the marginal investors? and the risk is the extra systematic risk that adds to their well diversified portfolio as a result of adding a particular security.

Marginal investors are institutions who manages a well diversified portfolio, such that they face no idiosyncratic risk or unsystematic risk. unsystematic risk is risk that affect a particular company or sector. unsystematic risk can be reduced to negligible amount through diversification and since this risk can be diversified away therefore they are not rewarded.

“Market only reward for systematic risk”

Systematic risk is Market risk which affect all the securities of the market and cannot be reduced through diversification.

We calculate expected return from the perspective of marginal investors as this entities are well diversified and are not affected by unsystematic risk and therefore are used to calculated additional risk in a equity market.

Importance of Equity risk Premium.

1. Used in calculation of Discount rate: Equity risk premium is a very important element of Cost of equity and Cost of capital calculation, a higher risk premium leads to higher discount rate which in turn reduces the present value of future cash flows which can make an asset look significantly overvalued compare to a situation where lower risk premium was used.

2. Investment Decision making: Investors can use Risk premiums to make their investment decisions across geography and asset classes. Equity risk premium is low at time markets are high, when investors don’t feel much fear. We know that price of an asset is equal to Present value of future cash flows, if we use lower risk premium in case of market is at its peak we will be paying more for an asset compared to what we would have paid is equity risk premium of the market was low.

   Price of Asset = PV of future cash flows / Discount rate

   So, if you believe that stock markets today are overvalued then you implicitly believe that the market has a lower equity risk premium than it should be, when comparing assets across geography and asset classes investors will prefer higher Risk premium over lower. This means if investor believe that equity risk premiums are low compared to corporate risk premium then they will invest their money in corporate bonds than in equities.

Notice the spike in equity risk premium in 2008 due to Lehman Brothers crisis and 2020 due to the Pandemic. The fall in equity risk premium after the Pandemic justifies the bull run global equities witnessed after the Pandemic.

Factors Effecting Equity risk premium

1. Risk aversion and consumption preferences: As investors became more risk averse the equity risk premium increases as investors are not demanding higher returns for a similar risk, risk aversion can change due to differences in investors age and consumption preferences. As investors grow old they became more and more risk averse, so it can be said that as global populations average age increases the risk aversion will also increase and thus increase equity risk premium.

Chart A

Chart B

As seen in Chart A and B we can say as the population in US is getting older we are seeing a increase in average equity risk premiums.

Consumption preferences, we will expect the equity risk premiums to increase if the investors prefer to consume today rather than save for future, in this situation you have to give an investor extra returns to defer his consumption. Thus ERP increases as savings in a economy decreases.

2. Economic risk: Fluctuations in economy affect all the firms irrespective of how diversified you are economic risk can affect your returns, simply more volatile a economy is greater is the ERP. Economic variables such as inflation, interest rate and GDP growth effect the return an investor can expect from the economy, More stable and predictable a economy is lesser is the ERP.

   

   Global Economic growth fluctuations have reduced in last one decade, as a result the Global ERP has reduced.

3. Liquidity and Fund flows : Another risk that affect all the equity investors around the globe in liquidity, if investor has to realize his security at a discount as their are less participants ready to purchase security in the market then market is said to be illiquid. Liquid market is a market in which investor can sell his investment quickly at a fair price. when liquidity decreases investors demand higher premium to compensate for less liquidity.

   Another way to measure liquidity is fund flow, either from other assets or geography. If fund flow into an equity market increases, equity risk premium shall decrease every thing else being constant. whereas fund flow out of market should increase the ERP. This argument justify lower equity risk premium in growing economies like China and India where there is restriction on investment in foreign markets.

Different methods to calculate equity risk premiums:

Now after understanding what equity risk premium is and how important it is for valuation, we now focus on different ways to calculate equity risk premium:

1. Survey Approach: Equity risk premium is what investors expect for investing in risky equities over and above risk free rate. so it sounds quite reasonable to use survey approach to ask investors about there expected returns. broadly we can ask retail investors and institutional investors about there expectations on returns from equity. The problem is that this approach may sound reasonable but it is quite unrealistic to ask each investors about there expectations on equity returns, one argument could be to not include retail investors and only ask institutional investors about their expected return but still this approach can be quite costly an impractical to use. One such institute that conduct such surveys is Natixis, below is the extract from their latest report.

Their are 2 main advantages of using a survey approach:

A.) They change responsively to recent stock price movement with survey number increasing and decreasing after a major market event.

B.) Survey numbers can be used to predict market movements as when investors became too optimistic about the market it is a sign of upcoming shortfall.

2. Historical Premiums: Most widely use measure of equity risk premium is historical risk premium. In this approach actual return earned by stock market over and above default free security is calculated and taken as equity risk premium. (RM- RF) i.e Return from market - returns from default free securities.

   Their exist some issues while using historical ERP:

• Question about how far to go? Ideally longer the time frame better the estimate as longer time frame means smaller standard error,

  Std error = Std deviation/√n

  As sample size increases standard error decreases, Some might argue that shorter time frame is better representative of current trends and going far back 100 years is irrelevant as market perception towards risk has changed significantly towards risk, they are right but the disadvantage due to increased std error will far succeed the benefit of using a shorter time frame.

• Secondly, question might arise on what type of average to take? Arithmetic or geometric, Academicians have proven that geometric average benefits far succeeds arithmetic average benefits when using the number in forecasting for multiple years.

• Lastly, we must understand what risk free rate to take to compare with the market return, 1 year risk free rate or a longer 10 year risk free rate? Some practitioners argue that using a short term risk free rate is better as it has no effect of changes in interest rates that long term risk free rate has, but they need to understand that there exist a re-investment risk that will emerge once a 1 year bond expire and you have to re invest it in another 1 year bond which might not be same as previous. therefore its better to use risk free rate to compare market returns same as risk free rate used in estimation of expected return.

All seen if we have to use historical ERP in our valuation it is best to use long term returns of market and bonds, use geometric average over arithmetic and being consistent with the risk free rate used in expected return calculation to be used when compared to market return,

Another issue that might be observed when using historical ERP is adding a troublesome year such as 2008 returns will reduce the risk premium as equity markets performed poorly and contrary to it bond market performed well,This will also increase if we a year such as 2009 which gave great returns due to smaller base. This is contrary to our research that we did that market feels more fear at bottom and less fear at the top.

2. Implied ERP: In valuation our inputs should be forward looking, when we discount future cash flows it does not make sense to use a discount rate which is backward looking and assuming same in future, rather our discount rates should also be forward looking. This method does not depend on historical data rather assumes that markets are perfectly priced.

DCF based model: Its based on simple valuation belief, the value of a security is present value of future cash flows. for example an asset pays you $5 till perpetuity and you are willing to pay $30 for the security than you are implicitly assuming a required rate of return of 16.66% (5/30).

Consider a simple equation: Value = Expected dividend and buybacks next year/(Required rate of return - Expected growth rate)

4 out of 5 inputs can be derived very easily being: Market price of index, Expected dividends and buybacks next year, Expected growth in earnings and dividends in long term. the only unknown is required rate of return which can be calculated using this equation.

Model assumes that companies pays out their residual cash flows in form of dividends

For example: Current price of S&P 500 is $1000, expected growth is 2.5%, Dividend yield is 10%. we can estimate required rate of return as

1000 = 100(1+2.5%)/(r-2.5%)

solving the equation gives us r of 7.75%. Subtracting Risk free rate lets assume 4% give us a ERP of 3.35%.

We normally divide the periods into high growth periods and terminal growth period cause we cannot assume growth rate to continue to be larger than economic growth till infinity, normally we attach risk free rate as terminal growth rate of index till infinity.

But why are we taking Dividends and buybacks as cash flows from an index but not the actual cash flows of each of the companies that makes up that index and then find required rate of return??

In this model we assume dividend and buybacks as proxy for Free cash flows from each firm as calculating free cash flows of each firm in an index can be a lengthy task,

The above chart shows how to calculate implied ERP for an index

Benefits of Implied ERP:

• Forward looking: In contrast to historical ERP implied ERP is forward looking as required by valuation, it forecast future cash flows from an index and try to find a rate which will bring the future cash flows to present price.

• Dynamic: Equity risk premium changes as price of index changes. Its sensitivity to market prices are tool to study market trends.

The Implied ERP of brazil showed volatility being stable during periods of 2007 to 2104 but then showing a spike from periods beyond that due to political turmoil

3. Spread Approach: The logic behind this approach is simple, not all equity markets are similar in terms of risk. Some are riskier than others for example, If you have been given $1000 and asked to invest in 2 markets :

   A. USA

   B. Mexico

   The expected return from both the market are 6% where will you invest?? Definitely in US because it is a less risky market compared to mexico. Now we know mexico is riskier than US but how much riskier and how can we quantify this risk ? Answer to this question lies in Country risk premium.

Country Risk

Surely some countries are riskier than others, you can’t say that the amount of risk a investor face in US is same as Brazil, India or Nigeria. definitely some countries are riskier than others, but what makes them riskier and should the investor be compensated for those risks? and why should we care ?

We should care about country specific risk as :

1. Investors are increasingly diversifying there portfolio to include companies of different countries to diversify their risk and to get extra returns, this exposes them to various country risk which they should know.

2. Domestic companies are also expanding their operations in different countries and thus getting exposed to their risk, an investor investing in that company should understand the country risk exposure the company has.

Sources of Country risk :

1. Stage of Life Cycle: Similar to Corporate Life cycle which shows how mature a company is to make estimates of its key features like growth, risk etc, we can use a country life cycle to see which stage the country fit and make estimate about the level of growth and risk we can expect from that country.

   Countries in early stages of life cycle can be expected to have a greater risk than country in mature stage.

2. Political Risk: Political risk can include components such as type of government (democratic or Autocratic) many individuals believe authoritarian style of government leading to more control can reduce country risk as the government can take actions on required matters quickly but the drawbacks of an authoritarian government far succeeds its advantages, various drawbacks cold include increases corruption, violence leading to increase in country risk.

3. Legal Risk : Companies and investors are more than concerned about a countries laws and regulations because they have to operate under it, if the legal system is not matured to provide justice to company in any matters, it can have serious consequences for the company. countries having an underdeveloped legal system can have a greater country risk

4. Economic structure: If a country derive maturity of its economic output from a single commodity than its a serious risk as a decline in commodities price or a decline in its demand can have a negative consequence for the country.

simply, a Emerging countries ERP can be calculated by Adding country risk premium to US ERP, Since we assume US to be risk free.

Emerging country ERP = US ERP + Country risk premium.

We can quantify country risk premium in 3 ways:

1. Market interest rate approach: If a government issues bond in foreign currency then the interest rate on the bond compared to a risk less investment in that currency gives us country risk premium of that country.

   For example: Brazilian govt 10 year $ denominated bond yield = 6.5%

   10 Year US treasury bond rate = 4.24%, US ERP = 2.5%

   Brazilian country risk premium = 2.3%

   Brazilian market ERP = 2.5 + 2.3 = 4.8%

2. Sovereign rating approach: We can use countries default rating and assume that the country has a similar country risk as all the countries in that rating and is any of the country in that rating has a US denominated bond we can use that spread and apply it every other country having similar ratings. This ratings are provided by moody’s and S&P.

   For example : India’s rating is Baa2, US ERP is 2.5%. we will look the ratings and equivalent spread let say 2.16% then Indian ERP will be

   US ERP + Country risk premium

   = 2.5% + 2.16%

   = 4.66%

3. CDS: We can also use countries CDS spread as representative of country risk premium. but here’s a catch, we will have to use countries CDS net of US CDS because even if US is assumed to be risk free it still has a CDS spread this means an emerging country even if it became mature will have at least this spread,

   US CDS spread = 0.50% US ERP = 2.5%

   Indian CDS spread = 0.84%

   Net of US = 0.34%

   India’s Country risk premium = 2.5% + 0.34%

   = 2.84%

   Relative Approach:

4. Goldman Approach: This approach calculated ERP by comparing Standard deviation of 2 equity market, the emerging market and a base market usually US

Emerging market ERP = (SD of country/ SD of US)* ERP of USA

For example: SD of Indian equity market is 3%, SD of US equity market being 1.5% , US ERP is 2.5% then using this approach India’s ERP will be 5%

5. Melded Approach: If we don’t want to use a mature countries ERP to calculate country risk premium we can calculate it using countries bond market data.

   simply stating,

   Equity risk premium = (Default spread on Govt bond/ SD of Bond market) * SD of equity market

   For example: Default spread on Indian govt bond = 2%

   Standard deviation of bond market in India = 1.5%

   Standard deviation of Equity markets in India = 3%

   India ‘s ERP = 4%

   Thanks for reading! Subscribe for free to receive new posts and support my work.

   Share

   ---

A risk free rate is a foundation pillar of valuation but it is often not given much importance as it deserve, Practitioners and Academician often take risk free rate as rate of long term government. But what is really a risk free rate, what is a risk free asset, how can we determine that an asset is really risk free and lastly how can we calculate risk free rate ?… lets answer all the question one by one in proper framework

What is a Risk free asset ?

In finance risk is defined as variance from expected return, whenever a investor invest in certain security, he expects some return from that security and in many instances he does not get what he expects, this is risk

A risk free asset is one which as zero probability of deviation from expected return i.e if an investor expect a number he will get that number. A simple example can be a government bond which promises 3% return in one year. After a year you will get exactly 3% returns from that asset.

Condition of assets to be risk free.

1. No Default Risk : A risk free asset shall not have any default risk. what is a default risk? It is a risk that the amount invested in a bond won’t return the investor his principle and interest amount. This condition practically means no private bond can be considered risk free as private bonds have some probability of default. So only government bonds can be treated as risk free. but, are all governments default free ? we know some government can default, we saw recent example of Sri Lanka where the government announced default on April 2022 as the country faced financial crisis and was unable to repay the amount borrowed. so the rates of certain countries government bond can’t be treated as risk free as they do contain default risk. so how do we deal with such issues?

   

In practice Mature / Developed countries governments with high credit rating are considered risk free such as US, Australia , Canada etc such governments are assumed to be default free. risk free rate for this countries are equal to their long term government bong rate .

US risk free rate = 10 year treasury bond yield

While developing countries like India, Brazil, Vietnam etc have some probability of default, which need to be removed to calculate countries risk free rate,

Risk free rate of India = 10 year government bond yield - Countries default spread

No reinvestment risk: It is a risk that you will not be able to reinvest the return at the same rate as the principle, we know that interest rate are forever changing now imagine you invested in a bond expecting a 10% yield till maturity, when you invested the rates were 10% but after an year the rates have fallen to 7% now you won’t be able to invest the receipts from the bond at the same rate as the principle. this is called reinvestment risk.

This means even if you invest in a risk free asset there is a chance the coupon from those asset are reinvested at a rate different from initial principle amount. One solution to this problem can be to take the coupon out of the bond i.e take rate of government zero coupon bond, this are the bonds that don’t pay coupon until maturity, since you don’t get the coupon you can’t reinvest it at a different rate and therefore the reinvestment risk is fully negated. but, an issues here is that zero coupon bonds are not actively traded as much as other government bonds, they lack liquidity and since they lack liquidity there is an ineffective price discovery therefore, we cannot take rate of zero coupon bond for valuation

A more practical Approach to this issue can be to match the duration of cash flows and maturity of bond. Through this approach we cannot guarantee to fully negate reinvestment risk but it will approximately negate the risk .

Understand it in this way, let say you invested in a 5 year government bond after year 1 the interest rates spiked up, as a result the coupon from the bond will be reinvested at a higher interest rate, year 2 the interest rates feel as a result the coupon from the bond will be reinvested in a lower rate , if you hold the bond till maturity you will be getting an approximately similar returns from the bond negating the interest rate fluctuation

Why is risk free rate Important ?

Risk free rate sets foundation of valuation, its is very important to estimate risk free rate carefully as risk free rate is used in calculation of Cost of equity as well as cost of debt as a result our discount rate i.e WACC ( weighted average cost of capital) can diverse if we take a diverted risk free rate .

calculation of Cost of Equity :

KE = RF+ ERP(1+beta)

calculation of Cost of debt:

KD = RF + Corporate default spread ( for companies in mature economies)

KD = RF + Country Risk premium + Corporate Default spread ( for emerging countries)

Calculation of WACC:

WACC = KE*( Equity/ Total capital) + KD*(debt/ Total capital)

WACC is used to discount future of cash flows to calculate present value of a firm, if we take distorted figures of RF we will diverse WACC as result our valuation will not be reasonable.

if we increase RF it will increase KE and KD as result WACC will be high and an increase in discount rate will decrease the valuation making a firm look over valued.

If we break down firms assets into asset in place and growth asset we can understand another explaining the importance of risk free rate.

“Assets in place” wo assets hain jo company ke paas already exist karte hain aur jo abhi cash flows generate kar rahe hain

“Growth assets” wo hain jo aaj exist nahi karte, lekin future mein value create kar sakte hain — naye projects, naye markets, naye products ke zariye

If Risk free rate increases value of growth assets decreases more than the value of asset in place because growth assets are assets that will provide future benefits/cash flows while asset in place are assets with current cash flows as a result its exposure to discount rate is lesser than growth assets

Why currency matters in Risk free rate ?

Risk free rate is currency specific rate, Risk free rate used in valuation should be consistent with the currency of the cash flows, reason is the nominal risk free rate is a sum of real risk free rate and inflation and the growth given to cash flows also include an aspect of inflation to it, if we use different currency in cash flow and a risk free rate of different currency we will be making a apple to orange comparison

Nominal risk free rate = Real risk free rate + inflation premium

for example: both Japan and US government are considered default free the 10 year Japanese government yen denominated bond rate is 1.65% and 10 year US government dollar denominated bond rate is 4.11% the reason 2 risk free rate differ from each other is expected inflation, the expected inflation in Japanese yen is less than US dollar if we use Japan yen denominated risk free rate and cash flows denominated in US dollar we will over value a firm, because cash flows contain higher inflation premium of US dollar while discount rate are lower due to lesser inflation premium

if we match the currency in risk free rate and cash flow we can value any company in any currency, the currency don’t have to be same of the country in which company is domicile. for example we can value apple in Indian rupee if we use Indian risk free rate to discount the cash flows denominated in Indian rupee.

Ways to calculate risk free rate:

1. $ Approach: If any countries government has issued a dollar denominated bond we can compare it to US dollar denominated bond of same tenor to calculated its Default risk premium. but we can only calculate default risk premium of countries those who have issued US denominated bonds,

   Emerging countries default spread = Emerging countries dollar denominated government bond rate - US government treasury bond rate of same tenor

   Brazilian Government 10 year dollar denominated bond rate is 8.875%,

   While the US government 10 year treasury bond rate is 4.11%

   Therefore, we can easily calculated Brazilian default risk premium as:

   8.875% - 4.11% = 4.765%

   If we value any Brazilian company by converting its cash flows into US dollar we can use 4.11% as risk free rate, otherwise we can value any Brazilian company in Brazilian currency ( Real) cash flows using risk free rate calculated as :

   Brazil government 10 year Real denominated bond rate = 13.80%

   Default spread = 4.765%

   Brazilian Real Risk free rate = 13.80% - 4.765%

   = 9.03%

2. CDS approach = We can calculate default risk premium of a country by seeing the Credit Default Swap (CDS) rate of a country and subtracting US CDS rate from it

   Emerging countries Default Spread = Emerging countries CDS rate - US CDS rate

we use CDS net of US because we have presumably assumed US to be default free and if there is any CDS rate attached to US that rate will be attached to any other country too even if it is default free therefore that rate is not specific to any countries default risk premium, for example current US CDS rate is 0.41% even if India become default free in coming years it will have a minimum CDS rate of 0.41% this means anything excess of 0.41% represents its default risk premium.

India’s CDS rate = 0.95% US CDS rate = 0.41%

India’s CDS net of US ( default spread ) = 0.95% - 0.41% = 0.56%

India government 10 year bond rate is 6.5%

India’s risk free rate = 6.5% - 0.56% = 5.94%

3. Ratings Approach: Under ratings approach default spread of a country can be calculated by seeing the country’s sovereign credit rating given by S&P or moody’s and taking the respective rating’s spread as default spread.

Moody’s Rating and respective spread

For Example: India’s rating as per moody’s is Baa3 which has a spread of 2.18%, if India’s 10 year government bond rate is 6.53%

India’s Risk free rate = 6.53% - 2.18%

= 4.35%

4. Philip Fisher Model: Under this model we can calculate any country’s risk free rate if we have following data:

• Expected Inflation in USA

• Expected Inflation in country for which risk free needed to be calculated

• Risk free rate of USA

RF = [(1+RFus)/(1+ expected inflation in US)]*(1+expected inflation of foreign country)-1

for example: Risk free rate US = 4.11% , Expected inflation in US is 3%, expected inflation India 6%.

Risk free rate of India = [(1+ 4.11%)/(1+3%)]*(1+6%) - 1

= 7.14%

It’s simple unitary method.

“Normalized Risk free rate” : A Myth

As interest rate feel during pandemic many analyst started using a rate that they called “ Normalized risk free rate”, they believed in countries where government introduced Quantitative easing using a normalized rate rather than current rate is more practical as the normalized rate is consistent with long term inflation. They calculated normalized rate by using historical data and running a regression. but their are some fundamental issues in using a normalized rate:

• They said they used normalized risk to stay consistent with long term inflation but no one can predict what will be the long term inflation.

• Risk free rate is minimum rate that an investor can get from market without taking a risk, Practically you can’t invest in a normalized rate their is no security providing a normalized rate in the market it exist only in spreadsheet.

Damodaran sir’s comment: “If you do your valuation, using a normalized risk free rate, instead of actual risk free rate and decide that stock is overvalued, I wish you the very best of luck putting your money in that normalized treasury bond, since it exist only in your estimation”.

Prof. Ibboton says: “ It is dangerous to adjust the data itself, because every period is special in its own way. The normalized risk free rate does not exist, it is nothing”.