Real Life Examples & Aswath’s Data
Need for Valuation
Mergers & Acquisitions
Equity Financing
Regulatory & Accounting
Requirements
Litigation & Disputes
ESOPs & Employee
Incentives
Strategic Decision Making
Performance Measurement
Approaches for Valuation
Income Approach (DCF)
Market Approach
Cost Approach
Projects future cash flows and discounts them back to the present using the cost of capital. The Cost of Equity (Ke) is critical here as it directly influences the discount rate in DCF models.
Uses valuation multiples from comparable companies or transactions (e.g., P/E, EV/EBITDA) to estimate value.
Does not directly use Ke; instead, it benchmarks valuation against similar publicly traded peers or deals.
Values a company based on the fair market value of its assets minus liabilities.
Introduction to Cost of Equity
What is Ke (Cost of Equity)?
•The required return that shareholders expect for investing in a company’s equity.
•Reflects the opportunity cost of capital, considering alternative investments with similar risk.
Why is Ke Required?
•Forms the discount rate in equity valuation models (e.g., DCF).
•Determines hurdle rates for projects, M&A deals, and strategic decisions.
•Guides capital structure choices (equity vs. debt). How to Derive Ke
Practical Insights into Ke
Investor Profile
Different investors (VCs, private equity, pension funds) have varying return expectations based on their own mandates, risk tolerance, and investment horizons
Business Risk
(Industry volatility, product concentration, or technology shifts.)
Market Conditions
Investor sentiment, liquidity, macroeconomic environment
Growth Stage
Startups vs. mature companies
Financial Risk
Leverage levels
Key Components of CAPM
Risk Free Rate (Rf)
The return on a theoretically riskless asset (typically long-term government bonds), representing the baseline cost of capital.
Beta (β)
A measure of the stock’s systematic risk, quantifying its sensitivity to market fluctuations relative to the overall market.
Market Risk Premium (ERP)
The market risk premium, reflecting the additional return investors require for bearing the risk of the market over a riskfree investment.
Expected Return (Ke)
“Expected return” is a long-term assumption about how an investment will play out over its entire life.
Adjustments to CAPM
Additional Premiums
Liquidity Premium: Accounts for the higher risk of stocks or assets that are not easily traded.
Small‐Size Premium: Smaller companies often face greater uncertainty and lower liquidity, necessitating an extra return above the standard ERP.
Deal‐Specific Adjustments
Control Premium: If you’re buying a controlling stake, you may pay more to reflect decision‐making power and potential synergies.
Discount for Lack of Marketability (DLOM): A downward adjustment for privately held or illiquid shares that can’t be easily sold.
Beyond the Basics:
In real‐world valuations, analysts often layer on liquidity, size, or other risk premiums to capture unique aspects of the target or market. Additionally, control premiums and DLOMs may be applied in final deal‐level adjustments to reflect ownership structure and marketability constraints.
Risk Free Rate (Rf )
Risk-Free Rate (Rf)
The risk‐free rate (Rf) is the return on an investment with effectively zero default risk, commonly proxied by stable government bond yields. Definition
Common Time Periods & Conventions
General Convention: 10 Year Government Bonds
• Frequently used due to their liquidity and a medium‐term horizon.
• It’s a general convention rather than a strict rule—shorter or longer maturities can be chosen based on the valuation’s time frame.
Examples of Benchmarks
• U.S. Treasuries for USD‐based valuations
• 10‐Year Indian Government Bond for INR valuations
Advanced Considerations
Negative Yields
• Certain regions (e.g., Japan, parts of the EU) have zero or even negative yields.
• Practical Question: “Does a negative Rf lead to a negative cost of equity, and how do we realistically handle that?”
Cross‐Border Valuations
• Some analysts use a ‘synthetic Rf’: start with a ‘safe’ foreign bond, then adjust for local inflation or country risk.
Practical Question: “Should we rely on local government yields, or is a synthetic Rf more appropriate when dealing with volatile or illiquid bond markets?”
Beyond the Basics:
In cross‐border valuations, the chosen Rf typically matches the currency (and often the inflation environment) of the projected cash flows.
Damodaran’s Method for emerging markets (subtracting a credit default spread to isolate a “pure” Rf)
Example: Estimating a Risk‐Free Rate in a Currency Without a Reliable Government Bond
In some emerging markets, long‐term, liquid government bonds may not provide a trustworthy benchmark. One workaround is to start with a known foreign risk‐free rate and adjust for inflation differentials. Given Data
• U.S. Risk‐Free Rate: 3.0%
• Expected U.S. Inflation: 2.0%
• Expected Indonesia Inflation: 5.0% The approximate risk‐free rate for IDR (Indonesian Rupiah) is 6.13%.
Equity Risk Premium (ERP)
Equity Risk Premium (ERP): Advanced Nuances
The Equity Risk Premium (ERP) is the extra return that investors expect to earn on stocks above the risk‐free rate
In CAPM, it quantifies how much compensation the market requires for taking on average equity risk.
As on 1st Jan 2025
BSE 500 Returns ( Geometric Mean ) Practical
Questions:
• Historical: Over how many years?
• Arithmetic or geometric mean (CAGR)?
Historical ERP Calculation
Step 02
Step 01
Step 03
Select an appropriate Mean to calculate the returns.
1. Arithmetic Mean: Simple average of historical differences.
2. Geometric Mean (CAGR): Reflects compound growth rates over the observed period.
Select an appropriate Data Window. Many analysts gravitate toward 10–20 years to balance recency with capturing multiple market cycles
Decide which market index (S&P 500, BSE 500, Sensex 50 etc.) best represents the “market portfolio.”
Beta (β)
Beta:
A measure of systematic (market-related) risk. Better framed as riskiness of business in relation with Market
Why It Fluctuates: Business model changes, leverage changes, market volatility regimes.
While textbooks define Beta as the slope in a regression of a stock’s returns on market returns, in realworld valuation, Beta is the lever that magnifies the ERP.
Practical Insights
Context Over Formula: A Beta of 1.5 might be “high,” but if the firm is in a rapidly growing sector, that might be normal.
Methods of Calculating Beta
1. Regression Method
• Uses historical stock returns versus a market index to derive Beta
• Used Primarily for listed companies with sufficient trading history
Methods of Calculating Beta
2. Bottoms Up
• Identifying comparable companies and making several adjustments to derive Beta
• Used primarily for Private Companies or when regression data is limited
In the absence of Indian comparables, consider selecting suitable peers from international markets. You can also reference Aswath Damodaran’s publicly available data as a substitute for industry Beta
Calculating Beta via Regression – For Listed Companies
Method
Perform a regression of the company’s historical returns against a representative market index (e.g., NIFTY, BSE 500, Sensex).
Data Requirements
Sufficient Trading History: Ideally 2–5 years.
Frequency: Daily, weekly, or monthly returns; monthly is common to balance noise and data availability.
Key Considerations
Time Window Trade‐Off:
• Too Short → Excessive noise, capturing short‐term anomalies.
• Too Long → May overlook structural changes (Ex: Reliance prior to Jio)
Check
for
Practical Tips & Pitfalls
Structural Breaks
: If the company pivoted significantly, split the regression period or adjust accordingly.
Liquidity Constraints: Thinly traded stocks may produce erratic daily returns.
Calculating Beta via Regression – For Listed Companies
Steps for Calculation
1. Get Target Index and Company Historical Data from BSE, NSE site.
2. Calculate % change over the selected time frame and plot down.
3. Use the Slope formula to calculate Beta.
Note: We have adjusted the Stock Split in the prices.
Beta for Private Companies – Bottom‐Up Approach
Why BottomUp?
If the stock is thinly traded, newly listed, or changed capital structure, private comp.
If you want to isolate “business risk” from “financial risk.”
Practical Tips and Issues
Selecting Comparables Leveraging & Tax Rate Differences Segment & Geographic Variations
Often challenging to locate public companies with the same business mix, risk profile, and market exposure.
Unlevering and re‐levering Betas requires assumptions about debt ratios and tax rates
If the target operates across different industries or countries, a single “average” Beta may fail to capture all the risks
Do we use the current D/E or a target D/E for re-levering?
Levered Beta and Unlevered Beta
Unlevered Beta Levered Beta
• Reflects the firm's inherent business risk by excluding financial leverage
• Ideal for comparing companies across varying capital structures, as it isolates operating risk.
• Captures both the operating risk and the financial risk from the firm's use of debt.
• The beta calculated using index returns (in the previous slide) is levered, reflecting the combined impact of business and financial risk.
Relevering Beta
Regression-derived Beta captures both operating and financial risk. We first unlever the industry Beta to remove the debt effect, then relever it using our company's target debt-to-equity ratio to arrive at our Levered Beta.
Bottoms Up Beta
Step 01
Step 02
Step 03
Step 04
Step 05
Compute a levered beta (equity beta) for your firm, using the market debt to equity ratio for your firm.
Compute a weighted average of the unlevered betas of the different businesses (Step 2) using weights from Step 3.
Estimate how much value your firm derives from each of the different businesses it is in.
Find publicly traded firms in each of these businesses and obtain their regression betas from previous method. Compute the simple average to arrive at average beta and then Unlever this average beta
Finding the business or businesses that your firm operates in.
Practical Case Studies
Valuation Challenge: Determining the Appropriate Cost of Capital
Imagine an SPV that is headquartered in India, operates its core activities in Brazil, and earns most of its revenue from the UK, while planning to raise funds from a Singapore-based investor. When a Singaporean entity is tasked with valuing this business, which country's WACC (cost of capital) should be used for discounting?
Options to Consider:
•Option 1: Brazil
•Option 2: India
•Option 3: United Kingdom
•Option 4: Singapore
•Option 5: A weighted average of all these countries, adjusted for risk or other relevant criteria.
•Option 6: Any other approach – please specify!
Discussion Prompt:
Which option best captures the true cost of capital for this SPV, and why?
Practical Challenge: Calculating Ke for a Private Firm
Scenario:
XYZ Electronics is a private limited company in the electronics drivers industry, catering exclusively to the Indian market. Despite rapid growth, it has a negative D/E ratio due to high leverage and limited equity base. With no publicly traded shares, you can’t directly run a regression Beta.
Additional Data:
Debt: 4,57,45,593
Equity: (1,26,69,934)
The company is planning additional equity fund raise of 9 Crore in the following years.
Question:
How would you estimate the company’s Cost of Equity (Ke) using a bottom‐up approach (or any other method), while factoring in its unusual capital structure and strictly Indian market focus?
Step 1: Beta Calculation
Step 2: ERP Calculation
Aswath’s Ready Beta’s
Source: https://pages.stern.nyu.edu/adamodar
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