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# The Art and Science of Valuation – Part 3

Updated: May 16

#### Income approach and methods – DCF valuation

The DCF Method or the Discounted Cash Flow method to valuation is an income-based approach to valuation. This approach to valuation is based on the assumption that the value of a business is equal to the present value of its cash flows (The cash flows here also include the terminal value of the company being valued). This valuation method can be used to derive both the equity value and the enterprise value. To calculate the Firm/Enterprise Value, one has to use the firm’s free cash flow. On the other hand, to estimate the equity value, one has to use the Free cash flow to equity. We can also arrive at the enterprise value by adding the equity value and net debts.

The two Key Parameters of the DCF Method are that the valuation of a business is the aggregate value of discounted cash flows for an explicit period plus the discounted value of its terminal value. It is the present value (PV) of the future cash flows.

#### The steps involved in estimating the present value of cash flows: ##### STEP 1

The first step for estimating the present value of cash flows is to evaluate the future cash flow for the discrete period. The future cash flow to be estimated and forecasted can either be free cash flow to the firm as in the case of enterprise value calculation or free cash flow to equity as in equity value calculation. The most important distinguishing factor between the free cash flow to the firm (FCFF) or the unlevered free cash flow and the free cash flow to equity (FCFE) or the levered free cash flow is that FCFF does not take into consideration the impact of the interest expenses and net debt repayments whereas FCFE takes this into account.

Formulas for the Calculation of FCFF:

• FCFF = EBIT*(1- Tax Rate) + Non-Cash Expenses – Changes in Operating Assets and Liabilities – Capital Expenditure

• FCFF = Cash Flow from Operations + Tax Adjusted Interest Expense – CapEx

• FCFF = Net Income + Tax Adjusted Interest Expense + Non-Cash Expenses – Changes in Operating Assets & Liabilities – Capital Expenditure

In FCFF, Interest (1- Tax Rate) is added back to the Profit after Tax. The outstanding debt is usually deducted from the Enterprise Value. The movement of debt is not usually captured in the cash flows. The projected cash flows and the terminal value are usually discounted using the Weighted Average Cost of Capital.

Formulas for the Calculation of FCFE:

• FCFE = Net Income + Non-Cash Charges – Changes in Operating Assets & Liabilities – CapEx + Net Debt Issued (Amount Repaid)

• FCFE = Cash Flow from Operations – Capital Expenditures + Net Debt Issued (Amount Repaid)

In FCFE, Interest (1- Tax Rate) is not added back to the Profit after Tax and the outstanding debt deductions are not usually done. The movement of debt is captured in the cash flows. The projected cash flows and the terminal value are usually discounted using the Cost of Equity.

##### STEP 2

The second step involves determining the terminal value, also known as the scrap value, at the end of the discrete period. There are three primary methods of computing the terminal value, and they are as follows:

##### Gordon Growth Model or Constant Growth Model

This method of determining the terminal value is only applicable and appropriate for assets that have infinite life. This method assumes that the company or the asset being valued will generate cash flows and grow at a constant rate forever.

The formula for Gordon Growth Method:

Terminal Value = Free Cash Flow (last year of the discrete period) * (1+ Growth Rate)/ (WACC – Growth Rate)

The Growth Rate here refers to the perpetuity growth rate.

##### Exit Value Method or Market Approach

The exit value method or the market approach method assumes that the business will be sold for some market multiple metrics. These multiples usually make use of the industry average of multiples of similar firms transacted or publicly traded companies and multiply the same with the latest financial statistics (e.g. sales, profits, EBITDA, etc.) Investment professionals most often use this method. This method is applicable to both finite and infinite lived assets.

Terminal Value = Last Twelve Months Exit Multiple x Projected Statistic

##### Salvage Value Method or Disposal Cost Method

Salvage Value Method or Disposal Cost Method is appropriate majorly for finite-lived assets such as mines, oil wells, etc.

The formula to calculate terminal value is:

Terminal Value = Salvage Value of the Asset – Cost of the asset

(Note: This value can be negative)

##### STEP 3

The third and one of the most critical steps in estimating the present value of future cash flows is the computation of the discount rate. The discount rate or the rate used to discount the future value of cash flows should provide for both the time value of money and the risks associated with the future value of the business or the asset being valued. Some of the most common methods used to come up with the discount rate are as follows: ##### Capital Assets Pricing Method (CAPM)

The cost of equity can be calculated with the help of the capital asset pricing model. This formula states that the return of an asset is equal to the risk-free rate plus a risk premium which is calculated as the difference between equity market risk and the risk-free rate and is based on its Beta.

Cost of Equity = Risk-Free Rate + Beta (Equity Market Risk – Risk-Free Rate)

• The Long term Government Bond Rate is usually taken as the Risk-Free Rate.

• (Equity Market Risk – Risk-Free Rate) is also called the equity risk premium.

• The equity risk premium or the Equity Market Risk for each country can be obtained from Prof. Aswath Damodaran’s website.

##### What are the types of risks, and how can they be adjusted for in a DCF?

There are two types of risks:

1. Systematic Risk

This type of risk is also known as the market risk or the risk which cannot be diversified. These risks occur due to factors that affect the market and economy as a result of macroeconomic factors such as inflation risk, interest rate risk, etc. This can be calculated by measuring the volatility of stock prices concerning the overall market index. Beta is one such measure that helps in calculating the systematic risk of a company’s stock.

2. Unsystematic Risk

The unsystematic risk also called the specific risk, is diversifiable and can be prevented if there is a diversified portfolio of stocks. Unlike systematic risks, this is caused due to microeconomic factors and, therefore, specific to the firm and industry in which the company operates.

Betas

Beta is the measure of the uncertainty or systemic risk or volatility of a security or portfolio compared to the larger market. This can be found online or can be calculated manually either with the help of regression or by choosing a group of similar companies, un-levering and re-levering their betas, and finding an average of the same.

A less than one beta indicates that the asset is less volatile in relation to the broader market. A beta of 1 indicates that the asset is as volatile as the broader market. An asset with a beta of greater than 1 indicates higher volatility in the market. A higher Beta indicates higher volatility and risk, but this can also provide higher returns. On the other hand, the low beta stocks possess less risk and usually provide meager returns. Therefore, Beta is generally used as a risk-reward measure.

We need to find betas to provide for the systematic risk in investing in a particular company. There are different methods to arrive at the Beta for a company.

The formula for calculating Beta can be given as follows:

Beta = Market Variance/ Covariance

The variance here is that of the market. It helps get a measure of how the market moves in relation to its average. On the other hand, covariance here refers to the stock’s return on the market.

Beta = Correlation of returns from the security* Standard Deviation of security returns/ Standard Deviation of market returns.

Regression Betas

One of the most standard and easy methods to arrive at the Beta of a stock is to conduct a regression analysis of the stock returns against the market returns.

The slope of the regression obtained would be the Beta of the company or stock, and it measures the risk involved with the stock. However, this method has many limitations, like the possibility of a high standard error and the reflection of a company’s financial leverage rather than the current leverage.

#### The Bottom-up Betas

Bottom-Up Betas provide a more accurate and better way of coming up with the Beta for a particular company or a stock. The steps involved in figuring out the Beta for a firm are as follows:

• This would involve finding the businesses (this could be many) in which the firm is operating.

• The second step involves finding a group of publicly traded companies in the same industry similar to the company and each type of business undervaluation. Then we will have to find their regression betas and find the average of the same. Once this is done, the average of their debt-to-equity ratio is to be taken into consideration. This can be used to un-lever the betas.

• Unlevered Beta = Simple Average of the publicly traded companies selected/ (1+ (1-T) (Average debt to equity ratio of the selected companies)

• In the case of a multi-business company, it is crucial to determine the value the firm derives from each business. Here, either business can be valued separately, or the revenues and the operating income of each business can be taken into account as weights.

• Once that is done, we will be required to compute a weighted average of each of the un-levered betas of the company’s different businesses undervaluation based on the weighted average derived from the third step.

Unlevered Beta for a firm = Weighted average of the un-levered Beta of the different businesses the company operates.

• The last and final step in determining the bottom-up Beta for a firm is levering the un-levered Beta based on the market debt-equity ratio of the firm. If there is an expectation of a change in the debt-to-equity ratio of the firm, there will also be a change in the levered Beta over time. The formula for levering the Beta is as follows:

Levered Bottom-up Beta = Unlevered Beta of the firm* (1+ (1-t) (Debt/Equity))

##### Example of Bottom-Up Beta Calculation

The group of publicly traded comparable companies selected to get a beta for X Company, a private limited company operating in the pharmaceutical industry, are Cadila Health, Aurobindo Pharma, Lupin, and Torrent Pharma. Once the Beta of these stocks is identified, the average of the same should be found. The average Debt to Equity Ratio of the company should also be found. The un-levered beta of X Company can be obtained by using the following formula:

Unlevered beta = Average of the Beta of Publicly traded comparable/ (1+(1-t)(Average of the Debt-to-Equity Ratio)

The “t” in this formal refers to the tax rate applied to those companies. The Unlevered beta so obtained is Once the Unlevered Beta for X Company is obtained, it should be levered again according to the D/E Ratio of the X Company. The formula for the same is

Levered Bottom-up Beta = Unlevered Beta of the firm * (1+(1-t)(Debt/Equity)) Applying the above formula, the levered beta of the X Company can be obtained as 0.48.

##### WACC – Weighted Average Cost of Capital

The weighted average cost of capital or WACC method helps find the cost of a company’s capital and is weighted according to its proportions. All types of capital, including preferred stock, bonds, equity, long-term debt, etc., are taken for computing the weighted average cost of capital.

WACC = Cost Of Equity * (Equity /(Equity +Debt)) + Cost Of Debt * (Debt /(Equity +Debt))

The cost of equity to be used in this method should be obtained with the help of the Capital Asset Pricing Model Method.

##### Computation of Cost of Debt

It is essential to consider the tax rate while computing the cost of debt because the interest expenses are tax-deductible. As a result, it should be factored into the cost of debt. T

Effective Cost of Debt = Rate of Interest (1-Tax rate)

##### IRR Method or the Internal Rate of Return Method

The IRR Method of finding the discount rate provides the rate of return earned by a project. This usually returns the rate that makes the total value of the initial outlay and the discounted cash inflows zero. The formula for calculating an IRR for a project is as follows:

IRR = ((Cash Flows)/(1+r)^i) – Initial Investment

##### Build-up Method for Discount Rate

Equity Discount Rate for cost of capital is calculated as follows:

Cost of Capital = Rf + Pe + Ps +/- Pi + Pc

• This formula does not take into account the betas.

• Rf is the risk-free rate of return – Most commonly, the long-term government bond yield is taken as the risk-free rate. E.g. the 10-year Indian Government Bond Yield.

• Pe is the Equity Risk Premium – Premium is the amount paid by investors over and above the amount paid on risk-free investments. That is the amount paid by the investors to participate in equity markets instead of risk-free investments

• Ps is the Size Premium – There is an increased risk of investing in small companies.

• Pi is the industry risk premium – The amount the investors usually expect the future expected return of the industry to exceed the market returns.

• Pc is the Company Specific Risk – Relates to the risks of the company being valued, such as managers, suppliers, customers, etc.

##### STEP 4

The fourth step involves the computation of the Present Value of the future cash flows, which includes both the Free Cash Flows and the Terminal Value. There are two methods of calculating the present value of a series of cash flows, and the method of calculating the same have been explained below:

The present value of a series of cash flows can be calculated with the help of the Present Value formula in Excel. This is a shorter, less time-consuming method. This method involves the use of the NPV formula available in Excel.

The procedure goes as follows.

= NPV (discount rate, series of cash flows)

Here, the series of cash flows should include the FCFF/FCFE and the Terminal Value.

The second method is making use of a formula that is the reverse of the compound interest formula. This method is time-consuming. Under this method, each cash flow has to be discounted separately. PV of a Single cash flow can be calculated using the formula:

Present Value = Cash Flow/ (1+i) ^n

Here, i = Discount Rate, n = the number of the period for which you are discounting. The NPV for a series of cash flows can be calculated with the help of the following formula:

NPV = FV*(1+i) ^0 + FV*(1+i)^1+FV*(1+i)^2 +…… + FV*(1+i)^n

FV = Refers to the future value of cash flows both FCFF and FCFE

The FV of cash flows of the last period of valuation should also consider the terminal value. The math behind this is

NPV = F/ ((1+i) ^n)

Where PV = Present Value

F = Future Cash flows

i = discount rate

n = the number of periods in the future where the cash flow is projected to occur.

##### STEP 5

The last and final step in valuation through DCF is adding all the present value of future cash flows and the terminal value. It is possible to ascertain the equity value by using FCFE and the Enterprise Value with the FCFF. The formula for arriving at the enterprise value is as follows.

Enterprise Value = Equity Value + Debt – Cash and Cash Equivalents

Firm Value = Equity Value + Debt

Equity Value refers to the business value to all the equity holders of the company. Firm Value can be obtained by adding the equity value and the debt.

#### Adjustments to be made to arrive at the equity value of shares:

Once the present value of cash flows both the series and the terminal value are added, the following adjustments should be made:

In the case of Free Cash Flow to a Firm

The Surplus Assets /Non-Operating Assets, Fair Value of Investments, and Cash & Cash Equivalent should be added to the obtained value. The Debts, Specific Contingent Liability, and Preference Shares should be subtracted to arrive at the equity value. The same should be divided by the number of shares to arrive at the fair value per equity share.

In the case of Free Cash Flow to Equity

The same steps which were followed for ascertaining the fair value per equity share using FCFF should be followed here except for the deduction of debt. Debt is not required to be deducted from the FCFE as it is already debt-adjusted.