Discounted Cash Flow

1 Introduction

Discounted Cash Flow (DCF) is a widely used method in the value analysis of any business. The value of an asset is the present value of expected cash flows from an asset. In this context, all the valuation methods including Net Asset Value (NAV),Profit Earning Capacity Value (PECV) and market price endeavour to determine the economic value of an asset but by using different approaches.

The relevance of Net Asset Value (NAV) derived from accounting books continues to diminish as self-generated intangible assets, which are key value drivers of modern corporations, are not recorded under accounting conventions. In PECV, profitability, sales and other relevant multiples derived from the market price of a comparable business is used as the metrics to arrive at the value of the subject business. It is assumed that market participants have paid for the expected future cash flows (FCF) from the asset when price under free market conditions is considered as indicative of value.

Though DCF is the application of the Net Present Value (NPV) rule, which in essence could be reduced to two variables – discount rate and cash flows, the application of DCF could be challenging as cash flows are impacted by several variables and the appropriate discounting rate is always a matter of debate. Several adjustments are also required to derive a finely calibrated value estimate. This article aims to provide an overview of the application of the DCF method in a practical context and the underlying theoretical concepts.

Description

The DCF method values a business based on the projected cash flows the subject business is expected to generate over a given period of time. The expected cash flows are discounted at an appropriate discount rate to determine its present value and thus the time value of money is provided for. A business is assumed to have a perpetual existence and DCF value is the summation of the present values of the cash flows expected in the projected horizon and estimated for perpetuity beyond the horizon.

Future cash flow (FCF) projections are the basic requirement for application of DCF. FCF usually forms part of the projected financial statements or may be derived from the projected income statements and the balance sheets. The FCF could be at the firm level available to the financiers of the business (both debt [D] and equity [E]) or to the equity holders. Generally the FCF to the Firm (FCFF), which represent business related cash flows available for distribution to both the owners (equity holders) of and the lenders to the business, is used in DCF . FCFF is equal to Profit before Interest, Tax, Depreciation and Amortisation (PBITDA) less Capital Expenditure (Capex), Taxes and adjustment for working capital changes. From the foregoing, it is evident that the FCFF is not impacted by the financing pattern of the enterprise. Conceptually, therefore, the value outcomes should not change whether the FCFF is used or Free Cash flow to equity (FCFE) is used.

Projections

1. The valuation estimate which is the output of a DCF model is only as good as the projections, which are built on subjective assumptions both at the macro level concerning the overall economy and business environment and at the micro level specific to the enterprise. In other words, integrity of the valuation output is largely determined by the thoroughness of the projections and its underlying assumptions. Projections review, therefore, entails a through understanding of the overall economy and the market in which the subject enterprise operates.

Common size statements, ratio analysis, peer group comparisons are analytical techniques employed in projections review. Inflationary expectations, currency movements, tariff levels are among the key macro assumptions. Business specific assumptions include pricing policy, salary levels and capital expenditure, which need to be consistent with the overall macro trends that are being projected. For example, it may not be realistic to assume a commodity would fetch prices higher than ruling market prices or to assume that raw material can be procured at lower than ruling market prices. In fact, it is likely that the prices may be influenced by the entry of other competitors prompting the incumbents to counter competition by reducing prices and influence the overall market.

At the micro level specific to the enterprise, working capital assumptions such as number of days of receivables and payables, inventories, trade advances and deposits will need to be estimated. Reasonableness of capex estimate may be ascertained through quotations/ orders placed for machinery and equipment. In this connection, it must be noted that maintenance capex should also be provided for in the projections. However, interest cost, if any, capitalized for accounting purposes is not be considered as capex for determining the FCFF.

Actual tax outflow must also to be projected with reference to the tax laws. Tax deduction on account of interest is to be ignored for computing the FCFF as the tax benefit on interest cost is captured in the discounting rate formula. Though the future FCF is derived from the accounting statements, it is the timing of the cash flows that is important and not the accounting distinction between revenue and balance sheet items. To illustrate- accounting of deferred tax does not impact cash flows but the actual outflow on payment of tax will affect the same.

2 A business entity under ordinary circumstances is expected to have a perpetual existence. But, projections are usually for a finite period. In a DCF model, the estimate of cash flows beyond the horizon is based on the cash flows generated in the last year of the horizon after appropriate adjustments. In order to fit the cash flow projections in a DCF model, the projections need to be at least up to the year in which the business is expected to achieve stable cash flows as the cash flows for perpetuity are based on the cash flows of the last year of the horizon after suitable adjustments. Conceptually the length of the forecast period should not impact value outcome.

It is important to note that it is not possible to forecast the behaviour variables with certainty and projected numbers may be considered as the outcome derived from various possibilities and the probability of their occurrence. In this context, a sensitivity analysis to assess the impact on cash flows by changes in the behaviour of variables is a necessary part of a value analysis exercise.

Theoretical Concepts

There are various theoretical concepts underlying the application of the DCF method. These are explained below:

Discount rate is the return expected by investors after taking into consideration the risk associated with the business. The investor raises return expectations when there appears to be an increase in risk.

Measurement of risk is at the heart of finance and we rely on theoretical insights and certain statistical concepts to arrive at the discount rate. In 1952, Harry Markowitz formulated the Portfolio Theory in a paper entitled “Portfolio Selection” wherein the principle of creation of the frontier of invest-ment portfolios is such that each of them had the highest expected return, given the level of risk that was set out and thus gave formal expression to the intuitive idea that diversification reduces risk. In Markwitz’s formula, Standard deviation (s) of the return on the security is considered as the risk. An investor is concerned with the risk of the portfolio which is the variance (s2) of the portfolio. A well diversified portfolio would encompass all securities in the market and would react to the general market movement and market risk.

Capital Asset Pricing Model (CAPM) is a theory about pricing assets in relation to the risks, which was independently formulated by John Lintner , Jan Mossin and William Sharpe in the 1960s. CAPM continues to be widely used although alternates such as Arbitrage Pricing Theory (APT) and Fama-French Three-Factor Model have been developed subsequently. Among other assumptions, CAPM assumes that all the investors employing Harry Markowitz theory are holding portfolios that are efficient and will maximize return at a given level of risk. An individual is concerned with the risk attached to the final portfolio and thus the risk of the individual asset will be assessed on the basis of the contribution to the variance of the portfolio.

Beta (b), which is the measure of sensitivity of a security in relation to the market as a whole, is the measure of risk. The statistical formula for Beta of a particular security is b = sim / s m2 where sim is the co-variance between the return of the particular security and the market return and s m2 is the variance of the market return.

Treasury bills/ government securities returns are assured and considered risk free thus assumed have a beta of 0. The aforementioned assumption is widely used although it is strictly not correct since only the nominal returns are assured while the real returns (inflation adjusted ) are not unless the security is inflation protected. An investor in a portfolio of well diversified stocks would require a premium for the market risk and this premium is the market risk premium.

Market risk premium = Market returns ( rm ) – Return from treasury/ government securities (rf).

A firm is exposed to business risk and financial risk. The value of a firm and business risk is dependent on its investment decisions and not by how the investments are funded. The theory that capital structure is irrelevant to the value of a firm is a proposition of Franco Modigliani and MH Miller. From a balance sheet perspective of an accountant, the value of the enterprise on the asset side is in-dependent of the ratios of debt and equity on the liability side. Leverage determines the financial risk. Cost of debt is lower than that of equity since debt holders claim ranks before that of equity holders. Increase in debt, however, increases the financial risk and thus the returns expectation of the equity holders (who are the residual claimants) would increase and the overall return expectations may not change. Equity holders have a limited liability and increase in debt may prompt the debt holder to demand a return closer to that of equity to cover the possibility of failure of debt repayment. In the real world, companies operating in sectors such as technology that have high degree of business risk and probability of failure do not have debt or have very low leverage so that the overall risk does not become unsustainable. In contrast utilities which have stable cash flows and thus lower business risks can afford to assume financial risk.

Usually the estimate of beta of the business that is valued is derived from the beta of a comparable company listed on the exchange. The leverage of the comparable company may be different from the leverage the target company has or intends to have. Under the circumstances the observed beta is to be unlevered to derive the asset beta and re-levered based on the firm’s targeted debt equity ratio. While the business risk exposure is reflected in the asset beta the financial risk element is captured on re-levering the beta. Levered beta increases as the proportion of debt increases to reflect the risk of volatility in earnings available to equity holders after providing for interest. It is assumed in practice that debt has a beta of 0. The equation bL = ba (1+(1-t)(D/E)) can be used for levering and re-levering the beta (wherein bL is the levered beta observed in the market, ba is the asset beta (unlevered beta), t is the tax rate and the tax shield on interest payments, D is the market value of debt and E is the market equity value).

Discount rate

It is important to link the discount rate to the as-sumptions underlying the FCF projections and also the expectations of the investor class who are the claimants of the cash flow. Real cash flows without inflation are to be discounted by the rate without inflation, while nominal cash flows, which have inflationary impact, are discounted using nominal rates. FCFE is to be discounted by the return expec-tations of equity holders while FCFF is discounted by the Weighted Average Cost of Capital (WACC). The WACC represents the returns required by the investors of both debt and equity weighted for their relative funding in the entity. WACC is de-rived based on the principles set out in the earlier paragraph.

WACC = Cost of equity (rE)* [E/ (D+E)] + Post tax cost of debt (rD)* [D / (E + D)]

rE = (rf )+ b * (market risk premium)

rD   = Interest rate on debt* ( 1- tax rate)

The equity and debt ratios are based on the mar-ket values and not book values. In practice, book value of debt may be considered its market value if it can be retired with minimum cost or has been contracted recently or can be called on by the lender. Exceptions such as sales tax deferral loan (which does not carry interest) may need to be valued suitably. Equity value may need to be obtained by an iterative process because of the interdependence between cost of equity (due to leverage) and the resultant value.

Thus, the WACC formula clearly illustrates the relationship between return expectations and assumption of risk. Risk that can be diversified away is not rewarded while non-diversifiable risk is compensated in the formula. The minimum re-turn, which is the risk free rate, and market risk are common to all companies. A Beta of 1 means the firm is as risky as the market or a well diver-sified portfolio. Beta of 1.5 means the firms return expectation is 50% more volatile than the market and thus the risk premium increases by 50% over the market risk premium. A firm’s beta of 0.5 would reduce the return expectation to 50% of the market risk premium as the firm is less volatile than the market and its addition to the portfolio reduces the volatility of the portfolio. The building blocks of discounting rate are very clearly visible in the WACC formula.

The WACC formula also implies that unlisted shares, which do not have an exit mechanism that a listed security affords, may have a higher return expecta-tion from investors because of their lack of market-ability. similarly, in certain cases the project may not be complete and the asset beta of a completed project would not capture the project completion risk. The WACC may have to be appropriately adjusted up to compensate for the aforementioned factors.

The formula for discounting factor to be applied for each period is 1/( 1+WACC)n where n is the year in which the cash flow occurs. In a business, cash flows are distributed through the year and do not occur as a lump sum at the year end. Therefore n is corrected for midyear (on an average).

Perpetuity value

A business is expected to have perpetual life though it is usual to have a financial projection for a limited time horizon. The value of business beyond the horizon is captured in the perpetuity value. Perpetuity value usually accounts for a large part of the business value and needs to be estimated with care.

Usually the starting point for estimating the FCF

for perpetuity is PBITDA in the terminal year of the horizon period. Capex/ incremental working capital requirement for perpetuity are to be linked to assumed growth and depreciation. In case full plant utilization has already been achieved in the horizon, growth is not possible without capex invest-ment. Tax is a major outflow and is to be modeled carefully. Tax depreciation benefit is not available unless there is capex. The depreciation benefit may be equated to the capex though the tax benefit is spread over a longer period and its present value is usually lower.

Additional working capital requirement may be estimated by applying the growth percentage to the net working capital available at the end of the horizon. Year on year growth in cash flows for per-petuity is assumed after considering factors such as the competitive environment of the business, stage of growth of the overall economy, actual growth achieved and expected in the horizon etc. Typically companies in a mature economy grow at a lower rate as compared to entities in a developing economy. The cash flow is capitalized at the rate (WACC – g ) where g is the % growth assumed. The value is discounted for the present using the appropriate discount factor.

Other adjustments

The entity being valued may have non -operating assets on the valuation date, the income streams of which do not form part of the cash flows. The market value of such assets (net of taxes and expenses on realization ) is to be added to the business value. Treasury investments, land holdings (surplus) are examples of non- operating assets. Contingent li-abilities on the valuation date needs to be adjusted after considering the probability of materialisation and notional tax relief on the same. Arrears of divi-dend on cumulative preference shares not recoded in books are to be adjusted, if necessary.

Merits and Limitations of DCF

DCF explicitly uses forecast of cash flow genera-tion while other methods use proxies to get to the present value of cash flows. DCF unbundles key value drivers and the sources of risk with a great deal of clarity, thus facilitating value analysis and informed decision making much more effectively as compared to other methods. In an acquisition scenario, the synergy benefits and costs can be mapped in the model and its valuation implica-tions clearly understood through a DCF analysis. PECV, for example, captures the risk related return and growth in a single number. Given the forego-ing, DCF is indispensable as a tool to understand value drivers and facilitate value discovery from a corporate finance perspective. To value a finite life project, DCF may be the better alternate as multiples of comparable companies usually factor in perpetual existence.

The various data parameters used in building the WACC appears objective. On a closer examination, however, each of the parameters is open to chal-lenge and interpretation. Beta estimate of a traded company varies with the time period which is used to obtain the estimate. Risk free rate is strictly not risk free and impacted by several factors. There are theoretical issues with market risk premium. The parameters based on historical data are used to discount future cash flows and there is no assurance that the future will be a repetition of the past (extensive theoretical literature giving the dimensions of the issues involved is outside the scope of this overview).

In sum, DCF value is as good as the projections it is based on. Any bias in the projections would impact the value. The reasonableness of value and the projections necessarily needs to be tested with market prices of comparable companies. In case the value outcome under DCF is at significant variance with the value derived from market comparables, it would be necessary to inter alia reassess the reasonableness of the projections / market benchmarks applied to attempt to reconcile the values under both the approaches.

Considering the high level of subjectivity, DCF is seldom used in isolation and market benchmarks are important sanity checks to assess the reasonableness of the value outcome as the fair value is defined as the “the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date”. Under various accounting standards, the projections being unobservable inputs are lower in the hierarchy as compared to market based inputs such as multiples. Thus DCF may have a limited application for pure value measurement required for financial reporting, statutory purposes.

Practical application (in the Indian context)

As already discussed application of CAPM in its pure form may not be very challenging particularly in the Indian context. Apart from subscription based data services, stock exchange websites (NSE, BSE) are rich sources of data an d qualitative information and are freely available. The return on 10 year Government of India security may be considered as the rf. A well diversified index (in India– BSE 100, NIFTY, Sensex) is considered as a proxy for the market. The return from the index may be used to derive an estimate of market risk premium. The beta estimate of a particular security (used as a comparable) can be derived from the historical data of the prices and the indices by applying the statistical formula. Betas of the shares that are part of the index are readily available on the websites of the exchanges. An illustrative DCF computation is set out in the annexure.

Notes:

Fixed assets include land not used for business which has book value of INR 100 and market value of INR 300.

The market value of Investments is INR 90 Excise duty claim of INR 25 is matter of legal dispute. Legal counsel has opined the probability of materialisation of the claim is ~ 25%.

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Suggested Reading / References:

Damodaran on Valuation ( 2nd Edition) by Aswath Damodaran; Published by John Wiley and Sons, Inc.

Principles of Corporate Finance (6th Edition) by Richard Brearley and Stewart C Myers; Published by Tata McGraw- Hill Publishing Company Limited.

Valuation – Measuring and Managing the Value of Companies ( 4th Edition) by Tim Koeller, Mark Goedhart and David Wessels; Published by John Wiley and Sons, Inc.