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Security analysis is about valuing the assets, debt, warrants, and equity of companies from the perspective of outside investors using publicly available information. The security analyst must have a thorough understanding of financial statements, which are an important source of this information. As such, the ability to value equity securities requires cross-disciplinary knowledge in both finance and financial accounting.

While there is much overlap between the analytical tools used in security analysis and those used in corporate finance, security analysis tends to take the perspective of potential investors, whereas corporate finance tends to take an inside perspective such as that of a corporate financial manager.

#### Equity Value and Enterprise Value

The equity value of a firm is simply its market capitalization; that is, the market price per share multiplied by the number of outstanding shares. The enterprise value, also referred to as the firm value, is the equity value plus the net liabilities. The enterprise value is the value of the productive assets of the firm, not just its equity value, based on the accounting identity:

Assets = Net Liabilities + EquityNote that net values of the assets and liabilities are used. Any cash and cash-equivalents would be used to offset the liabilities and therefore are not included in the enterprise value.

As an analogy, imagine purchasing a house with a market value of $100,000, for which the owner has $50,000 in equity and a $50,000 assumable mortgage. To purchase the house, the new owner would pay $50,000 in cash and assume the $50,000 mortgage, for a total capital structure of $100,000. If $20,000 of that market value were due to $20,000 in cash locked in a safe in the basement, and the owner pledged to leave the money in the house, the cash could be used to pay down the $50,000 mortgage and the net assets would become $80,000 and the net liabilities would become $30,000. The "enterprise value" of the house therefore would be $80,000.

#### Valuation Methods

Two types of approaches to valuation are discounted cash flow methods and financial ratio methods.

Two discounted cash flow approaches to valuation are:

- value the cash flow to equity, and
- value the cash flow to the enterprise.

The "cash flow to equity" approach to valuation directly discounts the firm's cash flow to the equity owners. This cash flow takes the form of dividends or share buybacks. While intuitively straightforward, this technique suffers from numerous drawbacks. First, it is not very useful in identifying areas of value creation. Second, changes in the dividend payout ratio result in a change in the calculated value of the company even though the operating performance might not change. This effect must be compensated by adjusting the discount rate to be consistent with the new payout ratio. Despite its drawbacks, the equity approach often is more appropriate when valuing financial institutions because it treats the firm's liabilities as a part of operations. Since banks have significant liabilities that are owed to the retail depositors, they indeed have significant liabilities that are part of operations.

The "cash flow to the enterprise" approach values the equity of the firm as the value of the operations less the value of the debt. The value of the operations is the present value of the future free cash flows expected to be generated. The free cash flow is calculated by taking the operating earnings (earnings excluding interest expenses), subtracting items that required cash but that did not reduce reported earnings, and adding non-cash items that did reduce reported earnings but that did not result in cash expenditures. Interest and dividend payments are not subtracted since we are calculating the free cash flow available to all capital providers, both equity and debt, before financing. The result is the cash generated by operations. The free cash flow basically is the cash that would be available to shareholders if the firm had no debt - the cash produced by the business regardless of the way it is financed. The expected future cash flow then is discounted by the weighted average cost of capital to determine the enterprise value. The value of the equity then is the enterprise value less the value of the debt.

When valuing cash flows, pro forma projections are made a certain number of years into the future, then a terminal value is calculated for years thereafter and discounted back to the present.

#### Free Cash Flow Calculation

The free cash flow (FCF) is calculated by starting with the profits after taxes, then adding back depreciation that reduced earnings even though it was not a cash outflow, then adding back after-tax interest (since we are interested in the cash flow from operations), and adding back any non-cash decrease in net working capital (NWC). For example, if accounts receivable decreased, this decrease had a positive effect on cash flow.

If the accounting earnings are negative and the free cash flow is positive, the carry-forward tax benefit is in effect realized in the current year and must be added to the FCF calculation.

#### Leverage

In 1958, economists and now Nobel laureates Franco Modigliani and Merton H. Miller proposed that the capital structure of a firm did not affect its value, assuming no taxes, no bankruptcy costs, no transaction costs, that the firm's investment decisions are independent of capital structure, and that managers, shareholders, and bondholders have the same information. The mix of debt and equity simply reallocates the cash flow between stockholders and bondholders, but the total amount of the cash flow is independent of the capital structure. According to Modigliani and Miller's first proposition, the value of the firm if levered equals the value if unlevered:

V

_{L}= V

_{U}

However, the assumptions behind Proposition I do not all hold. One of the more unrealistic assumptions is that of no taxes. Since the firm benefits from the tax deduction associated with interest paid on the debt, the value of the levered firm becomes:

V

_{L}= V

_{U}+ t

_{c}D

where t_{c} = marginal corporate tax rate.

When considering the effect of taxes on firm value, it is worthwhile to consider taxes from a potential investors point of view. For equity investors, the firm first must pay taxes at the corporate tax rate, t_{c}, then the investor must pay taxes at the individual equity holder tax rate, t_{e}. Then for debt holders,

After-tax income = ( debt income )( 1 – t

_{d})

For equity holders,

After-tax income = ( equity income )( 1 – t

_{c})( 1 – t

_{e})

The relative advantage (if any) of equity to debt can be expressed as:

Relative Advantage (RA) = ( 1 – t

_{c})( 1 – t

_{e}) / ( 1 – t

_{d})

RA > 1 signifies a relative advantage for equity financing.

RA < 1 signifies a relative advantage for debt financing.

One can define T as the net advantage of debt :

T = 1 – RA

For T positive, there is a net advantage from using debt; for T negative there is a net disadvantage.

Empirical evidence suggests that T is small; in equilibrium T = 0. This is known as Miller's equilibrium and implies that the capital structure does not affect enterprise value (though it can affect equity value, even if T=0).

**Calculating the Cost of Capital **

Note that the return on assets, r

_{a}, sometimes is referred to as r

_{u}, the unlevered return.

Gordon Dividend Model:

P_{0} = Div_{1} / ( r_{e} – g )

where

P_{0}= current stock price,

Div_{1}= dividend paid out one year from now,

r_{e}= return of equity

g = dividend growth rate

Then:

r_{e} = ( Div_{1} / P_{0} ) + g

Capital Asset Pricing Model:

The security market line is used to calculate the expected return on equity:

r_{e} = r_{f} + β_{e} ( r_{m} – r_{f} )

where

r_{f}= risk-free rate,

r_{m}= market return

β_{e}= equity beta

However, this model ignores the effect of corporate income taxes.

Considering corporate income taxes:

r

_{e}= r

_{f}( 1 – t

_{c}) + β

_{e}[ r

_{m}– r

_{f}( 1 – t

_{c}) ]

where t_{c} = corporate tax rate.

Once the expected return on equity and on debt are known, the weighted average cost of capital can be calculated using Modigliani and Miller's second proposition:

WACC = r_{e} E / ( E + D ) + r_{d} D / ( E + D )

Taking into account the tax shield:

WACC = r_{e} E / ( E + D ) + r_{d} ( 1 – t_{c} ) D / ( E + D )

For T = 0 (no tax advantage for debt), the WACC is equivalent to the return on assets, r_{a}.

r_{d} is calculated using the CAPM:

r

_{d}= r

_{f}+ β

_{d}[ r

_{m}– r

_{f}( 1 – t

_{c}) ]

For a levered firm in an environment in which there are both corporate and personal income taxes and in which there is no tax advantage to debt (T=0), WACC is equal to r_{a}, and the above WACC equation can be rearranged to solve for r_{e}:

r_{e} = r_{a} + (D/E)[ r_{a} – r_{d}(1 – t_{c}) ]

From this equation it is evident that if a firm with a constant future free cash flow increases its debt-to-equity ratio, for example by issuing debt and repurchasing some of its shares, its cost of equity will increase.

r_{a} also can be calculated directly by first obtaining a value for the asset beta, β_{a}, and then applying the CAPM. The asset beta is:

β

_{a}= β

_{e}( E / V ) + β

_{d}( D / V )( 1 – t

_{c})

Then return on assets is calculated as:

r_{a} = r_{f} ( 1 – t_{c} ) + β_{a} [ r_{m} – r_{f} ( 1 – t_{c} ) ]

In summary, for the case in which there is personal taxation and in which Miller's Equilibrium holds ( T = 0 ), the following equations describe the expected returns on equity, debt, and assets:

r_{e} = r_{f} ( 1 – t_{c} ) + β_{e} [ r_{m} – r_{f} ( 1 – t_{c} ) ]

r_{a} = r_{f} ( 1 – t_{c} ) + β_{a} [ r_{m} – r_{f} ( 1 – t_{c} ) ]

r_{d} = r_{f} + β_{d} [ r_{m} – r_{f} ( 1 – t_{c} ) ]

The cost of capital also can be calculated using historical averages. The arithmetic mean generally is used for this calculation, though some argue that the geometric mean should be used.

Finally, the cost of equity can be determined from financial ratios. For example, the cost of unleveraged equity is:

r_{e,U} = [ r_{e, L} + r_{f,debt} ( 1 – t_{c} ) D/E ] / ( 1 + D/E )

r_{e,L} = b(1+g) / (P/E) + g

where b = dividend payout ratio

g = ( 1 – b ) (ROE)

where (1 – b) = plowback ratio.

The payout ratio can be calculated using dividend and earnings ratios:

b = ( Dividend / Price ) ( Price / Earnings)

#### Share Buy-Back

Take a firm that is 100% equity financed in an environment in which T is not equal to zero; i.e., there is a net tax advantage to debt. If the firm decides to issue debt and buyback shares, the levered value of the firm then is:

V

_{L}= V

_{U}+ T (debt)

The number of shares that could be repurchased then is:

where the price per share after relevering is:

V

_{L}/ (original number of outstanding shares)

The buyback will lower the firm's WACC.

**Project Valuation **

The NPV of a capital investment made by a firm, assuming that the investment results in an annual free cash flow P received at the end of each year beginning with the first year, and assuming that the asset is financed using current debt/equity ratios, is equal to:

_{0}+ P / WACC

#### Warrant Valuation

Warrants are call options issued by the firm and that would require new shares to be issued if exercised. Any outstanding warrants must be considered when valuing the equity of the firm. The Black-Scholes option pricing formula can be used to value the firm's warrants.

#### Valuation Calculation

Once the free cash flow and WACC are known, the valuation calculation can be made. If the free cash flow is equally distributed across the year, an adjustment is necessary to shift the year-end cash flows to mid-year. This adjustment is performed by shifting the cash flow by one-half of a year by multiplying the valuation by ( 1 + WACC )^{1/2}.

The enterprise value includes the value of any outstanding warrants. The value of the warrants must be subtracted from the enterprise value to calculate the equity value. This result is divided by the current number of outstanding shares to yield the per share equity value.

#### PEG Ratio

As a rule of thumb, the P/E ratio of a stock should be equal to the earnings growth rate. Mathematically, this can be shown as follows:

P = D / r_{e} + PVGO

where

P = price

D = annual dividend

r

_{e}= return on equityPVGO = present value of growth opportunities.

For high growth firms, PVGO usually dominates D / r_{e}. PVGO is equal to the earnings divided by the earnings growth rate.

#### Treatment of Goodwill

Prior to 2002, amortization of goodwill was an expense on the income statement, but unlike depreciation of fixed assets, amortization of goodwill is not tax deductible.

In 2002, FASB Statement No. 142 discontinued the depreciation of goodwill and specified that it be kept on the books as a non-depreciating asset and written off only when its value is determined to have declined.

#### Glossary

APV: Adjusted Present Value

CAPM: Capital Asset Pricing Model

EBIT: Earnings Before Interest and Taxes

EBITDA: Earnings Before Interest, Taxes, Depreciation, and Amortization

Enterprise Value: Market value of a firm's equity plus the net market value of its debt.

- Enterprise value = market cap + LTD - net cash & investments

FCF: Free Cash Flow

LTD: Long-Term Debt

MRP: Market risk premium, defined as r_{m} – r_{f} , unless it specifically is referred to as tax-adjusted market risk premium, in which case there would be a factor to adjust r_{f} for taxes.

NOPLAT: Net Operating Profits Less Adjusted Taxes

OLS: Ordinary Least Squares (method of regression)

PEG: The ratio of P/E to growth rate in earnings.

RADR: Risk Adjusted Discount Rate

RAYTM: Rating-Adjusted Yield-To-Maturity

ROE: Return On Equity; equivalent to the expected return on retained earnings

YTM: Yield To Maturity

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