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**Firm Valuation: A Summary**

P.V. Viswanath Class Notes for Corporate Finance and Equity Valuation

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**Discounted Cashflow Valuation**

where, n = life of the asset CFt = cashflow in period t r = discount rate reflecting the riskiness of the estimated cashflows The value of any asset is the present value of the expected cash flows on the assets. P.V. Viswanath

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**Two Measures of Discount Rates**

Cost of Equity: This is the rate of return required by equity investors on an investment. It will incorporate a premium for equity risk -the greater the risk, the greater the premium. This is used to value equity. Cost of capital: This is a composite cost of all of the capital invested in an asset or business. It will be a weighted average of the cost of equity and the after-tax cost of borrowing. This is used to value the entire firm. The discount rate can be measured from the perspective of just equity investors or all suppliers of capital in the firm. P.V. Viswanath

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Equity Valuation The value of equity is the present value of cash flows to the equity investors discounted back at the rate of return that those equity investors need to make to break even (the cost of equity). In the strictest sense of the word, the only cash flow stockholders in a publicly traded firm get from their investment is dividends, and the dividend discount model is the simplest and most direct version of an equity valuation model. Reinvestment can be computed as change in non-cash working capital plus capital expenditures less depreciation Free Cash Flow to Equity = Net Income – Net Reinvestment (capex as well as change in working capital) – Net Debt Paid (or + Net Debt Issued) P.V. Viswanath

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Firm Valuation A firm includes not just the equity, but all claim holders. The cash flow to the firm is the collective cash flow that all claim holders make from the firm, and it is discounted at the weighted average of their different costs. Free Cash Flow to the Firm = Earnings before Interest and Taxes (1-tax rate) – Net Reinvestment Net Reinvestment is defined as actual expenditures on short-term and long-term assets less depreciation. The tax benefits of debt are not included in FCFF because they are taken into account in the firm’s cost of capital. P.V. Viswanath

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**Valuation with Infinite Life**

With an asset with an infinite life, you need to stop estimating cash flows at some point and estimate a terminal value. In a discounted cash flow framework, this can be done when the growth rate in cash flows becomes perpetual (less than or equal to the growth rate of the economy) Sets up the basic inputs: 1. Discount rates 2. Cash flows 3. Expected Growth 4. Length of the period that they can sustain a growth rate higher than the growth rate of the economy. P.V. Viswanath

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**Valuing the Home Depot’s Equity**

Assume that we expect the free cash flows to equity at Home Depot to grow for the next 10 years at rates much higher than the growth rate for the economy. To estimate the free cash flows to equity for the next 10 years, we make the following assumptions: The net income of $1,614 million will grow 15% a year each year for the next 10 years. The firm will reinvest 75% of the net income back into new investments each year, and its net debt issued each year will be 10% of the reinvestment. To estimate the terminal price, we assume that net income will grow 6% a year forever after year 10. Since lower growth will require less reinvestment, we will assume that the reinvestment rate after year 10 will be 40% of net income; net debt issued will remain 10% of reinvestment. The growth rate and reinvestment rate assumptions are linked. P.V. Viswanath

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**Estimating cash flows to equity: The Home Depot**

The free cash flow to equity is the cash flow after net debt payment or issues and reinvestment. Note that the debt creates a cash inflow for equity investors because it reduces how much they need to reinvest back into the firm. P.V. Viswanath

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**Terminal Value and Value of Equity today**

FCFE11 = Net Income11 – Reinvestment11 – Net Debt Paid (Issued)11 = $6,530 (1.06) – $6,530 (1.06) (0.40) – (-277) = $ 4,430 million Terminal Price10 = FCFE11/(ke – g) = $ 4,430 / ( ) = $117,186 million The value per share today can be computed as the sum of the present values of the free cash flows to equity during the next 10 years and the present value of the terminal value at the end of the 10th year. Value of the Stock today = $ 6,833 million + $ 117,186/(1.0978)10 = $52,927 million The terminal value of equity is discounted back to today at the cost of equity. Note that the cost of equity of 9.78% is used to estimate the terminal value of equity. P.V. Viswanath

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**Valuing Boeing as a firm**

Assume that you are valuing Boeing as a firm, and that Boeing has cash flows before debt payments but after reinvestment needs and taxes of $ 850 million in the current year. Assume that these cash flows will grow at 15% a year for the next 5 years and at 5% thereafter. Boeing has a cost of capital of 9.17%. These are the basic inputs for the valuation. P.V. Viswanath

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**Expected Cash Flows and Firm Value**

Terminal Value = $ 1710 (1.05)/( ) = $ 43,049 million Year Cash Flow Terminal Value Present Value 1 $978 $895 2 $1,124 $943 3 $1,293 $994 4 $1,487 $1,047 5 $1,710 $43,049 $28,864 Value of Boeing as a firm = $32,743 The cost of capital for Boeing of 9.17% is used as the discount rate for the cash flows. This is the value of Boeing as a firm and I would need to subtract out the outstanding debt to get to the value of equity. P.V. Viswanath

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**What discount rate to use?**

Since financial resources are finite, there is a hurdle that projects have to cross before being deemed acceptable. This hurdle will be higher for riskier projects than for safer projects. A simple representation of the hurdle rate is as follows: Hurdle rate = Return for postponing consumption Return for bearing risk Hurdle rate = Riskless Rate + Risk Premium The two basic questions that every risk and return model in finance tries to answer are: How do you measure risk? How do you translate this risk measure into a risk premium? Underlying the idea of a hurdle rate is the notion that projects have to earn a benchmark rate of return to be accepted, and that this benchmark should be higher for riskier projects than for safer ones. P.V. Viswanath

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**The Capital Asset Pricing Model**

Uses variance as a measure of risk Specifies that a portion of variance can be diversified away, and that is only the non-diversifiable portion that is rewarded. Measures the non-diversifiable risk with beta, which is standardized around one. Relates beta to hurdle rate or the required rate of return: Reqd. ROR = Riskfree rate + b (Risk Premium) Works as well as the next best alternative in most cases. This is a summary of the CAPM, before we get into the details. P.V. Viswanath

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**From Cost of Equity to Cost of Capital**

The cost of capital is a composite cost to the firm of raising financing to fund its projects. In addition to equity, firms can raise capital from debt Capital is more than just equity. It also includes other financing sources, including debt. P.V. Viswanath

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**Estimating the Cost of Debt**

If the firm has bonds outstanding, and the bonds are traded, the yield to maturity on a long-term, straight (no special features) bond can be used as the interest rate. If the firm is rated, use the rating and a typical default spread on bonds with that rating to estimate the cost of debt. If the firm is not rated, and it has recently borrowed long term from a bank, use the interest rate on the borrowing or estimate a synthetic rating for the company, and use the synthetic rating to arrive at a default spread and a cost of debt The cost of debt has to be estimated in the same currency as the cost of equity and the cash flows in the valuation. While the cost of debt can be estimated easily for some firms, by looking up traded bonds, it can be more difficult for non-rated firms. The default spreads can be obtained from P.V. Viswanath

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**Estimating Cost of Capital: Boeing**

Equity Cost of Equity = 5% (5.5%) = 10.58% Market Value of Equity = $32.60 Billion Equity/(Debt+Equity ) = 82% Debt After-tax Cost of debt = 5.50% (1-.35) = 3.58% Market Value of Debt = $ 8.2 Billion Debt/(Debt +Equity) = 18% Cost of Capital = 10.58%(.80)+3.58%(.20) = 9.17% Summarizes the inputs from the last 90 pages. The financing choice becomes simpler if the sources of capital can be boiled down to debt and equity. Consequently, we have condensed all of the debt -short as well as long term debt- into one figure and attached the long term cost of debt to it. (We are implicitly assuming that the rolled-over cost of short term debt is equal to the long term cost of debt) Special cases: Hybrid Securities: If you have convertible debt, it is best to break down the convertible debt into debt and equity components. Preferred Stock: This has to be treated as a third component of capital, with a cost set equal to the preferred dividend yield (without a tax benefit) P.V. Viswanath

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**Estimating the Expected Growth Rate**

Note that the approaches are similar, with the only difference being in how we define how much the firm reinvests and how well it reinvests. P.V. Viswanath

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**gEPS= b *ROEt+1 +{(ROEt+1– ROEt)BV of Equityt)/ROEt (BV of Equityt)}**

Expected Growth in EPS gEPS = (Retained Earningst-1/ NIt-1) * ROE = Retention Ratio * ROE = b * ROE ROE = (Net Income)/ (BV: Common Equity) This is the right growth rate for FCFE Proposition: The expected growth rate in earnings for a company cannot exceed its return on equity in the long term. In the short term, improvements in return on equity will translate into more than proportional increases in expected growth in earnings. In fact, the expected growth in earnings per share in any year can be written as: gEPS= b *ROEt+1 +{(ROEt+1– ROEt)BV of Equityt)/ROEt (BV of Equityt)} Note that the larger the firm, the greater the effect (in either direction) of changes in ROE. P.V. Viswanath

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**Expected Growth in EBIT And Fundamentals**

Reinvestment Rate and Return on Capital gEBIT = (Net Capex + Change in WC)/EBIT(1-t) * ROC = Reinvestment Rate * ROC Return on Capital = (EBIT(1-tax rate)) / (BV: Debt + BV: Equity) This is the right growth rate for FCFF Proposition: No firm can expect its operating income to grow over time without reinvesting some of the operating income in net capital expenditures and/or working capital. The reinvestment rate and the return on capital should be forward-looking numbers, rather than what they were last year. P.V. Viswanath

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**Getting Closure in Valuation**

A publicly traded firm potentially has an infinite life. The value is therefore the present value of cash flows forever. Since we cannot estimate cash flows forever, we estimate cash flows for a “growth period” and then estimate a terminal value, to capture the value at the end of the period: Firms have infinite lives. Since we cannot estimate cash flows forever, we assume a constant growth rate forever as a way of closing off the valuation. A very commonly used variant is to use a multiple of the terminal year’s earnings. This brings an element of relative valuation into the analysis. In a pure DCF model, the terminal value has to be estimated with a stable growth rate. P.V. Viswanath

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**Stable Growth and Terminal Value**

When a firm’s cash flows grow at a “constant” rate forever, the present value of those cash flows can be written as: Value = (Expected Cash Flow Next Period) / (r - g) where, r = Discount rate (Cost of Equity or Cost of Capital) g = Expected growth rate This “constant” growth rate is called a stable growth rate and cannot be higher than the growth rate of the economy in which the firm operates. While companies can maintain high growth rates for extended periods, they will all approach “stable growth” at some point in time. When they do approach stable growth, the valuation formula above can be used to estimate the “terminal value” of all cash flows beyond. If the stable growth rate is set below the growth rate of the economy (as it should be), you should never find g to be greater than r, which leads to absurd values. P.V. Viswanath

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Relative Valuation In relative valuation, the value of an asset is derived from the pricing of 'comparable' assets, standardized using a common variable such as earnings, cashflows, book value or revenues. Examples include -- • Price/Earnings (P/E) ratios and variants (EBIT multiples, EBITDA multiples, Cash Flow multiples) • Price/Book (P/BV) ratios and variants (Tobin's Q) • Price/Sales ratios This is the preferred mode of valuation on Wall Street. Philosophically, it is a different way of thinking about valuation. In relative valuation, we assume that markets make mistakes on individual investments, but that they are right, on average, in how they price a sector or the market. (In discounted cash flow valuation, we assume that markets make mistakes over time.) P.V. Viswanath

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**Multiples and DCF Valuation**

Gordon Growth Model: Dividing both sides by the earnings, Dividing both sides by the book value of equity, If the return on equity is written in terms of the retention ratio and the expected growth rate Dividing by the Sales per share, All multiples have their roots in fundamentals. A little algebra can take a discounted cash flow model and state it in terms of a multiple. This, in turn, allows us to find the fundamentals that drive each multiple: PE : Growth, Risk, Payout PBV: Growth, Risk, Payout, ROE PS: Growth, Risk, Payout, Net Margin. Every multiple has a companion variable, which more than any other variable drives that multiple. The companion variable for the multiples listed above are underlined. When comparing firms, this is the variable that you have to take the most care to control for. When people use multiples because they do not want to make the assumptions that DCF valuation entails, they are making the same assumptions implicitly. P.V. Viswanath

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