Unformatted text preview: Ch. 9: Stock Valuation 2/13/2015 The Present Value of Common Stocks • An asset’s value is determined by the present value of all future cash flows • Stocks provide 2 kinds of CF o Dividends paid on a regular basis o The sale price received by the stockholder when the stock is sold • To value common stock, make sure the price of a share of the stock equals 1) Discounted PV of the sum of next period’s dividend + next period’s stock price 2) Discounted PV of all future dividends o E.g. Given a one‐year holding period, the amount someone is willing to pay for a stock =
++ + Div1 = expected dividend paid at year’s end, P1 = expected price at year’s end, P0 = PV of common stock investment, R = discount rate for stock / required return for investor • The price of a share of common stock to the investor is the PV of all future dividends = +
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( + ) o Prices in market dominated by shortsighted investors who don’t look beyond their time horizon § Price second investor pays depends on dividends after date of purchase. o Applicable whether div expected to grow, decline, or remain the same § Case 1 (Zero Growth) – constant dividend, perpetuity = = + R may also be referred to as the cost of capital § Case 2 (Constant Growth), growing perpetuity = − • Div = dividend at the end of the first period, growing at rate g P0 = infinity when R = g = + − § Case 3 (Differential Growth) • E.g. Given growth over first X years and a different growth over subsequent Y years: o Calculate PV of dividends at the end of each of the first X years § Use growing annuity formula unless R = g o Calculate the PV of the dividends beginning at the end of year X+1. § Use procedure for deferred perpetuities and deferred annuities § Growing perpetuity formula calculates PV as of one year prior to the first payment. Dividend Discount Model, given: = − ∗ , = ∗ Ch. 9: Stock Valuation o 2/13/2015 When PB and ROE are constant, share price: = + − − = + − ( ∗ ) Paid out = 1 – PB Estimates of Parameters in the Dividend Discount Model • = – o Net investment of 0 when total investment = depreciation and the firm’s physical plant is maintained without growth in earnings o Net investment positive if some earnings are retained = + Increase in earnings = (Retained earnings this yr * Return on retained earnings) + = + ∗ = + ∗ 1+g : earnings next yr / earnings this yr 1 : earnings this yr / earnings this yr Retention ratio : retained earnings this yr / earnings this yr Return on retained earnings : return • Return on retained earnings will change each year Book value of equity – accumulation of historic retained earnings and issuance of stock ℎℎ ℎ: = ∗ =
∗ Use g = PB Ratio*ROE to calculate the share price: = + − o Assume projects selected in the current year have an anticipated return equal to returns from past projects § Anticipated return on current retained earnings by the historical return on equity (ROE), which is the accumulation of firm’s past projects ’ = ∗ § Payout ratio – ration of dividends to earnings % = The required returns – the return on assets with the same risks as the firm’s shares = + Used for dividend discount model ( − ) = + Div / P0 = Dividend yield, similar to current yield on a bond (Div / Stock price) g = Capital yield gains, which is the rate at which the value of the investment grows – both growth in dividends and growth in earnings Ch. 9: Stock Valuation • • 2/13/2015 ( + ) When =
−= − = ( + ) o Estimation of g, not a precise determination § Assume return on reinvestment of future retained earnings = firm’s past ROE Assume retention ratio = past retention ratio § Argue the estimation error for R is impractically large, and so it must be calculated for the entire industry § If firm initiates a dividend at some point, growth rate over the interval becomes infinite • Share price infinite when R = g • Erroneous to use a short‐run estimate of g when requiring perpetual growth rate Only a portion of earnings go to stockholders as dividends; remainder is retained to generate future dividends o Retained earnings = investment A firms with many growth opportunities faced with problem of paying out dividends now or forgoing dividends as to invest in what will generate even greater dividends in the future o Some pay no dividends, and some firm with high growth rates are likely to pay lower dividends Growth Opportunities • When a company is considered a cash cow, it’s an income stock = EPS = earnings per share, Div = dividends per share = Value of a share of stock • Many firms have growth opportunities to invest in profitable projects o Firms think in terms of a set of growth opportunities § E.g. firm retains entire dividend at Date 1 in order to invest in a particular capital budgeting project, it’s a growth stock Net present value per share at Date 0 = Net present value per share of growth opportunity (NPVGO) = + EPS / R = Value of firm if distributed all earnings to stockholders, NPVGO = additional value if firm retains earnings in order to fund new projects o Two conditions to increase value (positive growth) § Earnings must be retained so that projects can be funded § Projects must have positive NPV o Stock price of any real‐world company should reflect market estimate of the firm’s NPVGO o A firm’s value increases when it invests in growth opportunities with positive NPVGOs, and falls with negative § Investing in negative NPVs Ch. 9: Stock Valuation •
• 2/13/2015 Projects with rates of return below discount rate reduce value of firm Earnings and dividends of a firm will grow as long as its projects have positive rates of return Comparables • Value comparables to value stocks o In stock market, comparable firms are assumed to have similar multiples o Price‐to‐earnings ratio – ratio of stock prices (numerator) to its earnings (denominator) per share § Similar firms have similar PE ratio § Firms with growth opportunities should sell at a higher price, bec an investor is buying both current income and growth opportunities § Factors explaining PE ratio • Discount rate (R) is negatively related to PE ratio • Stock’s risk is negatively related to PE ratio § Stock’s PE ratio is function of three factors (explain the difference in PE value between companies) • Growth opportunities. Companies with significant growth opportunities likely to have high ratios • Risk. Low‐risk stocks have high PE ratios • Accounting practices. Conservative accounting practices have high PE ratios o In inflationary environment, FIFO understates true cost of inventory (inflates reported earnings), whereas LIFO values accd to most recent costs (implying lower reported earnings) § Taxes on FIFO are worse than LIFO, so value doesn’t necessarily go up. § Trailing earnings (historic) vs. projected earnings (future) • PE ratio tells you: how to value public and private companies o What you should be willing to pay for them o Whether or not it’s worth the investment § Misconception: want to invest in the company with a low PE and avoid the company with a high PE § = Note, the g is the percentage, so multiply the decimal by 100 o = Flawed: apples to oranges comparison; from perspective of equity holders – value to the equity holder (numerator) to the value to the bond and stock holders (denominator) o Enterprise Value Ratio – Enterprise value (EV) to Earnings before interest, taxes, depreciation, and amortization (EBITDA) = , = Improved: apples to apples; from perspective of all investors – going to all investors of the firm (num) over earnings available to all stock and bond holders (denom) Ch. 9: Stock Valuation 2/13/2015 Similar firms have similar EV / EBITDA ratios Questions that arise • There’s an advantage to EV / EBITDA ratio over PE ratio, as leverage increases risk of equity & affects R o Firms may be otherwise comparable but have diff PE if diff degrees of leverage • Numerator and denominator must be consistent, which is why EV is numerator (debt + equity) and EBITDA is denominator (unaffected by interest payments) • Denominator ignores depreciation and amortization because they aren’t cash flows and reflect a sunk cost • Denominators used in value ratios include: Earnings before interest and taxes (EBIT); Earnings before interest, taxes, and amortization (EBITA); and free cash flow • Cash is subtracted out because firms hold amounts of cash in excess of what is needed o Enterprise value ratio reflects ability of productive assets to create earnings or CF Security analyst – provide info to institutional investors upon valuing diff stocks o Buy Side – Institutional investor § Money manager (mutual fund, university endowment, pension plans, insurance company – IRR) o Sell Side – Investment Banks § Traditional services (M&A, facilitate bringing stock to the market e.g. IPO/ SEO) § Money management § Sales & Trading (receive commission for brokerage) • Retail investor, Institutional investors – greater profit in institutional, because the cost of the deal doesn’t increase, but the ability of the latter to invest a larger quantity increases the profit wedge of the transaction §
§ • Valuing the Entire Firm • Value entire firms by discounting CF (in a way similar to Ch 5 and 6) o Growing perpetuity formula to calculate PV as of Year X of all future CF § PV of terminal value PV of net CF during first X years § Note, investor might value via a multiple as opposed to growing perpetuity formula o Two estimates of value of a share of equity, reflecting diff ways of calculating terminal value § Value of estimate of the equity value per share uses constant growth discounted CF method for terminal value • Dividend discount model (NPVGO) and firm cash flow model are mutually consistent in determining value of a share of stock o Discount model – useful for firms with steady, large dividends o NPVGO model – useful for firms with growth opportunities Ch. 9: Stock Valuation 2/13/2015 Cash flow model – useful for non‐dividend paying firms with external financing needs Net investment includes net working capital and capital spending less depreciation o Net cash flow / Free cash flow grows at same rate as revenues o • ...
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 Fall '09
 CASH FLOW

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