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## Chapter 5: Stock Valuation

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**Chapter 5: Stock Valuation**Professor Thomson Finance 3013**Debt vs. Equity: Debt**• Debt securities represent a legally enforceable claim. • Debt securities offer fixed or floating cash flows. • Bondholders don’t have any control over how the company is run.**Common stockholders are residual claimants.**• No claim to earnings or assets until all senior claims are paid in full • High risk, but historically also high return Debt vs. Equity: Equity • Stockholders have voting rights on important company decisions. Debt and equity have substantially different marginal benefits and marginal costs.**Preferred Stock**Preferred stock is a hybrid having some features similar to debt and other features similar to equity. • Claim on assets and cash flow senior to common stock • As equity security, dividend payments are not tax deductible for the corporation. • For tax reasons, straight preferred stock held mostly by corporations. Promises a fixed annual dividend payment, but not legally enforceable. Firms cannot pay common stock dividends if preferred stock is in arrears (i.e. preferred stock is typically “cumulative”) - Preferred stockholders usually do not have voting rights. - May be convertible to common stock**Valuing Preferred Stock**• Because preferred stock pay a constant dividend, they are easy to value because the dividends are a perpetuity. • Recall the present value of a perpetuity is: Where : D1 is the constant dividend whose first payment is one period from today**Example 5.1: Valuing preferred**• You purchase a preferred stock with a $12 per year dividend. For a 10% market rate, what is its value?**Rights of Common Stockholders**• Common stockholders’ voting rights can be exercised in person or by proxy. • Most US corporations have majority voting, with one vote attached to each common share. • Cumulative voting gives minority shareholders greater chance of electing one or more directors. Shareholders have no legal rights to receive dividends. They are declared by the board of directors, and typically paid quarterly if it is a dividend paying stock. Dividends typically increase over time**Par value**Little economic relevance today Shares authorized by stockholders to be sold by the board of directors without further stockholders approval Shares authorized Shares issued and outstanding Number of shares owned by stockholders Additional paid-in capital Amount received in excess of par value when corporation initially sold stock Common Stock**Market capitalization**• Market price per share x number of shares outstanding Stock repurchased by corporation; Usually purchased for stock options Treasury stock Two-for-one split issues one new share for each already held; reduces per share price. e.g. A stock selling for $50 per share will sell for $25 per share after a 2 for 1 stock split Stock split Common Stock**Largest firms by market capitalization in the S&P 500**(5/31/2006)**Stock Valuation**• Like other assets in finance, the value of a stock is the PV of its CF’s • Stocks are typically valued as perpetual securities as corporations potentially have an infinite life, and thus can pay dividends forever.**How to make money in the stock market**• The standard answer – “Buy Low, Sell High” i.e. Earn capital gains • From dividends – Over the long run, historically speaking almost ½ of the total return to stock market investors was from dividends.**Example 5.2. Stock valuation with a one year holding period**• You expect that JK Corp stock will sell for $25 one year from today. You expect to receive $1.20 in dividends over the year you hold this stock. For a 15% required rate of return for this stock, how much should you pay for it? What is your projected capital gain?**Example 5.3. Stock valuation with a two year holding period**• You expect to sell MyCo for $28 two years from today. You expect to receive $1 dividend the first year, and a $1.10 dividend the second year. For a 16% discount rate, what is the maximum you should pay for this stock?**Example 5.4. Stock valuation with a three year holding**period • What you be willing to pay for a stock which pays a $2 dividend the first year, a $2.10 dividend the second year, and $2.21 in the third year if you will sell the stock for $40 after three years? Discount rate is 13%**Model assumption**• Probably the biggest weakness in the previous three examples was that we had to predict a selling price. • The buyer of the stock, when we sell it, will presumably go through a similar procedure to value the stock – in other words the buyer will be using future dividends to value the stock. • The selling price of the stock should thus be the value of all future dividends.**Valuation of Common StockAssume 1 year holding**• P0 = Present value or price of stock today • P1 = Price of stock next period • D1 = Dividends received in first period • i = discount rate**Valuation Fundamentals:Common Stock**• How was P1 determined? • PV of expected stock price P2, plus dividends • P2 is the PV of P3 plus dividends, etc... • Repeating this logic over and over, you find that today’s price equals PV of the entire dividend stream the stock will pay in the future: Must be able to predict future dividends to use this model**Zero growth model assumes a constant,**non-growing dividend stream. (Think preferred stock) • D1 = D2= ... = D Zero Growth Valuation Model • To value common stock, you must make assumptions about future dividend growth. • Plugging constant value D into the common stock valuation formula reduces to simple equation for the present value of a perpetuity:**Constant Growth Valuation Model**• Assumes dividends will grow at a constant rate (g) that is less than the required return (r) • If dividends grow at a constant rate forever, you can value stock as a growing perpetuity, denoting next year’s dividend as D1: Note: D1 = D0(1+g) Commonly called the Gordon growth model Also called a DDM : Dividend Discount Model**Dividends over time**• In the Gordon growth model:**Review Notation**• D0 = Current Dividend (time period 0) • D1 = Dividend one period from now • r = appropriate discount rate or rate of return for the particular stock (adjusts for time value of money and risk) • g = constant growth rate in dividends • P0 = the present value of the infinite series of dividends, which is the estimate stock price**Use the Gordon model when . . .**• A dividend is paid on a regular basis • Growth rate in the dividends is constant • r>g**Example**Dynasty Corp. will pay a $3 dividend in one year. If investors expect that dividend to remain constant forever, and they require a 10% return on Dynasty stock, what is the stock worth? What is the stock worth if investors expect Dynasty’s dividends to grow at 3% per year?**Example 5.5: Applying the DDM**• Sombria industries recently paid a $2 dividend, and its dividends have been growing at 5% per year. The appropriate discount rate for this stock is 12%. • What should its current price be? • What do you projects its price to be 5 years from now?**Example 5.6: Rate of Return**• Ootsa Corp. is trading for $50 per share. Next year you expect it to pay a $2 dividend, and dividends have been growing at a 6% rate. What rate of return do investors require from this stock? What is the dividend yield? What is the capital gain yield?**Example 5.7: Delayed Dividends**• Joogle is high tech start up that is not expected to pay a dividend for 10 years. At that time you expect it will pay an $8 dividend, with a growth rate of 7%. For a 12% required return, what should you be willing to pay for Joogle today? What will its stock price be 5 years from today?**Example 5.8: Variable Growth Model Example**• Estimate the current value of Morris Industries' common stock, P0 • Assume: • The most recent annual dividend payment of Morris Industries was $4 per share. • Investors expect that these dividends will increase at an 8% annual rate over the next 3 years. • After three years, dividend growth will level out at 5%. • The firm's required return, r, is 12%.**Review Smart Animation**• Chapter 5. “See a demonstration of the variable growth model.”**Other valuation models**• Free cash flow analysis • Similar to the DDM model, but rather than discounting the dividend, one discounts the free cash flows (see Chapter 2) • The discount rate used is the WACC (Weighted Average Cost of Capital) which is the weighted average of the discount rates for the firm’s bonds, stocks and preferred stocks.**Book value**• The value shown on the balance sheet of the assets of the firm, net of liabilities shown on the balance sheet Liquidation value • Actual net amount per share likely to be realized upon liquidation and payment of liabilities • Reflects the amount investors will pay for each dollar of earnings per share • P / E multiples differ between and within industries. • Especially helpful for privately-held firms. P / E multiples Common Stock ValuationOther Options**Trading Stock**• Why does any security trade? • Primary Market – a market for newly minted stock – funds go to the company whose name is on the stock • Initial Public Offering – the first time a primary market offering is made for a company – it represents the transition from a private firm to a public firm whose stock is freely traded**Secondary Stock Market**• Biggest stock market for existing stocks is the NYSE – New York Stock Exchange • Trading is at Wall and Broad Street • Second biggest market is the Nasdaq • Nasdaq was formerly, National Association of Securities Dealers Automatic Quotations • Trading is in cyberspace**How to choose stocks**• If you are not a stock analyst, and do not have a lot of money to invest, I suggest choosing broad based mutual funds, especially index funds • In general, don’t choose stocks based on hot tips • I invest with the Vanguard family of mutual funds www.vanguard.com**Variable Growth ModelValuation Steps 1 and 2**• Compute the value of dividends in year 1, 2, and 3 as (1+g1)=1.08 times the previous year’s dividend Div1= Div0 x (1+g1) = $4 x 1.08 = $4.32 Div2= Div1 x (1+g1) = $4.32 x 1.08 = $4.67 Div3= Div2 x (1+g1) = $4.67 x 1.08 = $5.04 • Find the PV of these three dividend payments: PV of Div1= Div1 (1+r)1 = $ 4.32 (1.12) = $3.86 PV of Div2= Div2 (1+r)2 = $ 4.67 (1.12)2 = $3.72 PV of Div3= Div3 (1+r)3 = $ 5.04 (1.12)3 = $3.59 Sum of discounted dividends = $3.86 + $3.72 + $3.59 = $11.17**Variable Growth ModelValuation Step 3**• Find the value of the stock at the end of the initial growth period using the constant growth model. • Calculate next period dividend by multiplying D3 by 1+g2, the lower constant growth rate: D4 = D3 x (1+ g2) = $ 5.04 x (1.05) = $5.292 • Then use D4=$5.292, g =0.05, r =0.12 in Gordon model:**Variable Growth ModelValuation Step 3**• Find the present value of this stock price by discounting P3 by (1+r)3**Variable Growth ModelValuation Step 4**• Add the PV of the initial dividend stream (Step 2) to the PV of stock price at the end of the initial growth period (P3): P0 = $11.17 + $53.81 = $64.98 Current stock price Remember: Because future growth rates might change, the variable growth model allows for a changes in the dividend growth rate.**Discount**Use weighted average cost of capital (WACC) to discount the free cash flows. Valuing the Enterprise: Free Cash Flow Valuation Discount estimates of free cash flow that the firm will generate in the future. WACC: after-tax weighted average required return on all types of securities that firm issues. We have an estimate of total value of the firm. How can we use this to value the firm’s shares?**An example....**Morton Restaurant Group (MRG) First quarter of 2001, traded in the $20 - $25 range Value of firm’s shares VS = VF– VD - VP • VS = value of firm’s common shares • VF = total enterprise value • VD = value of firm’s debt • VP = value of firm’s preferred stock We can use the free cash flow approach to estimate the value of MRG shares.**At end of 2000, MRG’s debt market value was $66 million.**• No preferred stock • 4,148,002 shares outstanding • Free cash flow in 2000 was $4.8 million. • Revenues and operating profits grew at 14% between 1998 and 2000. MRG An Example: Mortons Restaurant Group Assume that Mortons will experience 14% FCF growth from 2000 to 2004 and 7% annual growth thereafter. Mortons’ WACC is approximately 11%.**An Example: Mortons Restaurant Group**Use variable growth equation to estimate Mortons enterprise value.**VF = 163,386,865**VD = $66,000,000 VP = $0 VS = $163,386,865 - $66,000,000 - $0 = $97,386,865 An Example: Mortons Restaurant Group Divide total share value by 4,148,002 shares outstanding to obtain per-share value:**Stock Valuation**Preferred stock has both debt and equity-like features. Common stock represents residual claims on firms’ cash flows Investment bankers play an important role in helping firms issue new securities The same principles apply to valuation of both preferred and common stock