BF Chapter 8 Lecture Notes on Stock Valuation

FIN 7020 Dr. Amine Khayati **Chapter 8 Lecture Notes** =========================== **Stock Valuation** =================== **I- Common Stock valuation using Dividend Discount Valuation:** There are three factors complicating the valuation of common stocks. First, dividend payments are not fixed...

FIN 7020 Dr. Amine Khayati **Chapter 8 Lecture Notes** =========================== **Stock Valuation** =================== **I- Common Stock valuation using Dividend Discount Valuation:** There are three factors complicating the valuation of common stocks. First, dividend payments are not fixed over time and can change substantially from one year to another. Second, a share of a common stock has neither a maturity date nor a maturity value, unlike a bond which has a maturity date and a future value. Third, quite similar to the bond valuation, it is difficult to estimate the appropriate required rate of return for a stock. **Cash flows:** Investors purchase common stock expecting returns in the form of dividends and/or future price appreciation. So, an investor who plans to hold a stock for t years would value the stock using the current price as present value, the expected dividends payments to be received over the period of t years, the expected future selling price as future value and the required rate of return on that stock as the discounting interest rate. **1- Discounted dividend valuation:** **Dividend discount models (DDMs) discount the cash flows (dividends) to be received by the shareholders.** **- Advantages: the shareholder's investment today is worth the present value of the expected future cash flows and using the dividends as cash flows is theoretically justified. Even when the shareholder decided to sell the stock before receiving all the expected dividends, he will get from the buyers the present value of the expected future dividends. A second advantage of using dividends as a measure of cash flows is that dividends are less volatile than other measures of cash flows such as earnings.** **- Disadvantages: obviously we cannot use DDMs for firms that don't currently pay dividends.** **A second disadvantage of measuring cash flows with dividends is that we consider the perspective of a shareholder who owns a minority stake in the firm and cannot influence the dividend policy. The DDMs are appropriate for firms where the controlling shareholders dictate a dividend policy that is consistent with the firm's underlying profitability. However, DDMs are inappropriate if the firm's dividend policy is not in synergy with the firm's ability to create value.** **Example 1:** You decide to buy a stock today. You plan to sell the stock a year from today, and you estimate that the stock will be worth \$70 at that time. You also predict that the stock will pay \$5 per share dividend at the end of the year. If you require a 15% on that stock, what would you pay for that stock today? = = [\$\\frac{5 + 70}{1.15} = 65.22\$]{.math.inline} = stock price today = stock price at year 1 = expected dividend in year 1 R = required rate of return **Example 2**: same as example 1 except in this case you decide to hold the stock for three years. You predict that the dividend at the end of year 1 to be \$5, at the end of year 2 to be \$7 and at the end of year 3 to be \$9. You also predict that you can sell the stock at the end of year 3 for \$70. What would you pay for that stock today? = + + + = [\$\\frac{5}{1.15} + \\ \\frac{7}{{(1.15)}\^{2}} + \\ \\frac{9 + 70}{{(1.15)}\^{3}}\$]{.math.inline} = 61.58 **Some special cases:** Because of the difficulty of estimating the future dividends, we make three simplifying assumptions regarding the pattern of future dividends payments. They are: (1) zero growth in dividends, or constant dividends; (2) constant rate of growth in dividends; and, (3) a non-constant rate of growth in dividends. **2- Zero Growth or constant dividend:** A stock with constant dividends is perpetuity. The stock is assumed to pay the same amount of dividend forever. So its current price could be approximated by: = = stock price today D = the constant dividend R = the required rate of return on the stock **3- Constant Growth dividend:** Suppose that the dividend for some company always grows at a steady rate. Call this *growth rate g*. if we let be the dividend just paid, the next dividend, is: = Any future dividend can be computed with the following relation: \ [*D*~*n*~ = *D*~0~ × (1 + *g*)^*n*^]{.math.display}\ **Example 3**: ABC Corporation has a constant growth dividend policy. The company has just paid a dividend of \$2, and the dividend will grow at a steady rate of 5% per year. What will be the dividend in year 5? = 2 (1.05)^5^ = 2.55 **Example 4**: Assuming a 12% required rate of return, find the current price of ABC Corporation based the given the following *dividend growth model*: = stock price today = expected dividend in year 1 R = the required rate of return on the stock g = the constant grow rate = [\$\\frac{2\\ (1.05)}{0.12 - 0.05} = 30\$]{.math.inline} The dividend growth model can be used to get the stock price at any point in time. **Example 5**: Find the stock price of ABC Corporation in five years from today. = 2 (1.05)^6^ = 2.68 = [\$\\frac{D\_{6}}{R - g} = \\ \\frac{2.68}{0.12 - 0.05} = 38.2885\$]{.math.inline} **Example 6**: What is the implied rate of return given the change in price during the five years period? = PV= -30 = FV = 38.2885 N = 5 I/Y = ? 5 - The stock price grows as the same rate as the dividend = g. The dividend growth model makes the implicit assumption that the stock price will grow at the same constant rate as the dividend. What this tells us is that if the cash flows on an investment grow at a constant rate through time, so does the value of the investment. - We define the [Capital gain yield] as the rate at which the value of an investment grows; it is equal to the dividend growth rate. **Components of the Required Return:** We want to examine the implication of the dividend grow model on the Required Return. If we arrange to solve for R we get: R = *R = Dividend yield + Capital gain yield* The required return has two components. The first is, is called the dividend yield. - The dividend yield: is the stock's expected cash dividend divided by its current price. The second term of the required return is the growth rate, g. We know from the preceding example 4 that this growth rate can be interpreted as the capital gains yield, that is, the rate at which the value of the investment grows. **Example 7**: we observe a stock selling at \$20 per share; the next dividend will be \$1 per share. The dividend is estimated to grow by 10% a year indefinitely. What return does this stock offer if these assumptions are correct? R = Dividend yield + Capital gain yield R = [\$\\frac{1}{20} + \\ 0.1 = 0.15\$]{.math.inline} **4- Non-constant Growth:** Looking at the constant growth formula, we can see that the growth rate g cannot be greater that the required rate of return R. The denominator (R - g) would be negative and we would get a negative price. \- The assumption of non-constant growth is more realistic for many firms. The non-constant growth model allow for the growth rate to be greater that the required rate of return for some years. In reality, this cannot happen for ever, and for this reason we assume that after some number of years the dividend will grow at a constant rate. \- In a sense, the idea behind this model is that dividends change at different rates in different periods, until, at a specified future date, the growth rate settles at some constant equilibrium rate. The present value becomes the sum of the discounted values of all expected cash flows: \ [\$\$P\_{0} = \\frac{D\_{1}}{{(1 + R)}\^{1}} + \\frac{D\_{2}}{{(1 + R)}\^{2}} + \\ldots + \\frac{D\_{n} + P\_{n}}{{(1 + R)}\^{n}}\$\$]{.math.display}\ **Example 8:** suppose that you have come up with the following dividend forecasts for the next three years: +-----------------------------------+-----------------------------------+ | Year | Expected Dividend | +===================================+===================================+ | 1 | \$1.00 | | | | | 2 | \$2.00 | | | | | 3 | \$2.50 | +-----------------------------------+-----------------------------------+ : dividend After the third year, the dividend will grow at a constant rate of 5% per year. The required return is 10%. What is the value of the stock today? time line The price in three years will be: = [\$\\frac{2.5 \\times 1.05}{0.1 - 0.05} = 52.5\$]{.math.inline} Using the Cash flow function on the financial calculator: CF0 = 0; CF1 = 1; CF2 = 2; CF3 = 55; I = 10, NVP?\ 43.88 \* The strengths of the DDM are: \- The models have the flexibility to estimate the value of a firm under virtually an infinite number of scenarios. \- The models make it easier to see the relationship between assumptions and resulting estimates of value, therefore analyst can identify the impact of different assumptions on stock value. \* The limitations: \- Like in any forecasting exercise, the models are only as good as the assumptions and projections used as inputs. \- The estimate of stock value is very sensitive to the assumptions of the growth rate and the required return, which are in turn often difficult to estimate accurately. **II- Free Cash Flows Valuation Models:** \- **Free cash flow to the firm** (FCFF) is the cash flow resulting from the firm's business operations that is not required to be reinvested within the firm to continue to operate at its current level. Specifically, FCFF is the cash available to the firm's investors (shareholders and bondholders) after the firm sells products and services, pays its operating expenses and makes working capital investments and long-term investments. With the FCFF, the firm will first pay its bondholders and meet all of its obligations to its other investors and then the amount left thereafter is called the free cash flow to equity, which belongs to the shareholders. The firm has discretion over what to do with that money, either pay all or some of it out in dividend or plow it back into the firm for future needs. \- **Free cash flow to equity** (FCFE) is therefore defined as the cash flow available to shareholders after funding capital requirements, debt financing requirements and working capital needs. \* Advantages of free cash flow valuation models: \- They are applicable to almost any firm regardless of the firm dividend policy or capital structure. They are most suitable for firms that do not have a clearly defined dividend policy or a dividend policy that is not related to the firm's earnings. \- Free cash flow valuation is more appropriate from the perspective of controlling shareholders who have the ability to influence the distribution of the firms' free cash flows (dividend policy). However, it is pertinent to use free cash flow valuation when the valuation perspective is that of a minority shareholder since the firm can be acquired for a market price equal to the value to the controlling shareholders. The reason we distinguish between controlling and minority shareholders is that some investors are willing to pay a premium for control of the firm. \* Limitations: \- Firms may need significant capital investments if the industry is experiencing a major technological revolution which may result in negative free cash flow for many years in the future. \* Free cash flow valuation uses the typical discounted cash flow technique that we've seen already in the DDMs. So, we will forecast the future cash flows and discount them at the appropriate required return. Since we have two cash flows (FFCF and FFCE), we have two required returns. We discount the FCFF at the weighted average cost of capital (WACC), and we discount the FCFE at the firm's required rate of return. \- Firm value = FCFF discounted at WACC. Value of the firm = [\$\\frac{\\text{FCFF}\_{1}}{WACC - g}\$]{.math.inline} \- Equity value = FCFE discounted at the required return on equity. Value of equity = [\$\\frac{\\text{FCFE}\_{1}}{R - g}\$]{.math.inline} \- Equity value = firm value -- market value of debt. **a- Calculating FCFF from net income:** FCFF = Net Income + Depreciation + \[Interest [×]{.math.inline} (1- Tax rate)\] -- fixed capital investment -- working capital investment FCFF = \[EBIT [×]{.math.inline} (1-Tax rate)\] + Depreciation -- fixed capital investment -- working capital investment As you notice, we need to make some adjustment to net income (NI) to get to FCFF. These adjustments are: non-cash expenses, interest expenses, fixed capital investments and working capital investments. **Example 9:** ABC Corp. Income Statement +-----------------------+-----------------------+-----------------------+ | | **2009 Forecast** | **2008 actual** | +=======================+=======================+=======================+ | **Sales** | 950 | 850 | | | | | | **Cost of goods | 460 | 420 | | sold** | | | +-----------------------+-----------------------+-----------------------+ | **Gross Profit** | 490 | 430 | | | | | | **Depreciation** | 160 | 150 | +-----------------------+-----------------------+-----------------------+ | **EBIT** | 330 | 280 | | | | | | **Interest expenses** | 40 | 30 | +-----------------------+-----------------------+-----------------------+ | **Pre-tax earnings** | 290 | 250 | | | | | | **Taxes (30%)** | 87 | 75 | +-----------------------+-----------------------+-----------------------+ | **Net Income** | **203** | **175** | +-----------------------+-----------------------+-----------------------+ : income statement ABC Corp. Balance Sheet +-----------+-----------+-----------+-----------+-----------+-----------+ | | **2009 | **2008 | | **2009 | **2008 | | | Forecast* | actual** | | Forecast* | actual** | | | * | | | * | | +===========+===========+===========+===========+===========+===========+ | **Cash** | 180 | 150 | **Account | 140 | 120 | | | | | s | | | | **Account | 265 | 250 | payables* | 442 | 460 | | s | | | * | | | | Receivabl | 610 | 550 | | 582 | 580 | | es** | | | **Short-t | | | | | 1,055 | 950 | erm | | | | **Invento | | | debts** | | | | ry** | | | | | | | | | | **Current | | | | **Current | | | liabiliti | | | | assets** | | | es** | | | +-----------+-----------+-----------+-----------+-----------+-----------+ | **Fixed | 1,600 | 1,450 | **Long-te | 420 | 400 | | Assets** | | | rm | | | | | (250) | (220) | debt** | 1,000 | 1,000 | | **Accu. | | | | | | | Depreciat | 2,405 | 2,180 | **Common | 403 | 200 | | ion** | | | stock** | | | | | | | | 2,405 | 2,180 | | **Total | | | **Retaine | | | | assets** | | | d | | | | | | | earnings* | | | | | | | * | | | | | | | | | | | | | | **Total | | | | | | | liabiliti | | | | | | | es | | | | | | | and | | | | | | | owners' | | | | | | | equity** | | | +-----------+-----------+-----------+-----------+-----------+-----------+ : Balance sheet Additional information: \- The firm is expected to sell in 2009 a completely depreciated fixed asset for \$30. Fixed capital Invest. = capital expenditures -- proceeds from sales of long-term assets = (1600 -1450) -- 30 = 120 Working capital investment is the change in the working capital accounts, [excluding cash and short-term borrowings]: W. capital Inv. = (AcctsRec~2009~ + Inventory~2009~ -- AcctsPay­~2009~) -- (AcctsRec~2008~ + Inventory~2008~ -- AcctsPay­~2008~) = (265 +610-140) -- (250+550-120) = 55 FCFF = Net Income + Depreciation + \[Interest [×]{.math.inline} (1- Tax rate)\] -- fixed capital investment -- working capital investment = 203 + 160 + (40×0.7) -- 120 -- 55 = 216 **b- Single-Stage FCFF Model:** **Example 10:** Using the information from the last example, compute the value of the firm today if the FCFF is expected to grow at a rate of 5% forever and the firm will maintain an average WACC of 13%. \- Firm value = FCFF discounted at WACC. Value of the firm = [\$\\frac{\\text{FCFF}\_{1}}{WACC - g}\$]{.math.inline} = 216/(0.13-0.05) = 2,700 **c- Calculating FCFE:** **Example 11:** Using the same ABC Corp. income statement and balance sheet, compute the FCFE. FCFE = FCFF -- Interest (1- Tax rate) + Net borrowing FCFE = Net income + Depreciation -- capital investment -- working capital investment + net borrowing Net new borrowing = long and short-term new debt issues -- long and short-term debt repayments = (420+442) -- (460+400) = 2 FCFE = 216 -- (40×0.7) +2 =190 **Example 12:** If the FCFE is expected to grow at fixed rate of 5% forever and the required rate of return of the firm is 16%, compute the value of the equity. Value of equity = [\$\\frac{\\text{FCFE}\_{1}}{R - g}\$]{.math.inline} = 190/(0.16-0.05) = 1,727.27 **Example 13:** based on your estimates of FCFF and the FCFE, what is the estimated market value of ABC Corp. debt? Answer: 2,700 -- 1,727.27 = 972.73 **d- Two-Stage FCFF Model:** **Example 12:** ABC Corp. FCFF is now forecasted to grow at a higher rate of 10% a year for the next 5 years and then it is expected to grow at a long-term rate of 4%. If the WACC is 15% during the high growth stage and 13% during the stable stage, what should be the value of the firm today? FCFF~1~ = 216 FCFF~2~ = 216 × 1.1 = 237.6 Using the financial Calculator FCFF~3~ = 237.6 × 1.1 = 261.36 CF0 = 0 FCFF~4~ = 261.36 × 1.1 = 287.50 CF1 = 216 FCFF~5~ = 287.50 × 1.1 = 316.25 CF2 = 237.6 FCFF~6~ = 316.25 × 1.04 = 328.89 CF3 = 261.36 CF4 = 287.50 Terminal value = [\$\\frac{\\text{FCFF}\_{6}}{WACC - g}\$]{.math.inline} = 328.89/(0.13-0.04) = 3,654.33 CF5 = 316.25+3654.33 = 3970.58 I = 15 Value of the firm = 2,677.79 NPV = 2677.79 **III- Residual Income Valuation:** Residual income, or economic profit, is defined as the amount of earnings that exceed the shareholders' required return. The concept of economic profit is not reflected in traditional accounting income measures, whereby a firm can report a positive net income but not meet the return required by its shareholders. \* Strengths of residual income models: \- Can be applied to dividend and non-dividend paying firms and to firms with negative free cash flows. They are also appropriate when the cash flows are volatile. \- Residual income models use accounting data, which is usually easily accessible. \- Valuation with residual income models is relatively less sensitive to terminal value estimates, as in the case with dividend and free cash flow valuation models, which reduces forecast errors. \- These models focus on economic profitability rather than just on accounting profitability. \*Weaknesses: \- The reliance on accounting that can be manipulated by management. \- These models can be more difficult to apply since they require, significant adjustments, an in-depth analysis of the firm's accounting accruals; therefore, they are more appropriate for firms with high quality earnings and transparent financial reporting. \- We can forecast the residual income given some basic estimates of future earnings growth and accounting information: RI~t~ = E~t~ -- (R [×]{.math.inline} B~t-1~) = (ROE -- R) [×]{.math.inline} B~t-1~ Where: RI~t~ = residual income in year t E~t~ = expected EPS for year t R = Required return on equity B~t-1~ = book value in year t -1 ROE = expected return on equity **a- The single-stage residual income model:** \ [\$\$P\_{0} = B\_{0} + \\left\\lbrack \\frac{\\left( \\text{ROE} - R \\right) \\times B\_{0}}{R - g} \\right\\rbrack\$\$]{.math.display}\ **Example 14:** Saluki Corp. has a book value per share of \$45. The company payout ratio is 70% and the return on new investments (ROE) is 15%. If the required rate of return on equity is 12%, compute the value of the shares using a single-stage residual income model. Answer: First, we need to calculate the growth rate: g = retention ratio [×]{.math.inline} ROE = 0.3 × 0.15 = 0.045 Then use the single-stage model to compute the intrinsic value: \ [\$\$P\_{0} = B\_{0} + \\left\\lbrack \\frac{\\left( \\text{ROE} - R \\right) \\times B\_{0}}{R - g} \\right\\rbrack\$\$]{.math.display}\ = 63 **b- Multi-stage residual income model:** \ [\$\$P\_{0} = B\_{0} + \\left\\{ \\frac{\\text{RI}\_{1}}{{(1 + R)}\^{1}} + \\frac{\\text{RI}\_{2}}{{(1 + R)}\^{2}} + \\frac{\\text{RI}\_{3}}{{(1 + R)}\^{3}} + \\ldots \\right\\}\$\$]{.math.display}\ Where: B~0~ = current book value RI~t~ = E~t~ -- (R [×]{.math.inline} B~t-1~) = (ROE -- R) [×]{.math.inline} B~t-1~ R = Required return on equity ROE = expected return on equity **Example 15:** **Forecasting residual income:** As a stock analyst, you are assigned to forecast the residual income of XYZ, Corp. over the next three years. Using the information provided in the table below, forecast the firm's residual income assuming a 10% required rate of return. +-----------------------------------+-----------------------------------+ | Current market price | \$45 | +===================================+===================================+ | Current book value per share | \$30 | +-----------------------------------+-----------------------------------+ | Consensus annual EPS estimates: | \$3.75 | | | | | January 2009 | \$4 | | | | | January 2010 | \$4.25 | | | | | January 2011 | | +-----------------------------------+-----------------------------------+ | Dividend payout ratio for the | 60% | | next 3years | | +-----------------------------------+-----------------------------------+ : forecast **Answer:** **2009** **2010** **2011** ----------------------------------------------------------------- ---------- ---------- ---------- Beginning book value (B~t-1~) 30 31.5 33.1 Earnings per share forecast (E~t~) 3.75 4 4.25 Dividend forecast (D~t~ = E~t~ [×]{.math.inline} payout ratio) 2.25 2.4 2.55 Forecast book value per share (B~t-1~ + E~t~ - D~t~) 31.5 33.1 34.8 Equity charge per share (R [×]{.math.inline} B~t-1~) 3 3.15 3.31 Per share RI~t~ \[E~t~ -- (R [×]{.math.inline} B~t-1~)\] 0.75 0.85 0.94 : residual forecast **Example 16:** Using the forecasted residual income from the last example, compute the intrinsic value of the firm assuming that the residual income will be zero after 2011. Answer: \ [\$\$P\_{0} = B\_{0} + \\left\\{ \\frac{\\text{RI}\_{1}}{{(1 + R)}\^{1}} + \\frac{\\text{RI}\_{2}}{{(1 + R)}\^{2}} + \\frac{\\text{RI}\_{3}}{{(1 + R)}\^{3}} + \\ldots \\right\\}\$\$]{.math.display}\ CF0 = 0 CF1 = 0.75 CF2 = 0.85 CF3 = 0.94 I = 10   NPV  = ?? 2.09 P~0~ = 30 + 2.09 = 32.09 **Example 17:** Same as earlier example, except that after 2011 the firm's residual income is forecasted to remain constant at the 2011 level which \$0.94. Answer: After 2011, the residual income of \$0.94 is assumed to persist at the same level forever. This can be regarded as perpetuity. So the value of that perpetuity beginning in year 2012 is \$0.94/0.10=\$9.4 \ [\$\$P\_{0} = B\_{0} + \\left\\{ \\frac{\\text{RI}\_{1}}{{(1 + R)}\^{1}} + \\frac{\\text{RI}\_{2}}{{(1 + R)}\^{2}} + \\frac{\\text{RI}\_{3}}{{(1 + R)}\^{3}} + \\ldots \\right\\}\$\$]{.math.display}\ CF0 = 0 CF1 = 0.75 CF2 = 0.85 CF3 = 0.94 + 9.4 = 10.34 I = 10   NPV  = ?? 9.15 P~0~ = 30 + 9.15 = 39.15 **IV- Stock Valuation using Multiples:** It is obvious that the Dividend Discount Model cannot be applied to companies that don't pay dividends. There are other models that can be applied in that case like: the Free cash flow valuation model, the residual income valuation model and the price multiples. We briefly discussed two of the common price multiples below: 1. **P/E Ratio:** - Earnings power, as measured by earnings per share (EPS), is the primary determinant of investment value. - The P/E ratio is popular in the investment community. - Empirical research shows that P/E differences are significantly related to long-run average stock returns. However, the P/E ratio has some shortcomings which are: - The volatile, transitory portion of earnings makes the interpretation of P/Es difficult for analysts. - Earnings can be negative, which produces a meaningless P/E ratio. - Management discretion in the accounting practices can distort reported earnings, and impair the comparability of P/Es across firms. We can define two versions of the P/E ratio; a trailing and a leading P/E. The difference between the two is how earnings (the denominator) are calculated. Trailing P/E uses earnings over the most recent 12 months period in the denominator. Leading P/E ratio (also known as forward or prospective P/E) uses next year's expected earnings. \ [\$\$Trailing\\ P/E = \\ \\frac{\\text{Market\\ price\\ per\\ share}}{EPS\\ over\\ previous\\ 12\\ months}\$\$]{.math.display}\ \ [\$\$Leading\\ P/E = \\ \\frac{\\text{Market\\ price\\ per\\ share}}{Forcasted\\ EPS\\ over\\ next\\ 12\\ months}\$\$]{.math.display}\ \ [*P*~*t*~ = Benc*h*mark PE ratio × EPS~*t*~]{.math.display}\ Notice: Trailing P/E is not useful for forecasting and valuation if the firm's business has changed. Whereas, Leading P/E may not be relevant if earnings are sufficiently volatile so that next year's earnings are not easy to forecast with accuracy. **Example 18:** Consumer Products Inc. has a leading EPS of \$2, while the median peer group P/E is 23.25. Assuming there are no differences in the fundamentals among the peer firms and Consumer Products, what is your estimate of the firm stock price using the price multiples? P = 23.25 × 2 = 46.5 2. **P/S ratio:** The advantages of using the price-to-sales ratio (P/S) include: - P/S is meaningful even for distressed firms, since sales revenue is always positive. This is not the case for P/E and P/B ratios, which can be negative. - Sales revenue is not easy to manipulate or distort as EPS and book value, which is significantly affected by accounting conventions. - P/S is not as volatile as P/E multiples. - P/S ratios are particularly appropriate for valuing stocks in mature or cyclical industries and start-up companies with no record of earnings. - Like P/E and P/B ratios, empirical research finds that differences in P/S are significantly related to differences in long-run average stock returns. The disadvantages of using P/S ratios are: - High growth is sales does not necessarily indicate high operating profits as measured by earnings and cash flow. - P/S ratios do not capture differences in cost structures across companies - Revenue recognition practices can still distort the sales forecasts. \ [\$\$\\frac{P}{S}\\ \\text{ratio} = \\ \\frac{\\text{market}\\ \\text{value}\\ \\text{of}\\ \\text{equi}ty}{\\text{Total}\\ \\text{sales}} = \\frac{\\text{market}\\ \\text{price}\\ \\text{per}\\ sh\\text{are}}{\\text{sales}\\ \\text{per}\\ sh\\text{are}}\$\$]{.math.display}\ \ [*P*~*t*~ = Benc*h*mark price/sales ratio  × Sales per *Sh*are~*t*~]{.math.display}\ **Example 19:** Company Book value of equity 2010 (millions of \$) Sales 2010 (millions of \$) Shares Outstanding 2010 (millions) Price 2010 (\$) --------- -------------------------------------------- ----------------------------- ------------------------------------ ----------------- A 28,039 18,878 7,001 17.83 B 6,320 9,475 5,239 : Q19 If company A and company B have similar fundamentals, compute the implied price for company B using company's A P/S multiple. Company A: Sales per share = 18,878/7,001= 2.70 Company A: Price per sale ratio = 17.83/2.70 = 6.60 Company B: Sales per share = 9,475/5,239= 1.81 Company B: Price = 6.60 × 1.81 = 11.95 **V- Some Features of common and preferred stocks:** [Common stock features:] \- A common stock is a stock that has no special preference either in paying dividends or in bankruptcy. \- Shareholders control the corporation by electing directors who then hire the managers to run the corporation. Therefore, shareholders control the corporation through the right to elect the directors. \- Normally, each share entitles the shareholder to one vote. A shareholder may cast his votes in person at the annual meeting, or by *Proxy*. \- A proxy is the authority granted by a shareholder that permits another individual to vote the share. \- Straight voting: a procedure in which a shareholder may cast all votes for [each member] of the board of directors. With straight voting the directors are elected one at a time. \- Cumulative voting: a procedure in which a shareholder may cast all votes for [one member] of the board of directors. With cumulative voting, the directors are elected all at once. The total number of votes that each shareholder may cast is determined by multiplying the number of shares (owned or controlled) by the number of directors to be elected. \- Cumulative voting allows minority shareholders to have more chance in electing directors. \- If there are N directors up for election in a cumulative voting, then 1/(N+1) percent of the stock plus one stock will guarantee you a seat. \- Staggering elections is a devise used to minimize the effect of the cumulative voting. To stagger the voting for the board of directors is to put a fraction of the directorship up for election at a particular time. \- Staggering makes it more difficult for minority to elect a director and makes takeover attempts less likely to be successful. \- A corporation may have different classes of stock each with different voting rights. Shareholders generally have rights to: 1. The right to share proportionally in dividends paid. 2. The right to share proportionally in assets remaining after liquidation. 3. Vote on stockholder matters. \- Corporations, at the discretion of the board of directors, pay cash dividends to shareholders, but are not legally obligated to do so. Dividends, once declared, are liabilities of the firm. Dividends paid by the firm are not deductible for tax purposes. \- Preemptive right is the right of the shareholder to the buy a new issue of stock to maintain proportional ownership. [Preferred Stock Features:] \- Preferred stock is a stock with dividend priority over common stock, normally with a fixed dividend rate, sometimes without voting rights. \- Normally, preferred stocks don't have a voting right, so a firm which issues preferred stock raises equity without affecting control of the corporation. \- Dividends payable on preferred stock are either cumulative or non-cumulative. A corporation is not legally obligated to pay dividends on preferred stock. If dividends are cumulative, then any dividends not paid are accumulated and the entire amount must be paid before any dividends on common stock can be paid. \- Unpaid preferred dividends are not debts of the firm. Directors can elect to defer preferred dividends indefinitely. In such a case, common shareholders must also forgo dividends. **VI- The Stock Market:** \- Primary market: is a market in which new securities are originally sold to investors (initial public offering) \- Secondary market: is a market in which previously issued securities are traded among investors. \- A dealer: maintains an inventory of securities and stands ready to buy and sell at any time. \- A broker: is an agent who arranges security transactions among investors. In a sense, he brings buyers and sellers together and does not maintain an inventory. [Organization of the NYSE:] \- A member of the NYSE is the owner of a seat on the NYSE. \- Commission brokers are NYSE members who execute customer orders to buy and sell stock transmitted to the exchange floor. \- A specialist is a NYSE member acting as a dealer in a small number of securities on the exchange floor. He is also called a market maker. \- A specialist's post is a fixed place on the exchange floor where the specialist operates. \- Floor brokers are NYSE members who execute orders for commission brokers on a fee basis. \- Floor traders are NYSE members who trade for their own accounts, trying to anticipate temporary price fluctuations. \- SuperDOT system is an electronic NYSE system allowing orders to be transmitted directly to the specialist. \- Order flow is the flow of customer orders to buy and sell securities. [NASDAQ Operations:] NASDAQ is an electronic network without a single physical exchange floor. It is also a system of multiple market makers. There are approximately 4,000 securities listed on NASDAQ. All the trading is done through dealers. [Stock Market Reporting:] +-------+-------+-------+-------+-------+-------+-------+-------+-------+ | YTD | 52 | Stock | Div | YLd % | PE | Vol | Close | Net | | | Weeks | (Sym) | | | | 100s | | Chg | | \% | | | | | | | | | | Chg | Hi Lo | | | | | | | | +=======+=======+=======+=======+=======+=======+=======+=======+=======+ | -10.4 | 16.48 | Ford | 0.40 | 3.0 | 8 | 83841 | 13.12 | -0.04 | | | 12.61 | Motor | | | | | | | | | | s | | | | | | | | | | F | | | | | | | +-------+-------+-------+-------+-------+-------+-------+-------+-------+ : quotation