TBUS 350 Business Finance CH 7

The next dividend payment by DEF, Inc., will be $1.51 per share. The dividends are anticipated to maintain a growth rate of 4.04 percent forever. If the stock currently sells for $46.68 per share, what is the required return (in percent)? Answer to at least three decimals. The next dividend payment by DEF, Inc., will be $1.52 per share. The dividends are anticipated to maintain a growth rate of 3.89 percent forever. If the stock currently sells for $38.13 per share, what is the required return (in percent)? Answer to at least three decimals.

(1.51/46.68)+4.04%= 0.0323+4.04%= 3.23%+4.04%= 7.275% 1.51/46.68= 0.0323 + 0.0404 = 0.07275 or 7.275% (1.52/38.13)+3.89%= 0.04141+3.89%= 0.04303%+3.89%= 0.04470% 1.52/38.13= 0.03960 + 0.0389 = 0.07876 or 7.876%

Two Period Example: •What if you decide to hold the stock for two years?

-D1 = $2.00 CF1 = $2.00 -D2 = $2.10 -P2 = $14.70 ***CF2: $2.10 + $14.70= $16.80 -Now how much would you be willing to pay?$ P0= (D1/1+R) + (D2/(1+R) * (D3/1+R) P0= (2/1.20) + (2.10/1.20)^2 + [(2.205+15.4350/1.20]^3= $13.33

Constant Growth Model Conditions

1.Dividend expected to grow at g forever 2.Stock price expected to grow at g forever 3.Expected dividend yield is constant 4.Expected capital gains yield is constant and equal to g 5.Expected total return, R, must be > g 6.Expected total return (R): = expected dividend yield (DY) + expected growth rate (g) = dividend yield + g

Nonconstant + Constant growth

Basic PV of all Future Dividends Formula

Three Period Example Using TI BAII+ Cash Flow Worksheet

Cash Flows: CF0 = 0 CF1 = 2.00 CF2 = 2.10 CF3 = 17.64 Display You Enter CF C00 0 Enter, Down C01 2 Enter, Down F01 1 Enter, Down C02 2.10 Enter, Down F02 1 Enter, Down C03 17.64 Enter, Down F03 1 Enter, Down NPV I 20 Enter, Down NPV CPT 13.33

Estimating Dividends Special Cases

Constant dividend/Zero Growth -Firm will pay a constant dividend forever -Like preferred stock -Price is computed using the perpetuity formula Constant dividend growth -Firm will increase the dividend by a constant percent every period Supernormal growth -Dividend growth is not consistent initially, but settles down to constant growth eventually

BlueCorp. is growing quickly. Dividends are expected to grow at a rate of 18 percent for the next three years, with the growth rate falling off to a constant 4 percent thereafter. If the required return is 8.89 percent and the company just paid a $3.74 dividend, what is the current share price? Answer to two decimals. _______________________________________________________ BlueCorp. is growing quickly. Dividends are expected to grow at a rate of 20 percent for the next three years, with the growth rate falling off to a constant 3.6 percent thereafter. If the required return is 11.89 percent and the company just paid a $3.28 dividend, what is the current share price? Answer to two decimals.

Current dividend D0 = $3.74 growth rate for next 3 years = 18% (1+18%)= 1.18 so Dividend next year: D1 = 3.74*(1+0.18) = $4.41320 D2 = $4.4132*(1.18) = $5.20758 D3 = 3.8085*(1.18) = $6.14494 Value after year 3=(D3*Growth rate)/(Required return-Growth rate): =(6.14494*1.04)/(0.0889-0.04) = 6.39074 / 0.04890 = 130.68993 Hence current price=Future dividend and value*Present value of discounting factor(rate%,time period) (1+11.89%)= 1.089 (4.41320 / 1.089) + (5.20758 / 1.089^2) + (6.14494 / 1.089^3) + (130.68992 / 1.089^3) = 114.42704 _______________________________________________________ Current dividend D0 = $3.28 growth rate for next 3 years = 20% (1+18%)= 1.20 so Dividend next year: D1 = 3.28*(1.20) = $3.93600 D2 = $3.93600*(1.20) = $4.72320 D3 = $4.72320*(1.20) = $5.66784 Value after year 3=(D3*Growth rate)/(Required return-Growth rate): =($5.66784*1.036)/(0.1189-0.036) = 5.87188 / 0.08290 = 70.83091 Hence current price=Future dividend and value*Present value of discounting factor(rate%,time period) (1+11.89%)= 1.1189 (3.93600 / 1.1189) + (4.72320 / 1.1189^2) + (5.66784 / 1.1189^3) + (70.83091 / 1.1189^3) = 61.90150

Finding the Dividend: Gontier Corp stock currently sells for $53.95 Per share. The market requires a return of 12% on the firm's stock. If the company maintains a constant 5.5% growth rate in dividends, what was the most recent dividend per share

D0... Most recent P0= D0(1+g)/(r-g) = D1(r-g) rewrite: D0= P0(r-g)/(1+g)= 53.95(0.12-0.055)/(1+0.055) = $3.32

Suppose you know that a company's stock currently sells for $31.08 per share and the required return on the stock is 7.51 percent. You also know that the total return on the stock is evenly divided between capital gains yield and dividend yield. If it's the company's policy to always maintain a constant growth rate in its dividends, what is the current dividend per share? Answer to two decimals. Suppose you know that a company's stock currently sells for $45.28 per share and the required return on the stock is 8.15 percent. You also know that the total return on the stock is evenly divided between capital gains yield and dividend yield. If it's the company's policy to always maintain a constant growth rate in its dividends, what is the current dividend per share? Answer to two decimals.

Dividend yield = 1/2(0.0751) = 0.03755 capital gains yield Dividend = stock price * dividend yield 31.08*0.3755= 1.16705 D1 = Do (1 + g) 1.16705= D0 ( 1+ 0.03755) D0 = 1.16705/1.03755 D0= 1.12482 D0= 1.13 _______________________________________________________ Dividend yield = 1/2(0.0815) = 0.04075 capital gains yield Dividend = stock price * dividend yield 45.28*0.04075= 1.84516 D1 = Do (1 + g) 1.84516= D0 ( 1+ 0.04075) D0 = 1.84516/1.04075 D0= 1.77291 D0= 1.77

Features of Preferred Stock

Dividends -Must be paid before dividends can be paid to common stockholders -Not a liability of the firm -Can be deferred indefinitely -Most preferred dividends are cumulative •Missed preferred dividends have to be paid before common dividends can be paid •Preferred stock generally does not carry voting rights

Dividend Characteristics

Dividends are not a liability of the firm until declared by the Board of Directors -A firm cannot go bankrupt for not declaring dividends Dividends and Taxes -Dividends are not tax deductible for firm -Taxed as ordinary income for individuals -Dividends received by corporations have a minimum 70% exclusion from taxable income

Apocalyptica Corp is expected to pay the following dividends over the next four years: $3, $10, $15, & $3.08. Afterwards, the company pledges to maintain a constant 5% growth rate in dividends, forever. If the required return on the stock is 11%, what is the current share price.

Enter into calc.. straight hand R: 11% G 5%

Suppose XYZ company paid a dividend of $3. The dividend is expected to grow at a rate of 5% indefinitely. XYZ has a beta of 1.2 the return on the stock market is 12% and the risk-free rate is 4% What would the intrinsic value of XYZ stock be according to the dividend discount model.

First figure out the DR which is required rate of return by using the capital asset pricing model known as the CAPM. Then plug the discount rate along with other given figures into the constant growth dividend discount model the capital asset pricing model give us a discount rate of 13.6%. Required Rate = rf+ beta (rm-rf) 0.04+1.2(0.12-0.04) = 0.136

Cash Flows for Stockholders

If you own a share of stock, you can receive cash in two ways -The company pays dividends -You sell your shares, either to another investor in the market or back to the company As with bonds, the price of the stock is the present value of these expected cash flows -Dividends → cash income -Selling → capital gains

A mature manufacturing firm just paid a dividend of $4.41 but management expects to reduce the payout by 2.4 percent per year, indefinitely. If you require a return of 7.12 percent on this stock, what will you pay for a share today? Answer to two decimals. ____________________________________________________________________ A mature manufacturing firm just paid a dividend of $7.37 but management expects to reduce the payout by 3.01 percent per year, indefinitely. If you require a return of 7.75 percent on this stock, what will you pay for a share today? Answer to two decimals.

Last Dividend, D0: 4.41 Growth Rate, g = -2.40% Required Return, rs = 7.12% Expected Dividend, D1 = D0 * (1 + g) Expected Dividend, D1 = $4.41 * (1 - 0.0240) Expected Dividend, D1 = $4.41 * 0.97600 Expected Dividend, D1 = $4.30416 Current Price, P0 = D1 / (rs - g) Current Price, P0 = $4.30416 / (0.0712 + 0.024) Current Price, P0 = $45.1176 So, the current share price is $45.2118 ____________________________________________________________________ Last Dividend, D0: 7.37 Growth Rate, g = -3.01% Required Return, rs = 7.75% Expected Dividend, D1 = D0 * (1 + g) Expected Dividend, D1 = $7.37 * (1 - 0.0301) Expected Dividend, D1 = $7.37 * 0.96990 Expected Dividend, D1 = $7.14816 Current Price, P0 = D1 / (rs - g) Current Price, P0 = $7.14816 / (0.0775 + 0.0301) 0.04740 Current Price, P0 = $66.43274 So, the current share price is $66.43

Preferred stock as well as preferred stocks usually pay fixed diviends so there is no dividend growth. Let's assume a preferred stock that pays a fixed dividend of $1.50 and the discount rate is 8%.

Notice that since the growth is zero the constant growth dividend discount model becomes the equation to solve the PV of the perpetuity.

Constant Growth Stock

One whose dividends are expected to grow forever at a constant rate, g. D1 = D0(1+g)^1 D2 = D0(1+g)^2 Dt = D0(1+g)^t D0 = Dividend JUST PAID D1 to Dt = Expected dividends

Stock Value = PV of Dividends

P0 = ((D1/(1+R)^1 + ((D2/(1+R)^2 + ((D3/(1+R)^3 + --- + (D INFINITY/(1+R)^INFINITY

Zero Growth •Dividends expected at regular intervals forever = perpetuity P0 = D / R •Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?

P0 = (D/R) P0 = 0.50/(0.10/4) = $20

DGM - Example 2 •Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price? -D1 = $2.00 -g = 5% -r = 20% -

P0 = D1/R-g P0= 2.00/(0.20-0.05)= = $13.33

•What if the company starts increasing dividends by 3% per year beginning with the next dividend? The required return remains at 15%.

P0= 2.00(1.03)/(0.15-0.03)= = $17.17

Example 7.3 Gordon Growth Company - I •Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. •What is the current price?

P0= 4.00/(0.16-0.16)= =$40.00

You have found the following historical information for DEF Company: Yr1 Yr2 Yr3 Yr4 Stock Price: 48.12 50.84 54.87 59.05 EPS: 2.59 2.54 2.87 3.48 Earnings are expected to grow at 6 percent for the next year. Using the company's historical average PE as a benchmark, what is the target stock price in one year? Answer to two decimals. ___________________________________________________________________________ You have found the following historical information for DEF Company: Yr1 Yr 2 Yr 3 Year 4 Stock Price: $47.05 $50.95 $52.83 $57.91 EPS: $2.54 $2.85 $2.81 $3.29 Earnings are expected to grow at 4 percent for the next year. Using the company's historical average PE as a benchmark, what is the target stock price in one year? Answer to two decimals.

PE =Stock price/EPS Yr 1: (48.12/2.59) = 18.57915 Yr 2: (50.84/2.54) = 20.01575 Yr 3: (54.87/2.87) = 19.11847 Yr 4: (59.05/3.48) = 16.96839 Average PE=(18.57915 + 20.01575 + 19.1184669 + 16.96839) /4 = 18.67044 EPS1 = EPS0(1 + g)= 3.48*(1+0.06)= $3.68880 P1 = Benchmark PE ratio x EPS1 = 18.67044 * $3.68880 = 68.87152 Target price in one year: $68.87 ___________________________________________________________ PE =Stock price/EPS Yr 1: (47.05/2.54 = 18.52362 Yr 2: (50.95/2.85) = 17.87719 Yr 3: (52.83/2.81) = 18.80071 Yr 4: (57.91/3.29) = 17.60182 Average PE=(18.52362 + 17.87719 + 18.80071 + 17.60182) /4 = 18.20084 EPS1 = EPS0(1 + g)= 3.29*(1+0.04)= $4.33 P1 = Benchmark PE ratio x EPS1 = 18.20084 * $4.33 = 78.80964 Target price in one year: $78.81 Wrong: 62.28 correct answer

The stock price of XYZ Co. is $20.16. Investors require an 8.29 percent rate of return on similar stocks. If the company plans to pay a dividend of $1.29 next year, what constant growth rate (in percent) is expected for the company's stock price? Answer to two decimals. The stock price of XYZ Co. is $21.23. Investors require an 9.49 percent rate of return on similar stocks. If the company plans to pay a dividend of $3.85 next year, what constant growth rate (in percent) is expected for the company's stock price? Answer to two decimals.

Price (P) = $20.16 Required rate of return = 8.29% Dividend (D1) = $1.29 Growth rate = g g = Ke - (D1 / P) g = 0.0829 - ($1.29 / $20.16) g = - 0.0189 g = - 1.89% Growth is negative 1.89% _______________________________________________________ Price (P) = $21.23 Required rate of return = 9.49% Dividend (D1) = $3.82 Growth rate = g g = Ke - (D1 / P) g = 0.0949 - ($3.85/ $21.23) g = - 0.08645 g = - 8.645% Growth is negative 8.65%

The Stock Markets

Primary vs. Secondary Markets -Primary = new-issue market -Secondary = existing shares traded among investors Dealers vs. Brokers -Dealer: Maintains an inventor Ready to buy or sell at any time Think "Used car dealer" -Broker: Brings buyers and sellers together Think "Real estate broker"

Stock Valuation and PE. Sully Corp currently has an EPS of $2.35, and the benchmark PE for the co is 21. Earnings are expected to grow at 7% per year: P/E... Benchmark PE is actually P/E is 21 EPS= Earnings Per Share

Q1: What is your estimate of the current stock price? P/E= 21 E= 2.35 (P/E)*E (e's cancel out)= P 21*2.35= $49.35 You see the company selling at $54. $49.35 is a fair price for the stock. As an analyst seeing the stock priced at $54 is over priced by the market. Tell clients to sell their stock in Sully Corp and tell all clients not to purchase new shares of Sully. Relative Price Analysis not as great as other method. Logic works better on S&P 500. S&P before COVID was around 30... Now as of 05/12/2020= (-2.05%) Q2: What is the Target stock price in one year? P1= 21*2.35(1+0.07)= $52.80450 or $52.80 Q3: Assuming the company pays no dividends, what is the implied return on the company's stock over the next year? What does this tell you about the implicit stock returns using PE valuation? $49.35 expected price today with 7% growth rate with $52.80 in Time 1. r=P1-P0/P0 r- 52.80-49.35/49.35+ 0.07 or 7%. Coming from capital gains... It tells me using PE eval: using PE valuation is giving you a return that is coming from entirely the capital gain. No dividends means it comes from the capital gain. NOTE: numbers in picture might not add up to 21 as they are made up; however, this is the process of how they get it.

Quick Quiz: Part 2 •You observe a stock price of $18.75. You expect a dividend growth rate of 5% and the most recent dividend was $1.50. What is the required return?

R= D0(1+g)/P0+g = D1/P0+g R= 1.50(1.05)/18.75 + 0.05= 13.4%

PQR, Inc., has an issue of preferred stock outstanding that pays a $3.21 dividend every year, in perpetuity. If this issue currently sells for $35.33 per share, what is the required return in percent? Answer to two decimals. PQR, Inc., has an issue of preferred stock outstanding that pays a $3.94 dividend every year, in perpetuity. If this issue currently sells for $31.76 per share, what is the required return in percent? Answer to two decimals.

Required return on preferred stock = Annual dividend/Current market price Required return = $3.21/$35.33 Required return = 0.09086 Required return = 9.09% _______________________________________________________ Required return = $3.94/$31.76 Required return = 0.12406 Required return = 12.41%

Using the DGM to Find R

Start with the DGM: P0= D0(1+g)/(R-g)= D1/(R-g) Rearrange and solve for R: R= D0(1+g)/P0 + g = D1/P0 + g

ABC Corporation stock currently sells for $48.92 per share. The market requires a return of 12.47 percent on the firm's stock. If the company maintains a constant 5.24 percent growth rate in dividends, what was the most recent dividend per share paid on the stock? Answer to two decimal places. ________________________________________________________________________ ABC Corporation stock currently sells for $63.87 per share. The market requires a return of 12.69 percent on the firm's stock. If the company maintains a constant 3.83 percent growth rate in dividends, what was the most recent dividend per share paid on the stock? Answer to two decimal places.

Stock Price P0= 48.92 Required Return (r) = 12.47 Growth Rate (g)= 5.24 48.92(12.47%-5.24%) / (1+5.24%) 48.92(7.2300%) / (1.0524) = 3.4540 Dividend Per Share or $3.45 Dividend Per Share ________________________________________________________________________ Stock Price P0= 63.87 Required Return (r) = 12.69 Growth Rate (g)= 3.83 63.87 (12.69% - 3.83%) / (1+3.83%) 63.87(8.8600%) / (1.03830) = 5.45014 Dividend Per Share or $5.45 Dividend Per Share

PQR Co. has earnings of $2.15 per share. The benchmark PE for company is 19. What stock price (to two decimals) would you consider appropriate? _______________________________________________________ PQR Co. has earnings of $2.24 per share. The benchmark PE for company is 24. What stock price (to two decimals) would you consider appropriate?

Stock price= Earnings per share×PE Ratio If PE ratio is 12: = $2.15×12 = $25.80 If PE ratio is 19: = $2.15×19 = $40.85 _______________________________________________________ Stock price= Earnings per share×PE Ratio If PE ratio is 12: = $2.24×12 = $26.88 If PE ratio is 24: = $2.24×24 = $53.76

Dividend Discount Model

The dividend Discount Model is a model used to determine the intrinsic value of a stock by summing up the present value of all future expected dividends.

Stock Valuation and PE. Davis, Inc. Currently has an EPS of $2 and an earnings growth rate of 8%. If the benchmark PE ration is 22, what is the target share price five years from now....

They want P5 P5= 22*2(1.08)^5 P5= 44(1.08)^5 P5= 64.65044 P5= $64.65 expected price in year 5.

The equation that does not have the capital gains for the sale of the stock.

This does not mean the Dividend Discount Model ignores capital gains the main point is by using the DDM we are simply discounting future cash flows that we expect to receive from the stock. These future cash flows are the dividends and the sale price of the stock. The only reason why this equation does not show the sale price of the stock is because the future price itself is derived from the future dividends. Therefore under the dividend discount model (DDM) the value of the stock today is ultimately derived by all the future dividends the stock will payout. When investors apply the DDM they would know the date they plan on selling the stock and would solve for the expected value of the stock at that date then discount that price to its PV the constant growth dividend (CGD) was expected to grow at a constant rate.

Features of Common Stock

Voting Rights -Stockholders elect directors -Cumulative voting vs. Straight voting -Boards are often staggered, or "classified" -Proxy voting Classes of stock -Founders' shares -Class A and Class B shares Other Rights -Share proportionally in declared dividends -Share proportionally in remaining assets during liquidation -Preemptive right Right of first refusal to buy new stock issue to maintain proportional ownership if desired

Say there was a company that just paid a dividend of $3 and this dividend was expected to grow at a rate of 5%. What is the dividend in Year 1, Year 2, and Year 3:?

Year 1: (3*0.05)+3= $3.1500 Year 2: [(3+3.15)*0.05]+3= $3.3075 Year 3: [(3+3.3075)*0.05]+3= $3.4575 Only round when you are at the end of the problem or you will have a rounding error. Another word, if it is asking for year 3 do not round until you are at the end of the problem for year 3. We would keep solving for each year's dividend at the growth rate and then discount them by the discount rate the constant growth dividend discount model can be simplified as shown above.

HQZ Inc., has just paid a dividend of $4.09 per share and has announced that it will increase the dividend by $4 per share for each of the next four years, and then never pay another dividend. If you require a return of 7.79 percent on the company's stock, how much will you pay for a share today? Answer to two decimals. _______________________________________________________ HQZ Inc., has just paid a dividend of $4.67 per share and has announced that it will increase the dividend by $3.75 per share for each of the next four years, and then never pay another dividend. If you require a return of 6.63 percent on the company's stock, how much will you pay for a share today? Answer to two decimals.

Year Dividend 1 (4.09 + 4) = 8.09 2 (8.09 + 4) = 12.09 3 (12.09 + 4) = 16.09 4 (16.09 + 4) = 20.09 (1 + 0.0779) = 1.0779 Hence current price=Future dividends*Present value of discounting factor(rate%,time period) Yr 1: 8.09 / 1.0779 = + Yr 2: 12.09 / 1.0779^2 = + Yr. 3: 16.09 / 1.0779^3 = + Yr 4: 20.09 / 1.0779^4 = = 45.6407 (Approx). _______________________________________________________ Year Dividend 1 (4.67 + 3.75) = 8.42 2 (8.42 + 3.75) = 12.17 3 (12.14 + 3.75) = 15.92 4 (15.92 + 3.75) = 19.67 (1 + 0.0663) = 1.0663 Hence current price=Future dividends*Present value of discounting factor(rate%,time period) Yr 1: 8.42 / 1.0663 = + Yr 2: 12.17 / 1.0663^2 = + Yr. 3: 15.92 / 1.0663^3 = + Yr 4: 19.67 / 1.0663^4 = = 46.94684 or $46.95 (Approx)3.75

Future Dividends are discounted by

the cost of equity where bonds are discounted by cost of debt in the dividend discount model equation provided above. The V stands for value and the D's stand for the Dividend in cents for the year the stock is son and P of n is the sale price of the stock in year n. K is the required return or the discount rate.

Nonconstant Growth - Solution

•Compute the dividends until growth levels off -D1 = 1(1.2) = $1.20 -D2 = 1.20(1.15) = $1.38 -D3 = 1.38(1.05) = $1.449 •Find the expected future price at the beginning of the constant growth period: -P2 = D3 / (R - g) = 1.449 / (.2 - .05) = 9.66 •Find the present value of the expected future cash flows -P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67

Projected Dividends

•D0 = $2.00 and constant g = 6% •D1 = D0(1+g) = 2(1.06) = $2.12 •D2 = D1(1+g) = 2.12(1.06) = $2.2472 •D3 = D2(1+g) = 2.2472(1.06) = $2.3820

One Period Example: •Suppose you are thinking of purchasing the stock of Moore Oil, Inc. -You expect it to pay a $2 dividend in one year -You believe you can sell the stock for $14 at that time. -You require a return of 20% on investments of this risk -What is the maximum you would be willing to pay?

•D1 = $2 dividend expected in one year •R = 20% •P1 = $14 •CF1 = $2 + $14 = $16 •Compute the PV of the expected cash flows P0= (D+P1)/(1+R)= CF P0= (2+14)/1.20 P0= 16/1.20 CF= 13.3333333 or $13.33

ECNs

•Electronic Communications Networks provide direct trading among investors •Developed in late 1990s •ECN orders transmitted to NASDAQ •Observe live trading online at Batstrading.com

Valuation Using Multiples

•For stocks that don't pay dividends (or have erratic dividend growth rates), we can value them using the price-earnings (PE) ratio and/or the price-sales ratio: Price at time t = Pt = Benchmark PE ratio X Earnings per share t Price at time t = Pt = Benchmark price-sales ratio X Sales per share t •The price-sales ratio can be especially useful when earnings are negative. •

NASDAQ

•NASDAQ OMX (merged 2007) •Computer-based quotation system •Multiple market makers •Electronic Communications Networks •Three levels of information -Level 1 - median quotes, registered representatives -Level 2 - view quotes, brokers & dealers -Level 3 - view and update quotes, dealers only •Large portion of technology stocks

New York Stock Exchange (NYSE)

•NYSE -Merged with Euronext in 2007 -NYSE Euronext merged with the American Stock Exchange in 2008 •Members (Historically) -Buy a trading license (own a seat) -Designated market makers, DMMs (formerly known as "specialists") -Floor brokers -Supplemental liquidity providers (SLPs)

Work the Web

•Not only are stock price quotes readily available online. Some online trading sites display their "order book" or "limit order book" live online. •Batstrading is one of these. •Follow the link and see current buy and sell orders for Microsoft (MSFT). http://markets.cboe.com/us/equities/

NYSE Operations

•Operational goal = attract order flow •NYSE DMMs: -Assigned broker/dealer •Each stock has one assigned DMM •All trading in that stock occurs at the "DMM's post" -Trading takes place between customer orders placed with the DMMs and "the crowd" -"Crowd" = Floor brokers and SLPs

Finding the Required Return Example •A firm's stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. •What is the required return?

•P0 = $10.50. •D0 = $1 •g = 5% per year. •What is the required return? R= 1(1+0.05)/10.50 + 0.05= 15% Finding the Required Return Example: •P0 = $10.50 •D0 = $1 •g = 5% per year •What is the dividend yield? 1(1.05) / 10.50 = 10% •What is the capital gains yield? g = 5%

DGM - Example 1

•Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? •D0= $0.50 •g = 2% •R = 15% P0= D0(1+g)/R-g P0= 0.50(1+0.02) / 15-2= $3.92

Non-constant Growth

•Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock? •Remember that we have to find the PV of all expected future dividends.

Reading Stock Quotes

•What information is provided in the stock quote? •https://www.bloomberg.com/

Example 7.3 Gordon Growth Company - II

•What is the implied return given the change in price during the four year period? 50.50 = 40(1+return)4; return = 6% 4 N; -40 PV; 50.50 FV; 0 PMT; CPT I/Y = 6% v vThe price grows at the same rate as dividends

Example 7.3 Gordon Growth Company - II

•What is the price expected to be in year 4? P4= D4(1+g)/(R-g)= D5/(R-g) D5=D1(1+g)^4 P4= 4(1+0.06)^4/(0.16-0.06)= $50.50

Quick Quiz: Part 1

•What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%? P0= 2.00/0.15 = = $13.33

Developing The Model

•You could continue to push back when you would sell the stock •You would find that the price of the stock is really just the present value of all expected future dividends