FIN Ch 7 - Lecture notes Chapter 7 PDF

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Equity Market and Stock Variation, Cash Flows, Zero Growth, Examples...

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Chapter 7 Equity Market and Stock Variation - Stock Valuation - Constant Growth - Non-constant Growth - Features of stocks - Stock Market Characteristics In general… - Valuation of any financial asset is the reflection of the future performance - Apply sum of future value of cash flows as the value of any type of distant asset - The sum of PVs of future cash flows - Bond Value can be found by summing PVs of - Periodic coupon payments - Face Value - Nothing special in stock valuation Cash flows for stockholders - If you own a share of stock, you can receive cash in two days - The company pays dividends - You sell your shared, 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 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

Two period Example - What if you decide to hold the stock for two years? - D1 = $2.00 CF1 = $2.00 - D2 = $2.10 CF2 = $2.10 +$14.00 = $16.10 - P2 = $14.00

Three Period Example - What if you decide to hold the stock for three years? - D1 = $2.00 CF1 = $2.00 - D2 = $2.10 CF2 = $2.10 - D3 = $2.205 CF3 = $4.405 +14.00 = $16.205 - P3 = $14.00

Developing the model - You could continue to push back when you sell the stock

Stock Value = PV of Dividends

How can we estimate all future dividend payments? 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 (g) - Firm will increase the dividend by a constant percent every period

= D1/R-g

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Supernormal growth - Dividend growth is not consistent initially, but settles down to constant growth eventually Zero Growth - Dividends expected at regular intervals forever = perpetuity - Suppose stock is expected to pay a $2 dividend every year and the required return is 10%. What is the price? P= D/R= $2/0.1 = $20 Constant growth stock - One whose dividends are expected to grow forever at a constant rate, g. D0 = Dividend Just Paid D1-Dt = Expected dividends

Projected Dividends - D0 = 2$ and constant g =6% D1= 2x(1+0.06)=2.12 D2=2x(1+0.06)^2 = 2.2472 D3=2x(1+0.06)^3 = 2.382 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?

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Example Gordon Growth Company - 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? - D0 is current period - D1 is next period - Growth rate is 6% - Required return in 16% - P0 = D1/R-g = 4/0.16-0.06 = 4/0.1 = 40 - P0=D0*(1+g)/R-g - survey, publication/website, do own calculation - What is the price expected to be in year 4? P4? - D1 = $4 - g=6% - R=16%

Using the DGM to Find R - Start with the DGM

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Rearrange and solve for R

Finding the Required Return - example - Suppose a firm’s stock is selling for $10.50. They just paid a $2 dividend and dividends are expected to grow at 5% per year. What is the required return? - P0 = 10.50 - D0 = $2 - D1 = D0(1+g) = 2.10 - G = 5% - R=D1/P0+g = $2.10/$10.50+5% = 20% +5% = 25% Suppose a firm is expected to increase dividends by 20% in one year and by 15% in second year. 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? - P0? - 3 different growth rates on the dividend - Never use P=D/R or P=D1/R-g because dividend is not constant - Remember that we have to find the PV of all expected future dividends Nonconstant + Constant growth P0 = D1/1+R + D2/(1+R)^2 + D3/(1+R)^3 +.....+......+ D infinite/(1+R)^infinite |________________________________________| Can apply constant growth here because the growth is constantly 5% g1 = 20% g2 = 15% P0=D1/R-g (don't use this on second half of equation) -> P2=D3/R-g g3 = 5% P4=D5/R-g D0 = $1 R = 20% Nonconstant Growth - solution - Compute the dividends until growth levels off - D1 = 1(1.2)=$1.20 - D2 = 1(1.2)^2 = 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 - The constant growth phase beginning in year 3 can be valued as a growing perpetuity at time 2 - 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/(1.2)^2 + 9.66/(1.2)^2 = 8.67 PVz PV2 PV of P2

A differential Growth Example - A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity - What is the stock worth? The discount rate is 12%.

1-3 is nonconstant 4-infinity is constant - can use P3 = D4/R-g Price of stock formula for non constant

Features of Common Stock - Voting Rights - Stockholders elect directors - Cumulative voting vs. straight voting - 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 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

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Dividends are not tax deductible for firm Taxed as ordinary income for individuals Dividends received by corporations have a minimum 80% exclusion from taxable income - Firm A owns 60% of B - A’s taxable income including dividend income from B of $9,000 is $10,000 - 80% of dividend income is excluded from tax - So, total of$7,200 (=80% x $9,000)exclusion - Firm A owns 60% of B - A’s taxable income including dividend income from B of $10,000 is $7,000 - A could have been entitled to the exclusion of $8,000 (=80% x $10,000) - “Income Limitation Rule” applies - So, total of $5,600(=80% x $7,000) exclusion 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 The Stock Markets - Primary vs. Secondary Markets - Primary = new-issue market - Secondary = existing shares traded among investors - Dealers vs. Brokers - Dealers: Maintains an inventory. Ready to buy or sell at any time. Think “Used car dealer” - Broker: Brings buyers and sellers together. Think “Real estate broker” Chapter 7 Practice Questions When valuing a stock using the constant-growth model, D1 represents the: - expected difference in the stock price over the next year. - discount rate. - the next expected annual dividend. - expected stock price in one year. -

last annual dividend paid.

What is the market called that facilitates the sale of shares between individual investors? -

Initial

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Inside Secondary Proxy

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Primary

Newly issued securities are sold to investors in which one of the following markets? -

Inside Primary Proxy Stated value Secondary

The VIC Co. has preferred stock outstanding that pays a $4.50 dividend annually and sells for $48.20 per share. What is the rate of return? -

6.89 percent 7.70 percent 9.34 percent - R = $4.50/$48.20 = .0934, or 9.34 percent

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8.98 percent 8.23 percent

Delfino's expects to pay an annual dividend of $1.50 per share next year. What is the anticipated dividend for Year 5 if the firm increases its dividend by 2 percent annually? -

$1.50 x(1.02)^5 $1.50 x(1.02)^2 $1.50 x(1.02)^4 $1.50 x(1.02)^1 $1.50 x(1.02)^3

The dividend yield on a stock will increase if the: -

stock price decreases. dividend growth rate decreases. stock price increases. tax rate on dividends increases. capital gains rate decreases.

Triad common stock is selling for $27.80 a share and has a dividend yield of 2.8 percent. What is the dividend amount? -

$.31 $.78 - Dividend =.028 ×$27.80 $3.49

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$7.80 $4.25

Breakfast Hut pays a constant annual dividend of $1.39 per share. How much are you willing to pay for one share if you require a rate of return of 14.6 percent? -

$2.52 $11.87 $9.52 - P = $1.39 /.146 = $9.52 $14.72 $1.59

Sweet Treats pays a constant annual dividend of $2.38 a share and currently sells for $52.60 a share. What is the rate of return? -

5.39 percent 5.91 percent 4.52 percent - R = $2.38/$52.60 = .0452, or 4.52 percent 4.83 percent

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4.56 percent

Healthy Foods just paid its annual dividend of $1.62 a share. The firm recently announced that all future dividends will be increased by 2.1 percent annually. What is one share of this stock worth to you if you require a rate of return of 15.7 percent? -

$11.91 $12.95 $12.16 - P0 = ($1.62 × 1.021)/(.157-.021) = $12.16 $10.54 $13.07

Solar Energy will pay an annual dividend of $1.93 per share next year. The company just announced that future dividends will be increasing by 1.6 percent annually. How much are you willing to pay for one share of this stock if you require a rate of return of 11.75 percent? -

$15.14 $19.01 - Value of stock = Dividend next year / (Required return - growth rate of dividends) = 1.93 / (.1175 -.016) = $19.01 $16.12

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$19.32 $19.78

Braxton's Cleaning Company stock is selling for $32.60 a share based on a rate of return of 13.8 percent. What is the amount of the next annual dividend if the dividends are increasing by 2.4 percent annually? -

$2.71 $3.72 - D1 = $32.60 x(.138-.024) = $3.72 $3.84 $2.86 $2.78

The common stock of Up-Towne Movers sells for $33 a share, has a rate of return of 11.4 percent, and a dividend growth rate of 2 percent annually. What was the amount of the last annual dividend paid? -

$3.10 $2.61 $2.58 $3.04 - D0 = [$33 × (.114 - .02)] / (1 + .02) = $3.04

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$3.32

This morning, you purchased a stock that will pay an annual dividend of $1.90 per share next year. You require a 12 percent rate of return and the dividend increases at 3.5 percent annually. What will your capital gain be in dollars on this stock if you sell it three years from now? -

$2.43 - P0 = $1.90/(0.12 - 0.035) = $22.35 P3 = [$1.90 × (1.035)^3]/(0.12 - 0.035) = $24.78 Capital gain = $24.78 − $22.35 = $2.43 $2.92 $2.51 $2.63 $2.87

Horseshoe Stables is losing significant market share and thus its managers have decided to decrease the firm's annual dividend. The last annual dividend was $.86 a share but all future dividends will be decreased by 3.5 percent annually. What is a share of this stock worth today at a required return of 17.8 percent? -

$3.59 $3.41 $3.06 $3.95 $3.90 - P0 = {$.86 x [1 + (-.035)]} / [.178 - (-.035)] = $3.90

Lamey Gardens has a dividend growth rate of 5.6 percent, a market price of $13.16 a share, and a required return of 14 percent. What is the amount of the last dividend this company paid? -

$1.55 $1.60 $1.15 $1.05 - R = D/P + g 14 = x/13.16 + 0.056D = 1.05 $1.30

The Sports Club plans to pay an annual dividend of $1.20 per share next year, $1.12 per share a year for the following two years, and then a final liquidating dividend of $14.20 per share four years from now. How much is one share of this stock worth to you today if you require a rate of return of 18.7 percent of this risky investment? -

$7.56 $9.63 $8.36 $10.30 $12.60

River Rock, Inc., just paid an annual dividend of $2.80. The company has increased its dividend by 2.5 percent a year for the past 10 years and expects to continue doing so. What will a share of this stock be worth 6 years from now if the required return is 16 percent? -

$26.90 $24.65 - P6 = ($2.80 ×1.0257)/(.16 -.025) = $24.65 $25.50 $23.60

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$25.08

Dixie Mart plans to pay dividends of $1.36, $1.15, $1.35, and $.40 at the end of the next four years, respectively. After that, the company will be sold and shareholders are expected to receive $82.40 per share in Year 6 when the sale should be finalized. If the required return is 11.4 percent, what is the current value of one share of this stock? -

$47.29 $46.50 $51.87 $51.08 $47.71

The Three Amigos just paid an annual dividend of $.60 per share but plans to double that amount each year for three years. After that, the firm expects to maintain a constant dividend. What is the value of this stock today if the required return is 15 percent? -

$29.61 $27.05 -

D1 = $.60 × 2 = $1.20 D2 = $1.20 × 2 = $2.40 D3 = D4 = Dt = $2.40 × 2 = $4.80 P3 = $4.80 / .15 = $32 P0 = $1.20 / 1.15 + $2.40 / 1.15^2 + ($4.80 + 32) / 1.15^3 P0 = $27.05

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$23.05

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$26.67 $27.64...