Unit 9 finance
suppose a firm's dividends are expected to grow at a rate of 15%, for 3 years then stabilize at 5g forever. if the firm just paid $2 dividend and R is 10%, what is the value of a share of the firm's stock in year 3 (P3)?
$63.88 D3= Do (1+g1)t= 2(1.15)^3=3.04 D4= D3(1+g2)=3.04 x 1.05= 3.19 P3= D4/(r-g2)= 3.19/(.1-.05)= 63.88
components of the required return
R has 2 components if we rearrange R: R=D1/Po+g 1) D1/Po is called *dividend yield*; A stock's expected cash dividend divided by its current price. 2) *capital gains yield*: The dividend growth rate, or the rate at which the value of an investment grows.
preferred stock features
Stock with dividend priority over common stock, normally with a fixed dividend rate, sometimes without voting rights. -has preference over common stock in payment of divs and in distribution of corp assets in the event of liquidation. *preference* means only that the holders of the preferred shares must receive a div before holders of common shares are entitles to anything -pref stock is in form of equity from legal and tax standpoint. Holders of pref stock sometimes have no voting privileges
which are cash flows to investors in stocks?
capital gains dividends
The capital gains yield equals which one of the following?
Dividend growth rate
The constant growth model can be used to value the stock of firms that have which type(s) of dividends?
Dividends that are either constant or change annually at a constant rate
common stock features
common stock usually applied to stock that as no special preference either in paying divs or in bankruptcy
3 special case patters of dividend growth
nonconstant growth zero growth constant growth
Mitchell, Inc., is expected to maintain a constant 5.9 percent growth rate in its dividends, indefinitely. If the company has a dividend yield of 4.4 percent, what is the required return on the company's stock?
10.3% .044+.059=.103=10.3%
common stock valuation
a share of common stock is more difficult to value in practice than a bond bc: 1) with common stock, not even the promised cash flows are known in advance 2) life of the investment is essentially forever bc common stock has no maturity 3) no way to easily observe the rate of return that the market requires
a zero growth stock pays a dividend of $2 per share and has a discount rate of 10%. What will stock's price be?
20 1/.2
If the computer accessories line is added, what is the current value of the firm's stock?
6.84 5.71+1.13=6.84
clientele effect
how companies attract a certain type of investor -depending on stock type ex. if company has *income stock* (stable cash flow stream in form of dividends), it will attract retirees and risk averse investors ex. if company has *growth stock*, then it's going to attract younger investors looking for price appreciation, capital gains; high g value
stock valuation
involves the application of basic economic valuation principles: *Economic Value*: The market value of a stock is the present value of its expected future cash flows. -This is the stock's economic value: the maximum price its investors are willing to pay today for a share of the company's stock. *Growing Perpetuity*: Stocks are a residual of a corporation which has an indefinite life. -It is therefore reasonable to value stock dividends as a perpetuity. -Additionally, as the dividends may grow with the corporation's profitability, stocks can be valued as a growing perpetuity.
is preferred stock really debt?
it's debt in disguise, a kind of equity bond. -preferred shareholders are only entitled to receive a stated dividend and if the corp is liquidated, pref shareholders are only entitled to the stated value of their pref shares. -pref stock is sometimes convertible into common stock and pref stocks are often callable -many new issues pf pref stock have had sinking funds bc creates a final maturity bc means that entire issue will ultimately retire - for tax purposes, pref divs are treated like common stock divs even though seems a lot like debt
Burkhardt Corp. pays a constant $14.00 dividend on its stock. The company will maintain this dividend for the next eight years and will then cease paying dividends forever. If the required return on this stock is 12 percent, what is the current share price?
$69.55 The price of any financial instrument is the present value of the future cash flows. The future dividends of this stock are an annuity for eight years, so the price of the stock is the present value of an annuity, which will be: P0 = $14.00(PVIFA12%,8) P0 = $69.55
Shareholder Rights
*cumulative voting*: A procedure in which a shareholder may cast all votes for one member of the board of directors; permits minority participation -calculated as # of shares multiplied by # of directors to be elected if there are N directors up for election, then 1/(N+1) percent of the stock plus one share will guarantee you a seat. -Ex. 1/(4+1)=20%; the more seats that are up for election at one time the easier it is to win *straight voting*: A procedure in which a shareholder may cast all votes for each member of the board of directors; only way to guarantee a seat is to own 50% plus one share; guarantees that you'll win every seat -can freeze out minority shareholders staggered elections: -only a fraction of the directorships are up for election at a particular time --if 2 directors are up for election, it will take 1(2+1)= 33.33% of stock plus one share to guarantee a seat -often "classified" boards bc directors are placed into different classes with terms that expire at different times. staggering has 2 basic effects: 1) staggering makes it more difficult for a minority shareholder to elect a director when there is cumulative voting bc there are fewer directors to be elected at one time 2) staggering makes takeover attempts less likely to be successful bc it makes it more difficult to vote in a majority of new directors -but staggering proves institutional memory; continuity on the board of directors
proxy voting
*proxy*: A grant of authority by a shareholder allowing another individual to vote his or her shares. -much voting done in large public corps -management tries to get as many proxies as possible transferred to it --if shareholders are not satisfied with management, an outside group of shareholders can try to obtain votes via proxy --resulting battle is called a proxy fight
Price-Earnings (P-E) ratio
- a market-value ratio from -tells investors how much they are paying for $1 of current earnings -allows relative analysis of stock prices and is directly related to the present value of a company's growth prospects. PE ratio= Po/EPS -comparison of stock prices -comparison of stock markets
Needed to value stock
-A stock's value is the market's evaluation of a company's ability to create wealth for its shareholders and contribute to society's welfare. -The market value of the stock is what investors are willing to pay today for a share of the company's stock. Based on the magnitude, timing and risk of the future cash flows expected to stock owners. -*Dividends as declared*: The Board of Directors will declare—issue a dividend—only if they believe the company has enough cash or profits. -*Potential capital gains*: If the company's cash flows increase, the stock price in the secondary market will rise. Stockholders can sell the stock for more than they paid for it, thus having a capital gain. -*Stock buybacks*: The corporation can buy back its own stock, thus giving cash to its shareholders. * all of these cash flows are residuals—they will occur only if the company's managers are adept at making good decisions in a competitive market environment.*
growth in stock valuation
-growth comes from the ability of a company to produce profits and reinvest those profits to grow. -clientele effect, which shows that growth is not the dominant interest for all investors.
Dry Dock Marina is expected to pay an annual dividend of $1.58 next year. The stock is selling for $18.53 a share and has a total return of 9.48 percent. What is the dividend growth rate?
.95 percent g =.0948- ($1.58/$18.53) = .0095, or .95 percent
some special cases
1) dividend has zero growth rate 2) dividend grows at a constant rate 3) the dividend grows at a nonconstant rate
other rights
1) right to share proportionally in divs paid 2) right to share proportionally in assets remaining after liabilities have been paid in liquidation 3) the right to vote on stockholder matters of great importance. Voting done at the annual meeting or special meeting -shareholders sometimes have right to share proportionally in any new stock sold; called *preemptive right* --means that a company that wishes to sell stock must first offer it to the existing stockholders before offering it to the general public; gives stockholders the opportunity to protect their proprotionate ownership in the corporation
New Age now has the opportunity to add a line of computer accessories to the business. The immediate outlay (t = 0) for this opportunity is $75,000 (obtained via a bank loan), and the earnings from the line will begin one year from now (t = 1). The computer accessories business will generate $25,000 in additional earnings at the end of the year (which also take into account the interest necessary to pay back the debt). These earnings will also grow at 3% indefinitely. What is the per-share-value of the growth opportunities that the new line offers? Do not use dollar sign
1.13 Pv outflows= 75,000/250,000=$.30 Pv inflows= .1/(.1-.03)= $1.43 Po=PV inflows-Pv outflows = 1.43-.3= $1.13
The next dividend payment by Dizzle, Inc., will be $2.60 per share. The dividends are anticipated to maintain a growth rate of 6.25 percent, forever.
11.58 R = (D1 / P0) + g R = ($2.60 / $48.80) + .0625 R = .1158, or 11.58%
what is the total return for a stock that currently sells for $50, just paid a $1.75 dividend, and has constant growth rate of 8%?
11.78 1.75/50+.08
With this new line, what is the P/E ratio of the firm? (use EPS from part a)
17.1 PE= Po/EPS= 6.84/.4=17.1
What is the price of a stock at the end of the year (P1) if the dividend for year 2 (D2) is $5, the price for year 2(P2) and the discount rate is 10%?
22.73 (5+20)/1.1
For the past six years, the price of Slippery Rock stock has been increasing at a rate of 8.21 percent a year. Currently, the stock is priced at $43.40 a share and has a required return of 11.65 percent. What is the dividend yield?
3.44 11.65-8.21
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?
4.52 R = $2.38/$52.60 = .0452, or 4.52 percent
If joan owns 100 shares of ABC company and the company is electing 4 directors, under cumulative voting, Joan usually have ___ votes
400 100 shares x 4 directors
if a zero-dividend stock is purchased for $80 and sold one year later for $84, the 1 year return is
5%= ($84/$80)-1
New Age Electronics expects to earn $100,000 this year. Earnings will grow 3% indefinitely if the firm makes no new investments. The firm's discount rate is 10%, and 250,000 shares are outstanding. What is the price per share of stock without the new line, assuming that all of the earnings are paid out as dividends?
5.71 EPS= 100,000/250,000=$.40 PV=.4/(.4-.03)= 5.71
Graphic Designs has 68,000 shares of cumulative preferred stock outstanding. Preferred shareholders are supposed to be paid $1.60 per quarter per share in dividends. However, the firm has encountered financial problems and has not paid any dividends for the past three quarters. How much will the firm have to pay per share of preferred next quarter if the firm also wishes to pay a common stock dividend?
6.40 $1.6x4
constant growth
Dt= Do (1+g)^t -an asset with cash flows that grow at a constant rate forever is called a growing perpetuity -steady growth in divs is an explicit goal as long as the growth rate is less than the discount rate, the PV of this series of cash flows is: Po= (Do(1+g))/(R-g) = D1/R-g -aka *dividend growth model*; A model that determines the current price of a stock as its dividend next period divided by the discount rate less the dividend growth rate. Price stock of time: Pt= (Dt(1+g))/(R-g) = Dt+1/R-g if growth rate was greater than discount rate, it would be a negative stock bc R-g would be less than 0 if constant growth rate exceed discount rate, then stock price is infinitely large bc growth rate is bigger than discount rate, then PV of divs keeps increasing as well. -same is true if g rate and R rate are = equation for constant growth rate will work for any growing perpetuity: PV= C1/(R-g)= Co(1+g)/(R-g)
dividends
Payments by a corporation to shareholders, made in either cash or stock. characteristics: 1) unless a dividend is declared by the board of directors of a corporation, it's not a liability of the corporation. A corp cannot default on an undeclared dividend. As a consequence, corps cannot become bankrupt bc of nonpayment of dividends. The amount of the dividend and even whether it is paid are decisions based on the business judgement of the board of directors 2) payment of dics by the corp is not a business expense. Divs are not deductible for corp tax purposes. Divs are paid out of corp's aftertax profits 3) divs received by individual shareholders are taxable. Corps that owns tock in other corps are permitted toe exclude 70% of the div amounts they receive and are taxed only on the remaining 30%
cash flows
Po is current price of stock and P1 is price in one period D1 is cash dividend paid at end of period: Po= (D1 + P1)/(1+R) R=required rate of return on investment For price 1? P1= (D2+P2)/(1+R) overall: Po= (D1/(1+R)^1)+ (D2/(1+R)^2) + (D3/(1+R)^3) + (D4/(1+R)^4)...etc
which ratios might be used to estimate value of a stocK?
The Price/Earnings ratio Price/Sales ratio
stated value- pref stock
have states liquidating value. Cash div is described in terms of dollars per share
cumulative and noncumulative divs - pref stock
a preferred div is not like interest on a bond. Divs payable on pref stock are either cumulative or noncumulative; most are cumulative. If preferred divs are cumulative and aren't paid in particular year, they'll be carried forward as an *arrearage*. -both accumulated (past) preferred divs and current preferred divs must be paid before the common shareholders can receive anything -unpaid pref divs are not debts of the firm -holders of pref shares are often granted voting and other rights if pref dics have not been paid for some time.
zero growth
a share of a common stock in a company with a constant dividend is much like a share of preferred stock -the dividend on a share of preferred stock has zero growth and is constant through time - for a zero growth share of common stock, implies that: D1=D2=D3=D=constant value of the stock is: Po= (D/(1+R)^1)+ (D/(1+R)^2) + (D/(1+R)^3) + (D/(1+R)^4)...etc -stock can be viewed as ordinary perpetuity with cash flow = to D every period; per-share value is: Po=D/R
classes of stock
classes are created with unequal voting rights -Class B common stock which is not publicly traded; class has 40% of voting power even though it represents less than 10% of the total # of shares outstanding ex. google has 2 publicly traded classes of commons stock, A and B; Class A shares are held by the public, and each share has one vote -class B held by company insiders and Class B share has 10 votes -New York stock exchange doesn't allow companies to create classes of publicly traded common stock with unequal voting rights -primary reason for creating dual or multiple classes of stock has to do with control of the firm. --if such stock exists, management of a firm can raise equity capital by issuing nonvoting or limited voting stock while maintaining control
common stock vs preferred stock
common stock divs grow at a constant rate 3 points: 1) common shareholder get any increasing residual 2) regular growth is often a managerial goal and markets like steady performance 3) each quarterly dividend may not grow at exactly the same rate, the avg over time may approximate constant growth
a benchmark PE ratio can be determined using
company's own historical PEs PEs of similar companies
the dividend yield is determined by dividing expected dividend (D1) by:
current price (Po)
all else constant, the dividend yield will increase if stock price
decreases
what info do we need to determine the value of a stock using the zero growth model?
dividend discount rate
the constant growth model assumes that
dividends change at a constant rate
measuring growth rate
ex. The more productive the field and the more of the crop the farmer saves for the next planting season, the wealthier the farmer! g = ROE * (Retention ratio)
a pe ratio that's based on estimated future earnings is known as a ___PE ratio
forward
nonconstant growth
g rate cant exceed R indefinitely, but could do so for some # of years.
in the dividend discount model, the expected return for investors comes from which 2 sources?
growth rate dividend yield
If shareholders are granted a preemptive right they will:
have priority in the purchase of any newly issued shares.
a company's growth for years 1 through 3 is 20%, but stabilizes at 5% beginning in year 4, its growth pattern would be described as
non-constant
preferred stock has pref over common stock in the
payment of dividends distribution of corporation assets
stock valuation using comparables, or Comps
problem: many companies don't pay divs. -approach: make PE ratio; ratio of a stock's price per share to its earnings per share (EPS) over previous year Price at time t= Pt= Benchmark PE ratio x EPSt -ratio can be based on similar companies or based on company's own historical values
Kate could not attend the last shareholders' meeting and thus she granted the authority to vote on her behalf to the managers of the firm. Which term applies to this granting of authority?
proxy
growth stocks
small growing companies frequently plow back everything and pay no dividends -when value of the stock is = to pv of future dividends, don't rule out possibility that some # of those dividends are 0, bc not all can be 0
which are reasons that make valuing a share of stock more difficult than valuing a bond
stock has no set maturity dividends are unknown and uncertain required rate of return is unobservable
The dividend yield on a stock will increase if the:
stock price decreases
There are two open seats on the board of directors. If two separate votes occur to elect the new directors, the firm is using a type of voting that is best described as _____ voting.
straight
Using a benchmark PE ratio against current earnings yields a forecasted price called a ____ price
target
if the growth rate g = 0, the capital gains yield is
zero