Stock Valuation - Chapter 8
An 8 percent preferred stock sells for $54 a share. What is the rate of return?
((8% *100)/ $54 ) * 100 = $14.81
Features of preferred stock
- No ownership interest or no voting privileges - Second to debt holders on claim on a company's assets in the event of bankruptcy. -Annual dividend yield as a percentage of par value - Preferred dividends must be paid before common dividends - If cumulative preferred, all missed past dividends must be paid before common dividends can be paid.
Features of Common Stock
- Represents ownership - Voting rights (proxy voting) - Separation of ownership and control (One share one vote vs. dual class)(A share, B share)(cumulative voting vs. Straight voting) - Dividend payment ( not the firm's liability until declaration)
Non-constant CDG
After period "m", the dividends grow at a constant rate "g"
CDG
Constant Dividend Growth Model with the growth rate of "g"
What are the three common stock valuation methods?
Dividend growth model - CD -CDG -NCDG Free cash flow model -TVN -MV Valuation using multiples -PE -PS
Company A had just paid a dividend of $3 per share. the dividend of this company grows at a steady rate of 8% per year. What will the dividend be in 5 years?
Dt = D0 x (1+g)^t Dt= ? D0= $3/share g= 8% t= 5 years Plug in values: $3 x (1+ 8%)^5 = $3 X 1.4693 = $4.41. It will increase y $1.41 over the coming five years
Common Stock
Equity without priority for dividends or in bankruptcy
When firms don't pay dividends or when dividends are hard to forecast which model should you use? It suggest that the value of the entire firm equals the present value of the firm's free cash flows FCF . This model assumes that at some point "m" free cash flow will grow at a constant rate "g".
Free Cash Flow Model FCF = OCF - Change in NWC - CAPEX
What is the preferred stock valuation model?
P0= D/r or Annual dividend/ required rate of return; based on perpetunity!
How to calculate terminal value of a stock?
TVNm=FCFm+1/WACC -g
What are the differences between common stock and preferred stock?
Preferred stock gives no voting rights to shareholders while common stock does. Preferred shareholders have priority over a company's income, meaning they are paid dividends before common shareholders. Common stockholders are last in line when it comes to company assets, which means they will be paid out after creditors, bondholders, and preferred shareholders.
NCDG Example 2: Building on the previous example (NCDG Example 1), how would the value change if in addition to the $5 constant dividend paid in year 4 and later, the stock also paid a dividend of $1 in years 1 and 2 and a $3 dividend in year 3?
So, we know from the previous e.g that P4 = $50+$5 = $55 or P4+D4 = $55. R= 10% Year 1 D1: $1 Year 2 D2 : $1 Year 3 D3: $3 Year 4 P4+D4: $55 We simply plug these values into the following formula: P0= D1/(1+R)^1 + D2/(1+R)^2 + D3/(1+R)^3 + P4/(1+R)^4 After plugging in values: Answer: $41.56
What are the relevant cash flows for valuing a share of common stock?
The cash flow relevant to value the stock's value is the dividend paid by the company. Some firms pay a constant growth rate, others pay "supernormal growth rate and some does not have growth rate at all!!. Therefore, the dividend is the relevant cash flow to value the share!!
What if the constant growth rate is greater than the discount rate? What does this mean for the stock price? and why?
The stock price is infinitely large; the PV of the dividends continues to get larger.
A stock is selling for $11.90 a share given a market return of 14% and a capital gains yield of 5%. What was the amount of the last annual dividend that was paid?
Total market return on stock= capital gains yield + dividend yield 14% = 5% + dividend yield Dividend yield = 9% 9% *$11.90 = $1.07
True or False: We can use the dividend growth model to get the stock price at any point in time, not just today?
True; bc the price of the stock as of Time "t" is given in the dividend growth model. Pt= Dt (1+g)/(R-g) or Dt+1/R-g
When earnings are negatives do we use P/S multiple or P/E multiple? P/S = Price-sales ratio P/E = Price-Earning Ratio
We should use P/S multiple
Proxy
a grant of authority by a shareholder allowing another individual to vote his or her shares
cumulative voting
a procedure in which a shareholder may cast all votes for ONE member of the board of directors; permit minority participation
Capital gains yield
the dividend growth rate, or the rate at which the value of an investment grows
Constant Dividend (CD) Model
Pt = D/r
Dividend growth model calculates total return as
R = dividend yield + capital gains yield R = D1/P0 + g
straight voting
a procedure in which a shareholder may cast all votes for each member of the board of directors
How does google do its voting?
It has two classes of common stock, A and B. The class A shares are held by the public, and each has one vote. Class B shares are held by company insiders, and each Class B share has 10 votes. As a result, Google's founders and managers control the company.
CDG or Constant Dividend Growth Model
Pt= D t+1/ r - g
E.g. of "NCDG Example 1" Model: Consider a stock that pays no dividends for the first three years and then, starting at the end of year 4, pays a constant $5 dividend. At a 10% required rate of return, what should the stock be worth today?
Given: D4= $5 D5 = D4(1+0), and so on. r = 10% g = 0 m= 4 Step 1: P4 = D4*(1+0)/(r-g) P4= 5*(1+0)/(10%-0) P4 = 5/(10%) P4 = 50 Step 2: Now that we have P4 we can solve for P0 P0= (P4+D4)/(1+r)^4 P0= (50+5)/(1+10%)^4 P0= $37.57
Does the value of a share of stock depend on how long you expect to keep it?
It does NOT depend upon the holding period of the investors. It depends upon the required return of the investors, dividend paid by the company and growth rate in dividend. The value of the share is not a factor of holding period of investors.
What is the value of a share of stock when the dividend grows at a constant rate?
It is the present value of its cash flows discounted at the returns required by the investors Po = D1/r-g P0= current price of the stock D1 = Next dividend expected r= required return of investors and g= constant growth rate
Company A has just paid a cash dividend of $2 per share. Investors require a 16% return from investments such as this. If the dividend is expected to grow at a steady 8% per year, what is the current value of the stock? What will the stock be worht in five years?
P0 = D1/(R-g) = D0 X (1+g)/(R-g) D1= $2 g= 8% R= 16% $2 X (1+8%)/ (16%-8%) =$2.16/8% = $27 current value of the stock In five years, First Step: D5 = D0 x (1+g)^5 = $2 x (1+8%)^5 D5=$2.9387 Second Step P5= D5*(1+g)/(R-g) 2.9387*(1+8%)/(16%-8%) =$3.1738/0.08 P5=$39.67 or P5=P0 (1+g)^5 =$27X(1+8%)^5 =$39.67
E.g. of perpetunity: Gm prefferred stock has a $25 par value with an 8% divident yield. What price would you pay if your required return is 7%?
P= $25*8%/7% = $28.57
Stock price
Present value of expected future cash flows, discounted at an appropriate discount rate
NCDG or non-constant dividend growth model
Pm= D(M+1)/ r - g - combine all relevant cash flows Pt= (D(t+1)/1+r ) + (D(t+2)/(1+r)^2) +..... D(M+1)/(1+r)^m-1 ... etc.
Suppose D0 = $2.30, R= 13%, g=5% Find the price/share and the stock price in year 5
Price/share = D0 (1+g)/(R-g) = $2.30(1+5%)/(13%-5%) =$30.19 Stock Price: Find Dividend at Time 5; Dt = D0 x (1+g)^t D5 = $2.30 x 1.05^5 = $2.935 Dividend growth model: P5 = D5 (1+g) /R-g = $2.935 x 1.05/ 13%- 5% = $38.53
Perpetuity
Promises to pay the same dividend year after year FOREVER, never matures; P0=D/r ; similar to the CD Model
Valuation using multiples using PE and PS ratios
Pt = Benchmark PE ratio * EPSt or Pt = Benchmark price-sales ratio * Sales per sharet
(E.g. of a CDG model) Shares of common stock of the Samson Co. offer an expected total return of 20.0 percent. The dividend is increasing at a constant 6.8 percent per year. If the dividend just paid is $5.7, what is the current stock price today?
Pt= D t+1/ r - g P0= Today "0" D1 = $5.7 t+1 = 1+ 6.8% r = 20.0% g= 6.8% Input values in formula Answer = $46.12 is the current stock price today!
(E.g. of a CD model) Lisa's Unique Clothing Stores offers a common stock that pays an annual dividend of $1.70 a share. The company has promised to maintain a constant dividend. How much are you willing to pay for one share of this stock if you want to earn a 11.50 percent return on your equity investments?
Pt= D/r Price = ? D= $1.70 r=11.50% (plug in values) = 1.7/11.5% = 14.78
Stock sells at $20 per share. The next divident will be $1 per share. Grows by 10% per year more or less indefinitely. What return does this stock offer if correct? Next, based od the ___% return what is the price?
R = D1/P0 + g D1 - $1 P0 = $20 g =10% plug in! R = $1/20 +10% =5% +10% =15% return Price: P1 = D1 (1+g)/(R-g) = $1 (1+10%)/(15%-10%) = $1.10/5% = $22
why is preferred stock preferred?
It has PREFERENCE over common stock in the payment of dividends and in the distribution of corporation assets in the event of liquidation. Meaning holders of the preferred shares must receive a dividend before holders of common shares are entitled to anything