Stock Valuation  

Prepared By : Wael Shams EL-Din

Stocks and Stock ValuationStocks and Stock Valuation

Type of Stocks

Preferred Stocks Common Stocks

Preferred StockPreferred Stock Preferred stock is a Hybrid; it is similar to bonds

in some respects and to common stock in others.

Preferred stock has a par value and a fixed amount of dividends that must be paid before dividends can be paid on the common stock.

Despite Preferred Stock has a fixed payment like bonds however a failure to make this payment will not lead to bankruptcy.

The holder of the Preferred Stocks does not have

the voting right like the holder of the common stock.

Value of Preferred Stock Value of Preferred Stock The Value of Preferred Stock depend

on 2 factors:- The amount of annual dividends ( which is

fixed amount according to fixed rate)

The required rate of return which is function of ( RFR + Risk premium)

Value (PS)= Dividends

RRR

Example (1)Example (1)A preferred stock $10 par value, 10%

dividend (this amount is fixed) what is the value of the share if the required rate of return is equal 11%.

Answer

Value = Dividends

RRR

 Value PS = 10X10% = 1 = $ 9.09

0.11 0.11

Example (2)Example (2) Fee Founders Has Preferred Stock Outstanding

Which Pays A Dividend Of $5 At The End Of Each Year. The Preferred Stock Sells For $60 A Share. What Is the Preferred Stock’s Required Rate of Return?

Answer

Value = Dividends

RRR

 60 = $5 =

RRR

RRR = 5 X100 = 8.33% 60

Example (3)Example (3) What will be the nominal rate of return on a

Preferred Stock with a $100 par value, a stated dividend of 8 percent of par, and a current market price of (a) $60, (b) $80, (c) $100, and (d) $140?

Answer

Dividend = 100x8% = $8

Value = Dividends

RRR

Required Rate of Return Required Rate of Return  A) - RRR @ $60 = 8 X 100 = 13.33%

60

 B) - RRR @ $80 = 8 X 100 = 10%

80

 C) - RRR @ $100 = 8 X 100 = 8 %

100

 D) - RRR @ $140 = 8 X 100 = 5.71 %

140

Example (4)Example (4) Ezzell Corporation issued preferred stock

with a stated dividend of 10 % of par. Preferred stock of this type currently yields 8% & the par value is $100. Assume dividends are paid annually.

A. What is the value of Ezzell’s preferred stock?

B. Suppose interest rate levels rise to the point where the preferred stock now yields 12 percent. What would be the value of Ezzell’s preferred stock?

AnswerAnswer

Dividend = 100x 10% = $ 10

Value = Dividends

RRR

P = 10 = $ 125 0.08

 

P = 10 = $ 83.33 0.12

Common StocksCommon Stocks The Problem of a common stock is that the

amount of dividends, earning or cash flow of return is not fixed and there is no maturity, therefore we need to set several assumptions related to the holding period of the investment and cash flow that we may receive during that period.  

1)The Holding Period is one year

2)The Holding Period is more than one year

3)The Holding Period is unknown

The Holding Period is one year The Holding Period is one year

The cash that may be received at the end of the year is known as dividend and selling price of that stock will be at the end of same year.

Example (5)Example (5) XYZ Company has a share that is

expecting to pay $1 dividend next year and to be sold at $30 by the end of that year, what is the value of XYZ stock if the required rate of return is 14%.

 

AnswerAnswerToday Dividend (D1)= $ 1

Selling Price = $ 30

---------FV $ 31

Price (PV) = FV 1+RRR

Price (PV) = 31 = $ 27.19 1.14

The Holding Period is more The Holding Period is more than one yearthan one year In this case we need to estimate

dividends for the next years also the expected growth rate in that dividends during the coming holding period and the selling price at the end of that period.

Example (6)Example (6) ABC’s share is expecting to pay $2

dividend next year while the dividends of this stock will grow by 10% each year, ABC Share is expected to be sold at the end of 3 years for amount of $40, what is the value of ABC stock if the required rate of return is 14%.

Answer Answer

Y0Y1 Y2 Y3

Dividend 2

10%

2.20

10%

2.42

Selling Price 40

Total 2 2.20 42.42

AnswerAnswerPrice (PV) = 2 + 2.20 + 42.42

1.14 1.142 1.143

Price(PV)= 1.7544+ 1.6928 + 28.6331=

Price ( PV) = $ 32.08

The Holding Period is unknown The Holding Period is unknown In this case the company will be in the

mature stage then it will enjoy a constant growth rate.

Example (7)

ABC’s Share is expecting to Pay $ 3 dividends next year while it is expected to have a constant growth rate for 5 %, what is the value of ABC Stock if the required rate of return is 15%.

AnswerAnswer

Value = Dividends RRR- g

P0 = D1 RRR-g

g Growth Rate

P = 3 = $ 30

0.15-0.05

Example (8)Example (8) ABC’s share is expecting to pay $ 2

dividends next year while it is expected to have a constant growth rate for 10 % annually for the coming 2 years then it will fall to 4 % constantly, what is the value of ABC stock if the required rate of return is 14%.

AnswerAnswer

Y0Y1 Y2 Y3 Y4

Dividend 2

10%

2.20

10%

2.42

4%

2.52

Constant Growth

Selling Price

25.20

Total 2 2.20 27.62

AnswerAnswer

P3 = D4

RRR- g

P3 = 2.52 = $ 25.20

0.14-0.04

Price (PV) = 2 + 2.20 + 27.62 1.14 1.142 1.143

Price (PV) = 1.75+ 1.69 + 18.64 = $ 22.08

Variables & Relationship that affect the Variables & Relationship that affect the Value of common stock Value of common stock

 P0 = D1

RRR-g

Variables D1 Dividend which is affected by level of earning

RRR Required rate of return which is affected by

(Risk free rate + Risk Premium)

g Growth rate which is affected by payout ratio &

earning

Relationship Relationship There is positive relationship between

dividend and value. There is negative relationship between

required rate of return and value. There is a positive relationship between

growth rate and value

Growth Rate (g) Growth Rate (g) g

Retention Rate (RR) X ROE

(1- Payout Ratio) X Net Income

Equity

Example (9)Example (9)

Item Amount Sales $100 Million Cost of Goods Sold (COGS) $ 50 Million Book Value of ABC Share $ 10Interest rate on Co’s Debt 15%Tax Rate 40% Amount Of Debt $ 40 Million No. of outstanding Shares 4 Million Shares Risk Free Rate 10% Market Risk Premium 25%Beta 1.20Payout Ratio 40% The company is Financed by 50% Debt & 50% Equity

Example 9Example 9From the given data, Please find the

following:-The Required Rate of Return What is the Stock Value?

AnswerAnswerP0 = D1

RRR-g

RRR= RFR + (Market Risk Premium) x Beta

RRR = 10% + (25% )X 1.20 = 40%

In order to get the stock value we need to calculate g & D1

AnswerAnswer Sales 100,000,000

(-) COGS 50,000,000

EBIT 50,000,000(-) Interest (40,000,000 X 15% ) (-) 6,000,000

EBT 44,000,000(-) Tax @ 40% (-) 17,600,000Net Income After Tax 26,400,000

Retention Rate (60%) Pay Out Ratio (40%) 15,840,000 10,560,000 ÷

4,000,000 Shares Dividend (D0) = 2.64

Answer Answer g = RR X ROE  

ROE = Net Income X 100 Equity

ROE = 26, 400, 0000 X100 = 66%

40,000,000

g = RR X ROE

g = 60% x 66% = 39.60%

D1 = D0 X (1+g)

D1 = 2.64 X (1.3960) = 3.69

Answer Answer P0 = D1

RRR-g

D1 = 3.69

RRR = 40%

g = 39.60%

P0 = 3.99 = 3.69 = $ 92.25

0.4000- 0.3960 0.004

Example 10Example 10Sales Volume in Units : 10,000,000 Units

Selling Price per Unit : $3

Variable Cost per Unit : $1

Total Fixed Cost : $ 1,000,000

Fixed Assets : $ 2,000,000

Depreciation Rate of Fixed Assets : 5% Per Annum

Risk Free Rate (RFR) : 12%

Market Required Rate of Return : 20%

Beta : 1.20

Long Term Debt : $ 5,000,000 @ Interest Rate 15%

Number of Outstanding Shares : 1,000,000 Shares

Share Price (Book Value) : $30

Tax Rate : 35%

Payout Ratio : 50%

From the mentioned Data, Find From the mentioned Data, Find the Following:- the Following:- 1. Sales Revenue in Dollars

2. Total cost COGS= (Variable + Fixed + Depreciations)

3. Earnings Before Interest and tax (EBIT)

4. Retune on Equity (ROE)

5. Required Rate of Return (RRR)

6. Dividend for Current Year (D0)

7. Calculate Growth Rate (g)

8. Dividend For Next Year (D1)

9. Find the Value of ABC Share

10. If Share is traded in the stock Market at $250, what is your decision as investor and why?

AnswerAnswerRRR= RFR + ( RM - RFR) x Beta

RRR = 12+ (20-12)1.20 = 21.60%Sales = no. of units X Selling Price

Sales = 10 Million X3 = 30 Million

Variable Cost = No. of Units X Variable cost Per Unit

Variable Cost = 10 Million X 1 = 10Million

Depreciation = Fixed Assets X Deprecation Rate

Depreciation = 2Million X 5% = 100,000

Answer Answer Total cost COGS= (Variable + Fixed Cost + Depreciations)

COGS = 10M+1M+100,000 = 11,100,000

Sales 30,000,000

(-) COGS 11,100,000

EBIT 18,900,000

(-) Interest (5,000,000 X 15% ) 750,000

EBT 18,150,000

(-) Tax @ 35% 6,352,500

Net Income After Tax 11,797,500

Answer Answer

Net Income = 11,797,500

Retention Rate (50%) Pay Out Ratio (50%) 5,898,750 5,898,750 ÷

1,000,000 Shares

Dividend D0 = 5.90

ROE = Net Income X 100

Equity

Equity = 1,000,000 X 30 = 30,000,000

 ROE = 11, 797, 0000 X100 = 39.32%

30,000,000

 

Answer Answer g = RR X ROE

g = 50% x 39.32% = 19.66%

D1 = D0 X (1+g)

D1 = 5.90 X (1.1966) = 7.06  

P0 = D1

RRR-g

D1 = 7.06

RRR = 21.60%

g = 19.66%

Answer Answer P0 = 7.06 = 7.06 = $ 363.92

0.2160- 0.1966 0.0194

Since the Fair value of the stock is approximately is $364 while it is traded at $250 ( Under Price) , Therefore my decision as investor is to purchase stock as its has a potential to move up to $ 364 and achieve capital gain .

Thank You