Chap 10 CS Valuation

Chap 10Chap 10Common Common StockStock Valuation Valuation

Intro to cmIntro to cm

Common Stock Valuation Learning Objectives

Common Stock Valuation

Dividend Growth model

Zero Growth

Constant Growth

Multiple growth model

Intrinsic Value & Market price

Relative Valuation Techniques (P/E,P/S,P/S)

Components of Required Return

Capital Market Securities

Fixed Income (Bonds)

Treasuries

Corporates

Equities

Preferred Stock

Common Stock

Common Stock

It is an equity ownership in a corporation, initially issued to raise capital

Points to keep in mind!

C/F’s are NOT known in advance

Life of stocks is forever – no maturity

Difficult to observe required rate of return for discounting

Common stock valuation

The two approaches to valuing common stock using fundamental security analysis are:

1. Discounted Cash flow techniques

2. Relative valuation techniques

Common stock valuation

The two approaches to valuing common stocks using fundamental security analysis are:

1. Discounted Cash flow techniquesAttempts to estimate the value of a stock today using a present value analysis.

2. Relative valuation techniquesA stock is valued relative to other stocks based on the basis of ratios.

Key difference!

Discounted Cash Flow Techniques

The estimated value of a security is equal to the discounted value (Present Value) of the future stream of cash flows that an investor expects to receive from the security:

Estimated Value of any security = V0

V0 = Expected Cash Flows/ (1 + K)t

Where:K is the appropriated Discount Rate


To use Discounted Cash flow Model, an investor must:

1. Estimate the amount & timing of future stream of Cash flows.

2. Estimate an appropriate Discount Rate

3. Use these two components in PV Model to estimate the value of the security, which is then compared to the current Market Price of the security.


Two different approaches to the cash flows & discount rates can be used in the valuation of stocks:

1. Value the Equity of the Firm, using the required rate of Return to shareholders.

2. Value the entire firm using the Weighted Average Cost of Capital (WACC).


How to come up with the Price of a Stock?

Assumptions:

Assume a dividend the stock will pay.

Assume a selling price at the end of 1 year.

Come up with a required rate of return.

Discounted Cash Flow Techniques - Example

Example:

Stock selling price after 1 year is $70

Stock dividend will be $10

Investors require 25% return

PV = 80/(1.25)

= $64

Discounted Cash Flow Techniques - Example

Example:

Stock selling price after 1 year is $70

Stock dividend will be $10

Investors require 25% return

PV = 80/(1.25)

= $64Or,

Po = (D1+P1) / (1+k)


P1 at t1, could also be found the same way by assuming year 2 price & dividend:

P1 = (D2+P2) / (1+K)


Substituting P1 in Po equation:

Po = (D1+ (D2+P2)/(1+K)) / (1+K)

= [D1/(1+K)1] + [D2/(1+K)2] + [P2/(1+K)2]

Dividend Discount Model

Formula:

Po = E [Dn/ (1+K)n]

Present Value of all future dividends as a general valuation framework!

Dividend Discount Model

1. Investors must value a stream of dividends that may be paid forever, since common stock has no maturity value.

2. The dividend Stream is uncertain:

There is no specified number of dividends, if in fact any are paid at all.

Dividends are Expected to grow in most cases.

Dividend Discount Models – Special cases

Growth Rate Cases for the DDM:

The Zero Growth rate Case The Constant Growth rate Case The Multiple Growth rate Case

The Zero Growth Rate Model

Zero-growth:

A Dividend Stream resulting from Fixed dollar Dividend equal to the current Dividend, Do.

So,

Value of the stock is a Present value of a Perpetuity!

Po = D/K

The Zero Growth rate model- Example

A company pays a dividend of $2 per share, which is not expected to change. Required return is 20%. What’s the price per share today?

Discounted Cash Flow Techniques – Zero Growth - Example

A company pays a dividend of $2 per share, which is not expected to change. Required return is 20%. What’s the price per share today?

Po = Do / k= 2/0.2 = 10

The Constant Growth Rate ModelThe constant Growth rate Case for the DDM reflects a dividend stream that is expected to grow at a constant rate g, forever.

Which implies:

If dividend just paid is Do, then the next D1 is:

D1 = Do*(1+g)

Dividend for period 2, D2:

D2 = D1*(1+g)

= [Do*(1+g)] * (1+g)

= Do *(1+g)2

The Constant Growth Rate Model

Stock Price with constant growth dividends:

Po = Do *(1+g) / (K-g)

OR

P0 = D1 / (K – g)

Dividend Discount Model - Assumptions

Dividend paying stock

Required Return by investors is greater than the Growth Rate of Dividends.

Dividends will grow at a constant Rate forever.

The Constant Growth Rate Model - example

Suppose Do = 2.30, K=13%, g=5%. What’s the price per share?


Suppose Do = 2.30, K=13%, g=5%. What’s the price per share?

P0 = D1 / (k – g)= 2.3 *(1.05) / (0.13 - 0.05)= 2.415 / 0.8= 30.19

The Constant Growth Rate Model

Constant Growth Model can be used to find the stock price at any point in time!

1. Find the Dividend for that year.

2. Grow it at (1+g)

3. Divide by K-g


Suppose Do = 2.30, K=13%, g=5%.What’s the price per share in 5 years?

Hint:

P5 = D6 / (K – g)


Suppose Do = 2.30, K=13%, g=5%.What’s the price per share in 5 years?

P5 = D6 / (K – g)

= [2.3 *(1.05)^6] / (0.13-0.05) = 3.0822 / .08 = 38.53


Suppose Company XYZ’s next dividend will be $4. Required return is 16%. Dividend increases by 6% every year, forever.

What’s the price per share today?

& in 4 years?



What’s the price per share today? P0 = D1 / (k – g)

= 4/(.16-.06) = 4/.1 = $40



Price in 4 years?

P4 = D5 / (k – g)

D5 = D1 * (1+g)4 = 4(1.06)4 = 5.05

P4 = 5.05/0.1 = 50.50

Dividend discount models -Multiple Growth Rate Case

For many companies, it is inappropriate to assume that dividends will grow at a constant rate as Firms typically go through life cycles.

P0 = PV of Expected Future Cash flows


For many companies, it is inappropriate to assume that dividends will grow at a constant rate as Firms typically go through life cycles.

P0 = PV of Expected Future Cash flowsP0 = PV of Dividends during the non Constant period

PLUSPV of Dividends during the constant

Growth Period

Multiple Growth Rate Case

To find Value of Stock with Non Constant Growth, we go through the following three steps:

1. Find the PV of Dividends during the period of Non Constant Growth.

2. Find the PV of Stock at the end of Non Constant Growth period at which point it has become a constant growth Stock, and discount the price back to the present.

3. Add these two components to find the intrinsic Value of the Stock.


Multiple Growth model

Company grows at a certain high rate first, then slows down to grow at a constant sustainable rate.


Multiple Growth model

Company grows at a certain high rate first, then slows down to grow at a constant sustainable rate.

Value = PV of dividends + PV of terminal price

= E [Dt /(1+k)t] + {[Dn+1 /(k-g)]*[(1/1+k)n]}

Multiple Growth Rate Case - Example

The last dividend paid by Klein Company was $1.00. Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever. Klein’s required rate of return on equity (ks) is 12 percent. What is the current price of Klein’s common stock?



0 1 2 3 Years | | | | 1.00 1.05 1.1025 1.21275 P0 = ? 2P̂ = 60.6375 = CFt 0 1.05 61.7400

k = 12% gs = 5% gs = 5% gn = 10%

10.012.0

21275.1



Financial calculator solution:Enter in Cash register CF0 = 0, CF1 = 1.05, and CF2 = 61.74.

Then,Enter I = 12, and press NPV to get NPV=P0= $50.16.


Your company paid a dividend of $2.00 last year. The growth rate is expected to be 4 percent for 1 year, 5 percent the next year, then 6 percent for the following year, and then the growth rate is expected to be a constant 7 percent thereafter. The required rate of return on equity (ks) is 10 percent. What is the current stock price?



Time line: 0 1 2 3 4 Years | | | | |

2.00 2.08 2.1840 2.31504 2.4770928 P0 = ?

3P̂ = 82.56976 =

0.070.10

2.4770928

CFt 0 2.08 2.1840 84.88480

g1 = 4% g2 = 5% g3 = 6% gn = 7%

k = 10%



Financial calculator Solution: CF0= 0; CF1= 2.08; CF2= 2.1840; and CF3=

84.8848; I = 10; and press NPV to get NPV = P0 = $67.47.

Intrinsic Value & Market Price

If

Intrinsic Value > Market Price = under-valued

Intrinsic Value < Market Price = over-valued

Assignment (7 Questions)

Q1:A stock is expected to pay $0.45 dividend at the end of the year. The dividend is expected to grow at a constant rate of 4 percent a year, and the stock’s required rate of return is 11 percent. What is the expected price of the stock 10 years from today?

Q#2

A stock that currently trades for $40 per share is expected to pay a year-end dividend of $2 per share. The dividend is expected to grow at a constant rate over time. The stock has a required rate of return of 11%. What is the stock’s expected price seven years from today?

Q#3

Motor Homes Inc. (MHI) is presently in a stage of abnormally high growth because of a surge in the demand for motor homes. The company expects earnings and dividends to grow at a rate of 20 percent for the next 4 years, after which time there will be no growth (g = 0) in earnings and dividends. The company’s last dividend was $1.50. MHI’s required return on stock is 18%. What should be the current common stock price?

Q#4

A stock is not expected to pay a dividend over the next four years. Five years from now, the company anticipates that it will establish a dividend of $1.00 per share. Once the dividend is established, the market expects that the dividend will grow at a constant rate of 5 percent per year forever.. The required rate of return on the company’s stock is expected to remain constant at 12%. What is the current stock price?

Q#5

R. E. Lee recently took his company public through an initial public offering. He is expanding the business quickly to take advantage of an otherwise unexploited market. Growth for his company is expected to be 40 percent for the first three years and then he expects it to slow down to a constant 15 percent. The most recent dividend (D0) was $0.75. Based on the most recent returns, his company’s required return is 20%. What is the current price of Lee’s stock?

Q#6

DAA’s stock is selling for $15 per share. The firm’s income, assets, and stock price have been growing at an annual 15 percent rate and are expected to continue to grow at this rate for 3 more years. Dividend of $0.50 has been declared recently. After super normal growth, dividends are expected to grow at the firm’s normal growth rate of 6 percent. The firm’s required rate of return is 18 percent. Determine whether the stock is under or overvalued. State reasons for your answer!

Q#7

Philadelphia Corporation’s stock recently paid a dividend of $2.00 per share (D0 = $2), and the stock is in equilibrium. The company has a constant growth rate of 5 percent. The required rate of return on its stock is 29.5%. Philadelphia is considering a change in policy that will increase its required return to 33.25%. If market conditions remain unchanged, what new constant growth rate will cause Philadelphia’s common stock price to remain unchanged?

Discounted Cash flow approaches

1. Dividend Discount Model2. Free Cash Flow to Equity (FCFE) Model3. Free Cash Flow to Firm (FCFF) Model

Free Cash Flow to equity Model

Free Cash Flow to Equity (FCFE) is defined as the cash flow remaining after principle & interest payments have been made & Capital Expenditures have been provided for.

FCFE Model differs from the DDM in the sense that FCFE measures what firm could pay out as dividends rather than what they actually paid out.

FCFE= NI + NCC – Debt repayments – Capital Expenditures – Investment in Working capital + New Debt Issues

Free Cash Flow to equity Model – Special Cases

1. Zero Growth Case P0 = FCFE / K

2. Constant Growth CaseP0 = FCFE1 / (K – G)

3. Multiple Growth CaseP0 = PV of FCFE during the non Constant period

PLUSPV of FCFE during the constant Growth

Period

Free Cash Flow to equity Model – Zero Growth example

An analyst has collected the following information about Franklin Electric:

Projected NI for the next year $300 million. Projected depreciation expense for the next year $50 million. Projected capital expenditures for the next year $100 million. Projected increase in operating working capital next year $60

million. Interest Expense for the year was $5 million & Company paid

back 50 Million of its debt outstanding but also issued $4 million of new debt.

Cost of equity 13%. Number of shares outstanding today 20 million. The company’s free cash flow is NOT expected to grow. What

is the stock’s intrinsic value today?

Free Cash Flow to equity Model – Zero Growth example

Step 1: Calculate Free Cash Flow To EquityFCFE= NI + NCC – Debt repayments – Capital Expenditures – Investment in Working capital +

New Debt Issues= 300 + 50 – 50 – 100 – 60 +4= 144 Million

FCFE Per Share = 144 / 20= $ 7.2 Per Share

Step 2: Calculate Intrinsic ValueP0 = 7.2 / 0.13 = $55.38

Free Cash Flow to equity Model – Constant Growth example

An analyst has collected the following information about Franklin Electric:


million. Interest Expense for the year was $5 million & Company paid

back 50 Million of its debt outstanding but also issued $4 million of new debt.

Cost of equity 13%. Number of shares outstanding today 20 million. The company’s free cash flow is expected to grow at a

constant rate of 6% forever. What is the stock’s intrinsic value today?


Step 1: Calculate Free Cash Flow To EquityFCFE= NI + NCC – Debt repayments – Capital Expenditures – Investment in Working capital +




Step 2: Calculate Intrinsic Value

P0 = Expected FCFE / (K – G)

= 7.2 / (0.13 – 0.06)= 102.8571

Free Cash Flow to equity Model – Multiple Growth example

Projected NI for the next year $300 million. Projected depreciation expense for the next year $50

million. Projected capital expenditures for the next year $100

million. Projected increase in operating working capital next

year $60 million. Interest Expense for the year was $5 million & Company

paid back 50 Million of its debt outstanding but also issued $4 million of new debt.

Cost of equity 13%. Number of shares outstanding today 20 million. The company’s free cash flow is expected to grow at a

constant rate of 12% for two years & then will grow at 6%forever. What is the stock’s intrinsic value today?


Step 1: Calculate Free Cash Flow To Equity for year 1FCFE= NI + NCC – Debt repayments – Capital Expenditures – Investment in Working capital +




Step 2: Calculate FCFE for Non Constant Growth PeriodFCFE in Year 2 = 7.2 * (1 + 0.12)

= 8.0640FCFE in Year 3 = 8.0640 * (1 +0.12)

= 9.03

Step 3: Calculate FCFE for Constant Growth periodFCFE in Year 4 = 9.03 * ( 1+ 0.06)

= 9.57


Step 4: Calculate PV of CF during Non Constant Growth PeriodPV = [CF1 / (1+K)] +[CF2/(1+K)2] + [CF3/(1+K)3]

= [7.2 / (1.13)] + [ 8.06/(1.13)2]+ [9.03/(1.13)3]

= 18.94Step 5: Calculate PV of CF during Constant Growth PeriodPV = P3 / (1+K)3 P3 = 9.57/0.07

= 136.71/ (1.13)3 = 136.71= 94.75


Step 6: Calculate Intrinsic Value

P0 = PV of FCFE during the non Constant period

PLUSPV of FCFE during the constant Growth

Period= 18.94 + 94.75= 113.69

Free Cash Flow to Firm Model

FCFF is defined as cash amounts available to be paid to both bondholders & stockholders.

FCFF = FCFE + Interest (1 – T) +Principle Repayments – New Debt issues – Preferred Dividends

ORFCFF = EBIT(1-T) + NCC – Capital Expenditure –

Change in working CapitalOR

FCFF = NI + NCC + INT (1-T) – Capital Expenditures – Changes in Working Capital

Free Cash Flow to Firm Model – Implementing the model

1. Forecast Expected FCFF2. Estimate the Discount Rate (WACC)3. Calculate the Value of the Corporation4. Calculate Intrinsic Stock Value

= Value of Corporation MINUS Value of Debt MINUS Value of Preferred Stock.

Free Cash Flow to Firm Model – Special Cases

1. Zero Growth Case V0 = FCFF / WACC

2. Constant Growth CaseV0 = FCFF1 / (WACC – G)

3. Multiple Growth CaseV0 = PV of FCFF during the non Constant period

PLUSPV of FCFF during the constant Growth

Period

Free Cash Flow to Firm Model – Example

Today is December 31, 2003. The following information applies to Addison Airlines:

After-tax, operating income [EBIT(1 - T)] for the year 2004 is expected to be $400 million.

The company’s depreciation expense for the year 2004 is expected to be $80 million.

The company’s capital expenditures for the year 2004 are expected to be $160 million.

No change is expected in the company’s net operating working capital.

The company’s free cash flow is expected to grow at a constant rate of 5 percent per year.

The company’s WACC is 10 percent. The current market value of the company’s debt is $1.4

billion. The company currently has 125 million shares of stock outstanding.


Step 1: Calculate the free cash flow amount:FCFF = EBIT(1-T) + NCC – Capital Expenditure –

Change in working Capital=$400 million+$80 million-$160

million-$0=$320 million.

Step 2:Calculate the firm value today using the constant growth corporate value model:V0 = FCFF1 / (WACC – G)

= 320 / (0.10 – 0.05)= 6,400 Million

This is the total firm value today!


Step 3: Determine the market value of the equity and price per share:

MVTotal = MVEquity + MVDebt$6,400 million = MVEquity + $1,400

millionMVEquity = $5,000 million.

This is today’s market value of the firm’s equity.

Divide by the number of shares to find the current price per share:

$5,000 million/125 million = $40.00.

Relative Valuation Techniques

The relative value concept is based on making comparisons in order to determine value. Relative Valuation measures include:

1. Price / Earnings Ratio2. Price / Book Ratio3. Price / Sales Ratio

Earnings Multiplier Approach - The P/E Ratio

The P/E ratio is simply the number of times investors value earnings as expressed in stock’s price.

Companies with higher P/E ratio as compared to a benchmark are considered over valued & Vice Versa.

However, sometimes investors realize that the P/E ratio should be higher for companies whose earnings are expected to grow rapidly, which then, does not necessarily indicate overvaluation!

The P/E Ratio FOR A Constant Growth Company- Determinants

P0 = D1 / (K – G)

Dividing both sides of Equation by Expected Earnings:

P0/E1 = (D1/E1) / (K – G)


Let’s break down the K, discount rate which we used in the Dividend Discount Model or DDM

Po = D1 / (K-g)

if we rearrange to solve for K….

then…

K-g = D1/Po

K = (D1/ Po) + g


K = (D1/ Po) + g

This means TR has two components:

D1/Po = Dividend Yield

g = same rate as the increase in stock price

= Capital gains yield

Components of Required Return - Example

If a stock is selling for $20 per share. Next dividend will be $1 per share. Dividend will grow by 10% per year forever.

What is the return on this stock?

Components of Required Return - Example

If a stock is selling for $20 per share. Next dividend will be $1 per share. Dividend will grow by 10% per year forever.

What is the return on this stock?K = Div yield + Cap gains yield

= 1/20 + 10%= 5% + 10% = 15%

Thank you for your time & Patience

Assignment # 9 Assignment # 9 (6 Questions)(6 Questions)Q1: ABC Co. recently had FCFE of $120 Million. Company

had 50,000 Bonds outstanding trading @ par with a Coupon Rate of 8%. Capital Expenditure & Change in Working Capital during the year were 15 Million & 5Million, respectively. Company had Depreciation & Amortization charges of 2 Million & 0.5 Million, Respectively. XYZ Co. has a tax rate of 35% with Cost of equity of 12% & WACC equivalent to 10%. No debt outstanding was paid during the year. Although, company issued new bonds worth of 1 million. Company has 500,000 shares of preferred stock outstanding with a par of $120 & dividend rate of 5%. Company is expected to grow at a constant rate of 5% forever. With the given information, calculate Value of the firm & intrinsic value per share using FCFF Model assuming 1 million Common Stock shares outstanding.

Assignment # 9 Assignment # 9 (6 Questions)(6 Questions)

Q2: ABC Co. recently had EBIT of $100 Million. Company had 20,000 Bonds outstanding trading @ par with a Coupon Rate of 7%. Capital Expenditure & Change in Working Capital during the year were 5 Million & 1Million, respectively. Company had Depreciation & Amortization charges of 2.5 Million & 1.5 Million, Respectively. XYZ Co. has a tax rate of 35% with Cost of equity of 12% & WACC equivalent to 9%. Company is expected to grow at a constant rate of 7% forever. With the given information, calculate Value of the firm & intrinsic value per share using FCFF Model assuming 1.5 million shares of common stock outstanding.


Q3:An analyst has collected the following information about XYZ Co.:


million. Interest Expense for the year was $2.5 million & Company

paid back 20 Million of its debt outstanding but also issued $4 million of new debt.

Cost of equity 12%. Number of shares outstanding today 20 million.


Q3:A. The company’s free cash flow to firm is

expected to grow at 15% for first two years, then @ 10% for year 3 & year 4 & then it will grow @ 5% forever. What is the stock’s intrinsic value today using FCFF Model?

B. The company’s free cash flow to Equity is expected to grow at 10% for first two years, then @ 8% for year 3 & then it will grow @ 5% forever. What is the stock’s intrinsic value today using FCFE Model?


Q4: The analyst has estimated the company’s free cash flows for the following years:

Year Free Cash Flow 1 $3,000 2 4,000 3 5,000

The analyst estimates that after three years (t = 3) the company’s free cash flow will grow at a constant rate of 6 percent per year. The analyst estimates that the company’s weighted average cost of capital is 10 percent. The company’s debt and preferred stock has a total market value of $25,000 and there are 1,000 outstanding shares of common stock. What is the (per-share) intrinsic value of the company’s common stock?


Q5: Lamonica Motors just reported earnings per share of $2.00. The stock has a price earnings ratio of 40, so the stock’s current price is $80 per share. Analysts expect that one year from now the company will have an EPS of $2.40, and it will pay its first dividend of $1.00 per share. The stock has a required return of 10 percent. What price earnings ratio must the stock have one year from now so that investors realize their expected return?


Q6: Dean Brothers Inc. recently reported net income of $1,500,000. The company has 300,000 shares of common stock, and it currently trades at $60 a share. The company continues to expand and anticipates that one year from now its net income will be $2,500,000. Over the next year the company also anticipates issuing an additional 100,000 shares of stock, so that one year from now the company will have 400,000 shares of common stock. Assuming the company’s price/earnings ratio remains at its current level, what will be the company’s stock price one year from now?

Chap 10 CS Valuation

Documents

Transcript of Chap 10 CS Valuation