1 FINC4101 Investment Analysis Instructor: Dr. Leng Ling Topic: Equity Valuation.

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FINC4101 Investment Analysis

Instructor: Dr. Leng Ling

Topic: Equity Valuation

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Learning objectives1. Distinguish between the intrinsic value and price

of a share of common stock.2. Calculate the intrinsic value of a firm using

dividend discount models Constant dividend growth model Multistage dividend growth model

3. Use the constant growth model to relate growth opportunities to stock value.

4. Calculate the P/E ratio for a constant growth firm.5. Discuss the free cash flow valuation methods.

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Concept Map

FI400

Portfolio Theory

Asset Pricing

Equity

Fixed Income

Market Efficiency

Derivatives

Foreign Exchange

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Why equity valuation?Identify mispriced equity securities.

How? By calculating “intrinsic” or “true” value of a

stock using valuation models. These valuation models make use of

information concerning current & future profitability.

This approach of identifying mispriced stocks is called fundamental analysis.

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Intrinsic value vs. market price (1)

Intrinsic value, V0

Present value of all expected future cash flows to the stock investor. The cash flows are discounted at the appropriate required rate of return, k.

Expected future cash flows consist of:1. cash dividends 2. sale price: proceeds from the ultimate sale

of the stock

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Intrinsic value vs. market price (2) Intrinsic value is your (the analyst’s)

estimate of what a stock is really worth. Intrinsic value (V0) can differ from the

current market price (P0). If V0 > P0: stock is underpriced => buy

If V0 < P0: stock is overpriced => sell or don’t buy.

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Market equilibriumIn market equilibrium, Everyone has the same intrinsic value. So,

intrinsic value equals market price, i.e., V0 = P0.

Everyone also demands the same required rate of return from the stock. So everyone has the same k. In addition, expected HPR = k.

This common required rate of return is called the market capitalization rate. Market capitalization rate: required rate of return

which the market (i.e., everyone) uses to discount future cash flows.

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Equity valuation models Dividend discount models

Constant dividend growth model Multistage (non-constant) dividend growth

model Price-earnings ratio (P/E) Free cash flow models

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Dividend discount models (DDMs) Dividend discount models say that the

intrinsic value of a stock is equal to the present value of all expected future dividends. What about cash flow from the ultimate sale

of the stock? Is that included? Yes, because stock price at time of sale is

again determined by expected dividends at the time of sale.

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Dividend discount model: General formula

1 2 30 2 3 ....

1 (1 ) (1 )D D D

Vk k k

= + + ++ + +

This formula cannot be implemented because it requires dividend forecasts every year into the indefinite future.

To implement the DDM, we make assumptions about how dividends evolve over time.

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Two versions of DDM We look at 2 assumptions:

Dividends grow at constant rate Constant dividend growth modelDividends grow at different rates over

different periods. At some future date, dividend growth settles down to a constant rate.

Multistage (non-constant) dividend growth model

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Constant dividend growth model (1)

1. Assume that dividends grow at a constant rate, g, per period forever.

2. Given this assumption, the intrinsic value equals

0 10

(1 )D g DV

k g k g+

= =- -

D0 = Dividend that the firm just paid

Required rate of return or discount rate

Dividend growth rate

Don’t panic.

D1 = D0(1 + g)

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Constant dividend growth model (2) Warning: The model works only if k > g.

Useful properties. All other things unchanged,

• If D1 increases (decreases), V0 increases (decreases).

• If g increases (decreases), V0 increases (decreases).

• If k increases (decreases), V0 decreases (increases).

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Constant dividend growth model (3) Suppose the market is in equilibrium. This

means that stock price is equal to intrinsic value, i.e., P0 = V0.

Then, stock price is expected to grow at the same rate as dividends.

That is, the expected rate of price appreciation in any year will equal the constant growth rate, g.

P1 = P0 ( 1 + g ) = V1 = V0 ( 1 + g )

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Expected HPR and k (1) Continue to assume that P0 = V0 . Then, expected HPR, E(r) is,

1 1 0

0 0

1

0

( )D P P

E rP PD

gP

-= +

= +

Dividend yield Capital gains yield

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Expected HPR and k (2) If stock is selling at intrinsic value, P0 = V0 Then required rate of return, k, must equal the

expected HPR. Therefore,

When everyone agrees on the same k (in equilibrium), we can use the above formula to compute market capitalization rate.

1

0

Dk g

P= +

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Constant dividend stream If g = 0, then dividends do not grow and

stay the same forever. We have a constant dividend stream – a perpetuity.

The constant dividend stream assumption is a special case of the constant growth model with g = 0.

Implication: with constant dividend stream, we continue to use the preceding equations but set g to 0.

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Applying the constant growth DDM (1)

A common stock pays an annual dividend per share of $2.10. The risk-free rate is 7% and the risk premium for this stock is 4%. If the annual dividend is expected to remain at $2.10 forever, what is the value of the stock? (to two decimal places)

Verify that V0 = $19.09

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Applying the constant growth DDM (2) The risk-free rate of return is 10%, the

required rate of return on the market is 15%, and High-Flyer stock has a beta coefficient of 1.5. If the dividend per share expected during the coming year, D1, is $2.50 and g = 5%, at what price should a share sell?

Hint: use the CAPM to get the market capitalization rate.

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Applying the constant growth DDM (3)

Big Oil Inc. just paid a dividend of $10 (i.e., D0 = 10.00). Its dividends are expected to grow at a 4% annual rate forever. The market capitalization rate is 15%. What is the price of Big Oil’s common stock? (to 2 decimal places)

Verify that price = $94.55

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Applying the constant growth DDM (4)

The price of a stock in the market is $62. You know that the firm has just paid a dividend of $5 per share (i.e., D0 = 5). The dividend growth rate is expected to be 6 percent forever. What is the market capitalization rate for this stock (to 2 decimal places)?

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Applying the constant growth DDM (5)

A firm is expected to pay a dividend of $5.00 on its stock next year. The current price of this stock is $40 and investors require a return of 20%. The firm’s dividends grow at a constant rate. What is the constant dividend growth rate (g)?

use k = (D1/P0) + g

Verify that g = 7.5%

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Applying the constant growth DDM (6)

In order to use the constant dividend growth model to value a stock it must be true that:

a. The required rate of return is less than the expected dividend growth rate.

b. The expected dividend growth rate is greater than zero.

c. The next dividend (D1) is expected to be greater than $1.00.

d. The expected dividend growth rate is less than the required rate of return.

Which statement is correct?

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Stock prices & investment/growth opportunities

How do we figure out dividend growth rate, g ?

Growth rate depends on:

1. Investment opportunities embodied in return on equity, ROE

2. Reinvestment of earnings, represented by earnings retention ratio, b.

Earnings retention ratio is also called the plowback ratio.

Growth rate, g = ROE x b

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Earnings retention ratio and dividend payout ratio

Earnings retention rate

= reinvested earnings/ total earnings. A related measure is the dividend payout

ratio.

Dividend payout ratio

= dividends paid/ total earnings

= 1 – retention rate

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Problem Geoscience Corp. has a beta of 1.2 and its most

recent EPS is $10 per share. The company just paid 40% of its earnings in dividends. Geoscience Corp will earn an ROE of 20% per year on all reinvested earnings forever. The risk-free rate is 8% and the expected return on the market portfolio is 15%.

a) What is the intrinsic value (V0) of a share of Geoscience’s stock (to two decimal places)?

b) If the market price of a share is currently $100, and you expect the market price to be equal to the intrinsic value one year from now, what is your expected one-year HPR on Geoscience Corp.’s stock?

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Earnings retention ratio affects growth

Suppose ROE > 0 Growth policy

No-growth policy

Earnings retention ratio, b b > 0 b = 0

Growth rate, g g > 0 g = 0

Bottomline: If a company reinvests some portion of earnings back into the business (b > 0), future earnings and dividends will grow (i.e., g > 0). Otherwise, earnings and dividends will not grow.

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Is growth always beneficial? Does having positive growth always

increase stock price? No. It depends on the attractiveness of the

firm’s investment opportunities, ROE. Compared to a no-growth policy,

If ROE > k, then retaining earnings (i.e., b > 0) will increase stock price.

If ROE < k, then retaining earnings will decrease stock price.

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Consider two companiesGrowth Prospects, Inc (GP)

Dead Beat, Inc (DB)

No-growth earnings per share $5 $5

Market capitalization rate, k 12.5% 12.5%

No-growth price per share 5/0.125 = 40 5/0.125 = 40

ROE 15% 10%

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Suppose both companies reinvest 60% of next year’s earnings…

Growth Prospects, Inc (GP)

Dead Beat, Inc (DB)

Earnings retention ratio, b 0.6 0.6

Next year’s dividend per share, D1 = (1 – b) x 5

$2 $2

Dividend growth rate, g= ROE x b

9% 6%

Constant dividend growth model share price

2/(0.125 – 0.09) = 57.14

2/(0.125 – 0.06) = 30.77

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Compare GP and DBGrowth Prospects, Inc (GP)

Dead Beat, Inc (DB)

ROE 15% 10%

Market capitalization rate, k 12.5% 12.5%

No-growth price per share (1) 40 40

Constant div. growth Price (2) 57.14 30.77

Present value of growth opportunities, PVGO = (2) – (1)

17.14 -9.23

PVGO = Price per share – no-growth price per share

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Problems involving growth (1)

MF Corp. has an ROE of 16% and a plowback ratio of 50%. If the coming year’s earnings are expected to be $2 per share. The market capitalization rate is 12%.

A. At what price will the stock sell today?

B. At what price do you expect MF shares to sell for in 3 years?

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Problems involving growth (2)Even Better Products has come out with a new and improved product. As a result, the firm projects an ROE of 20%, and it will maintain a retention ratio of 0.30. Its earnings in one year will be $2 per share. Investors expect a 12% rate of return on the stock.

a) Calculate the stock price.b) What is the present value of growth

opportunities (PVGO)?c) What would be the stock price and PVGO if the

firm reinvests only 20% of its earnings?

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Multi-stage dividend growth 1 With this assumption, dividends grow at

different rates for different periods of time. Eventually, dividends will grow at a constant rate forever.

Time line is very useful for valuing this type of stocks.

To value such stocks, also need the constant growth formula.

Best way to learn is through an example.

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Multi-stage dividend growth 2 ABC Co. is expected to pay dividends at the end of the

next three years of $2, $3, $3.50, respectively. After three years, the dividend is expected to grow at 5% constant annual rate forever. If the market capitalization rate for this stock is 15%, what is the current stock price?

T = 0

$2.00 $3.00 $3.50 Dividends grow at 5% forever

T =1 T = 2 T = 3 T = 4

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What to do?

1. Place yourself at t = 3 and use the constant growth formula to find PV of dividend stream after year 3. Call this P3.

2. Find the PV of P3.

3. Find PV of dividends at t=1, t=2 and t=3.

4. Current stock price = sum of 2, 3 and 4.

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Apply the method to find ABC’s stock price

P3 = (3.5 x (1.05))/(0.15 – 0.05) = 36.75

Current stock price, P0

( ) ( )

( ) ( )

0 2 33

2 3

2 3 3.50 36.751.15 1.15 (1.15) 1.152 3 3.50 36.75

1.15 1.15 1.15

$30.47

P = + + +

+= + +

=

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Another type of multi-stage growth problem

Malcolm Manufacturing, Inc. just paid a $2.00 annual dividend (that is, D0 = 2.00). Investors believe that the firm will grow at 10% annually for the next 2 years and 6% annually forever thereafter. Assuming a required return of 15%, what is the current price of the stock (to 2 decimal places)?

Use timeline to ‘see’ the problem better.

Verify that stock price = $25.29

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Price-earnings (P/E) ratios P/E ratio is the ratio of current price per

share (P0) to next year’s expected earnings per share (EPS).

How do we use P/E ratio to value a stock?

1. Forecast next year’s EPS, E1.

2. Forecast P/E ratio, P0/E1.3. Multiple P/E by EPS to get current

estimate of price.

(P0/E1) x E1 = P0

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P/E ratio and constant growth model

If a company has a constant dividend growth rate and the market is in equilibrium (i.e., V0=P0), then we have an explicit formula for the P/E ratio!

Recall that b = retention ratio, k = market capitalization rate.

)(

1

1

0

bROEk

b

E

P

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P/E questions (1) ABC Co. has an ROE of 25%, a CAPM

beta of 1.2 and a retention ratio of 40%. The risk-free rate is 6% and the market risk premium is 5%. What is ABC’s P/E ratio?

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P/E questions (2)Analog Electronic Corporation has an ROE = 9% and a beta of 1.25. It plans to maintain indefinitely its traditional plowback ratio of 2/3. The most recent earnings per share is $3 per share. The expected market return is 14% and the risk-free rate is 6%.

a) What is Analog’s stock price?

b) Calculate the P/E (P0/E1) ratio.

c) Calculate the PVGO.

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Free Cash Flow Valuation Approach

Dividend discount models don’t work for companies which do not pay dividends.

For non-dividend paying companies, we can use free cash flow valuation approach.

There are two versions: Free cash flow to the firm (FCFF) Free cash flow to equity holders (FCFE)

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Free Cash Flow to the Firm (FCFF) (1) FCFF: cash flow that accrues from the firm’s

operations, net of investments in capital and net working capital.

FCFF represent cash flows available to both debt and equity holders.

FCFF = EBIT(1 – tc) + Depreciation – capital expenditures – increase in NWC

EBIT = earnings before interest and taxes tc = corporate tax rate NWC (net working capital) = current asset – current

liability

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Free Cash Flow to the Firm (FCFF) (2)

Capital expenditure includes:1. acquiring fixed, and in some cases, intangible assets

2. repairing an existing asset so as to improve its useful life

3. upgrading an existing asset if its results in a superior fixture

4. preparing an asset to be used in business

5. restoring property or adapting it to a new or different use

6. starting or acquiring a new business

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Free Cash Flow to the Firm (FCFF) (3)

Find the PV of the firm by discounting the year-by-year FCFF plus some estimate of terminal value, PT.

Firm Value=

where Market value of equity = Firm value – market value of debt.

)1()1(1 WACC

P

WACC

FCFF TT

tt

t

gWACC

FCFFP TT

1

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Free Cash Flow to Equity Holders (FCFE)

FCFE: Free cash flow available to equity holders. FCFE = FCFF – interest expense(1 – tc) + increases in

net debt Find the market value of equity by discounting the year-

by-year FCFE plus some estimate of terminal value, PT.

is the cost of equity.EK

gk

FCFEPwhere

k

P

k

FCFEequityofvaluemarket

E

TT

TE

TT

tt

E

1

1 )1()1(

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Summary1. Distinguish between the intrinsic value and price.

2. Calculate intrinsic value using dividend discount models

Constant dividend growth model Multistage dividend growth model

3. Discuss the use of the P/E ratio to value common stock.

4. Calculate the P/E ratio for a constant growth firm.

5. Discuss the free cash flow valuation methods.

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Practice 5 Chapter 13: 5,6,7,10,11,13,15, 17,19,