The Model:

Value of Stock = DPS1 / ( r - g)

where DPS1 = Expected Dividends one year from now

r = Required rate of return for equity investors

g = Annual Growth rate in dividends forever

• If the company is a multinational, the real growth rate will be the growth rate of the world economy, whch is about one percent higher.
• The inflation rate used should be consistent with the currency being used in the valuation.

• firms with stable growth rates
• firms which pay out dividends that are high and approximate FCFE.
• firms with stable leverage.

Some obvious candidates for the Gordon Growth Model

• Regulated Companies, such as utilities, because
  • their growth rates are constrained by geography and population to be close to the growth rate in the economy in which they operate.
  • they pay high dividends, largely again as a function of history
  • they have stable leverage (usually high)
• Large financial service companies, because
  • their size makes its unlikely that they will generate extraordinary growth
  • Free cash flows to equity are difficult to compute
  • they pay large dividends
  • they generally do not have much leeway in terms of changing leverage
• Real estate investment trusts, because
  • they have to pay out 95% of their earnings as dividends
  • they are constrained in terms of invesment policy and cannot grow at high rates.

Illustration 1: To a utllity: Con Edison - Electrical Utility (North East United States)

Rationale for using the model

• The firm is in stable growth; based upon size and the area that it serves. Its rates are also regulated; It is unlikely that the regulators will allow profits to grow at extraordinary rates.
• The beta is 0.75 and has been stable over time.
• The firm is in stable leverage.
• The firm pays out dividends that are roughly equal to FCFE.

Background Information

Earnings per share in 1995 = $ 2.95

Dividend Payout Ratio in 1995 = 69.15%

Dividends per share in 1995 = $2.04

Expected Growth Rate in Earnings and Dividends = 5%

Con Ed Beta = 0.75

Cost of Equity = 6% + 0.75*5.5% = 10.13%

Value of Equity = $2.04 *1.05 / (.1013 -.05) = $ 41.80

Con Ed was trading for $ 30 on the day of this analysis. (January 1996)

What growth rate would Con Ed have to attain the justify the current stock price?

The following table estimates value as a function of the expected growth rate (assuming a beta of 0.75 and current dividends per share of $2.04).



Solving for the expected growth rate that provides the current price,

$30.00 = 2.04 (1+g) /(.1013-g)

Solving for g,

g = (.1013*30-2.04)/ (30.00+2.04) = 3.12 %

The growth rate in earnings and dividends would have to be 3.12% a year to justify the stock price of $30.00.

Illustration 2: To a financial service firm: J.P. Morgan

A Rationale for using the Gordon Growth Model

• As a financial service firm in an extremely competitive environment, it is unlikely that J.P. Morganís earnings are going to grow much faster than the economy over the long term. Allowing for expansion, the expected growth rate used is 7%.
• As a financial service firm, free cash flows to equity are difficult to estimate. Hence, the dependence on dividends.
• The leverage of financial service firms is high and unlikely to change over time.

Background Information

Current Earnings per share = $ 6.30

Current Dividend Payout Ratio = 47.62%

Dividends per share = $ 3.00

Expected Growth Rate in Earnings and Dividends = 7%

Stock Beta = 1.15

Cost of Equity = 6% + 1.15 *5.5% = 12.33%

Value of Equity = $3.00 *1.07 / (.1233 -.07) = $ 60.23

J.P. Morgan was trading for $ 80 on the day of this analysis. (January 1996)

Notes of Concern

• The beta is high for a stable growth firm. It reflects the additional risk that many financial service firms have encountered and exposed themselves to in the last few years.

Illustration 3: To the overall market: S&P 500 Index on January 1, 1996

• The average dividend yield (Dividends/ Price) for stocks in the index at the end of 1995 was 2.32%.
• The level of the index on January 1, 1996 was 611.83.
• Using the T.Bond rate of 6.00% and an expected growth rate in the nominal GNP of 6%, the level of the index can be obtained from the Gordon Growth model:

Dividends per share in year 0 = 2.32% of 611.83 = $ 14.19

Infinite growth rate = 6%

Required return of return for equity investors = 6.00% + 1 * 5.5% = 11.50%

Intrinsic Value of the market = 14.19 * 1.06 / (.115 - .06) = 273.57

Scary! So what are we missing?

• Maybe dividend yields do not reflect the capacity of firms to buy back stock. With stock buybacks, this measure rises to about 3% of the overall index.
• The risk premium may be trending down, reflecting
  • the greater willingness of investors to go with the flow - take losses and continue in the market, rather than panic
  • the greater flow of cash into pension funds
  • other paradigm shifts
• With a 3% dividend yield and a 3.5% premium, you can arrive at an index level of 524.43.

The Model:

• The model is based upon two stages of growth, an extraordinary growth phase that lasts n years, and a stable growth phase that lasts forever after that:

Extraordinary growth rate: g% each year for n years Stable growth: gn forever

|____________________________________________|____________________>

• Value of the Stock = PV of Dividends during extraordinary phase + PV of terminal price

• In the case where the extraordinary growth rate (g) and payout ratio are the same for the first n years, this formula can be simplifed as follows:

• The growth rate for the Gordon Growth Rate model (within 2% of growth rate in nominal GNP) apply here as well.
• The payout ratio has to be consistent with the estimated growth rate. If the growth rate is expected to drop significantly after year n, the payout ratio should be higher. This can be estimated in one of two ways ñ
  • from fundamentals

• from other stable firms

• firms where the growth rate is not yet stable, but is moderating
• firms which pay out dividends that roughly approximate FCFE (or) FCFE cannot be estimated easily.

Illustration 4: Valuing a firm with the two-stage dividend discount model::American Express

A Rationale for using the Model

• Why two-stage? While American Express is a large financial service firm in a competitive market place, normally not a candidate for above-stable growth, it has gone through an extended period of depressed earnings . It is expected that the recovery in earnings will create higher growth over the next five years.
• Why dividends? As a financial service firm, free cash flows to equity are difficult to estimate.
• Leverage is stable.

Background Information

• Current Earnings / Dividends
  • Earnings per share in 1995 = $3.10
  • Dividends per share in 1995 = $ 0.90
• Inputs for the High Growth Period
  

Length of the High Growth Period = 5 years

Beta during High Growth Period = 1.45

Cost of Equity during High Growth Period = 6.0% + 1.45 (5.5%) = 13.98%

• Return on Assets during high growth period = 14.56% (this was the 1995 return on assets)
• Dividend Payout Ratio = 29.03%
• Debt/Equity Ratio = 100% (slightly higher than the current debt/equity ratio of 92.14%)
• Interest rate on debt = 8.50% (Tax Rate = 36%)

• Inputs for the Stable Growth
  • Expected Growth Rate = 6%
  • Beta during stable growth phase = 1.10 : Cost of Equity = 6.00% + 1.1 (5.5%) = 12.05%
  • The ROA is expected to drop to 12.50%; D/E Ratio and interest rate are assumed to remain unchanged during the stable growth period.

Estimating the value:

• The first component of value is the present value of the expected dividends during the high growth period. Based upon the current earnings ($3.10), the expected growth rate (16.81%) and the expected dividend payout ratio (29.03%), the expected dividends can be computed for each year in the high growth period.

Year	EPS	DPS	Present Value
1	$3.62	$1.05	$0.92
2	$4.23	$1.23	$0.95
3	$4.94	$1.43	$0.97
4	$5.77	$1.68	$0.99
5	$6.74	$1.96	$1.02

The price at the end of the high growth phase (end of year 5), can be estimated using the constant growth model.

Terminal price = Expected Dividends per sharen+1 / (r - gn)

Expected Earnings per share6 = 3.10 *1.16815*1.06 = $ 7.15

Expected Dividends per share6 = $7.15 * 0.6933 = $ 4.95

Terminal price = $ 4.95 /(.1205 -.06) = $ 81.87

The present value of the terminal price can be then written as -

|_______________________________| |_____________________| |_________|

Extraordinary Growth Stable Growth Assets in place

where

DPSt = Expected dividends per share in year t

r = Required rate of return

Pn= Price at the end of year n

gn= Growth rate forever after year n

• The discount rate from the stable growth phase is used for this calculation.

Value of stable growth = Current EPS * Payout ratio * (1+gn)/(r-gn)- $ 7.47

= ($3.10* 0.2903 *1.06)/(.1205 -.06) - $ 7.47 = $ 8.30

Value of extraordinary growth = $ 47.42 - (7.47+8.30) = $ 31.65

The Determinants of the Value of Growth

• Length of the high growth period
• Extent of the extraordinary growth
• Costs of higher growth , i.e., how much risk is added and how much cash is drained as a consequence.

The Model

• The value of the stock is then the present value of expected dividends during the high growth and the transitional periods, and of the terminal price at the start of the final stable growth phase.

High growth phase Transition Stable growth phase

where,

EPSt = Earnings per share in year t

DPSt = Dividends per share in year t

ga= Growth rate in high growth phase (lasts n1 periods)

gn= Growth rate in stable phase

Pa= Payout ratio in high growth phase

Pn= Payout ratio in stable growth phase

r = Required rate of return on equity

Works best for:

It is best suited for firms which are

• paying out and plan to continue paying dividends which are roughly equal to FCFE
• growing at
  • an extraordinary rate now and are expected to maintain this rate for an initial period,
  • after which the differential advantage of the firm is expected to deplete leading to gradual declines in the growth rate
  • to a stable growth rate.
• in stable leverage

Illustration 6 : Valuing with the Three-stage DDM model: The Home Depot

A Rationale for using the Three-Stage Dividend Discount Mode;

• Why three-stage? The Home Depot is still in very high growth. Analysts project that its earnings per share will grow at 36% for the next five years.
• Why dividends? The firm has had a track record of paying out dividends that roughly approximate FCFE
• The financial leverage is stable.

Background Information

• Current Earnings / Dividends
  • Earnings per share in 1994 = $ 1.55
  • Dividends per share in 1994 = $ 0.19
• Inputs for the High Growth Period
  • Length of the High Growth Period = 5 years
  • Expected growth rate = 36.00% (Based upon analyst projections)
  • Beta during High Growth Period = 1.60
  • Cost of Equity during High Growth Period = 7.5% + 1.60 (5.5%) = 16.30%
  • Dividend Payout Ratio = 12.03% (based on existing payout ratio)
• Inputs for the transition period
  • Length of the transition period = 5 years
  • Growth rate in earnings will decline from 36% in year 5 to 6% in year 10 in linear increments.
  • Payout ratio will increase from 12.03% to 60% over the same period in linear increments.
  • Beta will drop from 1.60 to 1.00 over the same period in linear increments.
• Inputs for the Stable Growth
  • Expected Growth Rate = 6%
  • Beta during stable growth phase = 1.00 : Cost of Equity = 7.50% + 1.0 (5.5%) = 13.00%
  • Payout Ratio = 60%

Estimating the Value

• These inputs are used to estimated expected earnings per share, dividends per share and costs of equity for both the high growth and stable periods. The present values are also shown.

Period	EPS	Payout Ratio	DPS	Cost of Equity	Present Value
1	$1.81	12.03%	$0.22	16.30%	$0.19
2	$2.46	12.03%	$0.30	16.30%	$0.22
3	$3.35	12.03%	$0.40	16.30%	$0.25
4	$4.55	12.03%	$0.55	16.30%	$0.30
5	$6.19	12.03%	$0.74	16.30%	$0.35
6	$8.04	21.62%	$1.74	15.64%	$0.71
7	$9.97	31.22%	$3.11	14.98%	$1.10