The DDMand Common Stock Valuation

• Some quick examples, courtesy of Harcourt– The Effect of Evolving Growth Rates

– Valuation via Operating Cash Flow

Assume beta = 1.2, kRF = 7%, and kM = 12%. What is the required rate of return

on the firm’s stock?

ks= kRF + (kM – kRF)bFirm

= 7% + (12% – 7%) (1.2) = 13%.

Use the SML to calculate ks:

D0 was $2.00 and g is a constant 6%. Find the expected dividends for the next

3 years, and their PVs. ks = 13%.

0 1

2.247

2

2.382

3g = 6%

1.87611.7599

D0 = 2.00

1.6509

13%2.12

= =

What’s the stock’s market value? D0 = 2.00, ks = 13%, g = 6%.

Constant growth model:

P0 = = D1

ks – g 0.13 – 0.06

$2.12

$2.12

0.07$30.29.

• D1 will have been paid, so expected dividends are D2, D3, D4 and so on. Thus,

Could also find P1 as follows:

ks – g 0.13 – 0.06 P1 = =

What is the stock’s market value one year from now, P1?

^

^

^

D2 $2.247^

= $32.10.

P1 = P0(1.06) = $32.10.

Find the expected dividend yield, capital gains yield, and total return during the

first year.

Dividend yld = = =

Cap gains yld = =

Total return = 7.0% + 6.0% = 13.0%.

D1

P0

P1 – P0

P0

^$30.29$2.12

7.0%.

$32.10 – $30.29$30.29

= 6.0%.

Rearrange model to rate of return form:

.PD

k g

D

Pg

s0

1 1

0

to k s

Then, ks = $2.12/$30.29 + 0.06= 0.07 + 0.06 = 13%.

^

P0 = = = $15.38.

What would P0 be if g = 0?

The dividend stream would be a perpetuity.

2.00 2.002.00

0 1 2 313% ...

^ PMTk

$2.000.13

^

• Can no longer use constant growth model.• However, growth becomes constant after 3

years.

If we have supernormal growth of 30% for 3 years, then a long-run constant g = 6%, what is P0? k is still 13%.

^

Nonconstant growth followed by constantgrowth:

0

2.301

2.647

3.045

46.116

1 2 3 4ks = 13%

54.109 = P0

g = 30% g = 30% g = 30% g = 6%

D0 = 2.00 2.600 3.380 4.394 4.658

.. .

$66.54P34.65813 0 06

0

...

^

What is the expected dividend yield and capital gains yield at t = 0?

At t = 4?

Div. yield0 = = 4.81%.

Cap. gain0 = 13.00% – 4.81% = 8.19%.

$2.60$54.11

• During nonconstant growth, D/P and capital gains yield are not constant, and capital gains yield is less than g.

• After t = 3, g = constant = 6% = capital gains yield; k = 13%; so D/P = 13% – 6% = 7%.

25.72

Suppose g = 0 for t = 1 to 3, and then g is a constant 6%. What is P0?

0

1.771.571.39

20.99

1 2 3 4ks=13%

g = 0% g = 0% g = 0% g = 6%

2.00 2.00 2.00 2.00 2.12

.P3

2.12

0 0730.29.

^

...

t = 3: Now have constant growth with g = capital gains yield = 6% and D/P = 7%.

$2.00$25.72

What is D/P and capital gains yield at t = 0 and at t = 3?

t = 0:D1

P0

= = 7.78%.

CGY = 13% – 7.78% = 5.22%.

If g = -6%, would anyone buy the stock? If so, at what price?

Firm still has earnings and still paysdividends, so P0 > 0:

PD

k g

D g

k gs s0

1 0 1=

=

$2.00(0.94) $1.880.13 – (-0.06) 0.19

= = = $9.89.

What is the annual D/P and capital gains yield?

Capital gains yield = g = -6.0%,

Dividend yield= 13.0% – (-6.0%) = 19%.

D/P and cap. gains yield are constant,with high dividend yield (19%) offsettingnegative capital gains yield.

Free Cash Flow Method

• The free cash flow method suggests that the value of the entire firm equals the present value of the firm’s free cash flows (calculated on an after-tax basis).

• Recall that the free cash flow in any given year can be calculated as:

NOPAT – Net capital investment.

• Once the value of the firm is estimated, an estimate of the stock price can be found as follows:– MV of common stock (market capitalization) =

MV of firm – MV of debt and preferred stock.– P = MV of common stock/# of shares.

Using the Free Cash Flow Method

^

• Free cash flow method is often preferred to the dividend growth model--particularly for the large number of companies that don’t pay a dividend, or for whom it is hard to forecast dividends.

Issues Regarding the Free Cash Flow Method

(More...)

• Similar to the dividend growth model, the free cash flow method generally assumes that at some point in time, the growth rate in free cash flow will become constant.

• Terminal value represents the value of the firm at the point in which growth becomes constant.

FCF Method Issues Continued

416.942

FCF estimates for the next 3 years are -$5, $10, and $20 million, after which

the FCF is expected to grow at 6%. The overall firm cost of capital is 10%.

0

-4.5458.264

15.026398.197

1 2 3 4k = 10%

g = 6%

-5 10 20 21.20

21.200.04

...

*TV3 represents the terminal value of the firm, at t = 3.

530 = = *TV3

If the firm has $40 million in debt and has 10 million shares of stock, what is

the price per share?

Value of equity = Total value – Value of debt

= $416.94 – $40

= $376.94 million.

Price per share = Value of equity/# of shares

= $376.94/10

= $37.69.