Principles of Managerial Finance

CHAPTER 7 Stock Valuation 329

Time line for finding
Warren Industries
current (end-of-2003)
value with variable
growth

2003

Present Value

of Dividends

During Initial

Period = $4.14

Present Value

of Stock Price

at End of

Initial Period

2004

End of Year

D 2004 = $1.65

PVIF15%, 1 × $1.65 = 0.870 × $1.65

PVIF15%, 2 × $1.82 = 0.756 × $1.82

PVIF15%, 3 × $2.00 = 0.658 × $2.00

PVIF15%, 3 × $21.00 = 0.658 × $21.00

P 2006 =

ks – g 2

=

0.15 – 0.05

= $21.00

2005

D 2005 = $1.82

2006

D 2006 = $2.00

1.44

1.38

1.32

13.82

P 2003 = $17.96

$

D 2007 $2.10

The zero-, constant-, and variable-growth valuation models provide useful

frameworks for estimating stock value. Clearly, the estimates produced cannot be

very precise, given that the forecasts of future growth and discount rates are

themselves necessarily approximate. Furthermore, a great deal of measurement

error can be introduced into the stock price estimate as a result of the imprecise

and rounded growth and discount rate estimates used as inputs. When applying

valuation models, it is therefore advisable to estimate these rates carefully and

round them conservatively, probably to the nearest tenth of a percent.

Free Cash Flow Valuation Model

As an alternative to the dividend valuation models presented above, a firm’s value

can be estimated by using its projectedfree cash flows(FCFs). This approach is

appealing when one is valuing firms that have no dividend history or are startups

or when one is valuing an operating unit or division of a larger public company.

By using D 2007 $2.10, a 15% required return, and a 5% dividend

growth rate, we can calculate the value of the stock at the end of 2006 as

follows:

P 2006 $21.00

Finally, in Step 3, the share value of $21 at the end of 2006 must be con-

verted into a present (end-of-2003) value. Using the 15% required return,

we get

PVIFks,N PNPVIF15%,3 P 2006 0.658 $21.00$13.82

Step 4 Adding the present value of the initial dividend stream (found in Step 2)

to the present value of the stock at the end of the initial growth period

(found in Step 3) as specified in Equation 7.6, we get the current (end-of-

2003) value of Warren Industries stock:

P 2003 $4.14$13.82$



1



7



.



9



6



per share

The stock is currently worth $17.96 per share. The calculation of this

value is depicted graphically on the following time line.

$2.10



0.10

$2.10



0.15 0.05

D 2007



ksg 2