Principles of Managerial Finance

(Dana P.) #1
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
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