dividend of $2.25 a share. In addition, the future annual rate of growth in dividends
for each of the three companies has been estimated as follows:
Buggies-Are-Us Steady Freddie, Inc. Gang Buster Group
g 0% g 6% Year 1 $2.53
(i.e., dividends (for the 2 $2.85
are expected foreseeable 3 $3.20
to remain at future) 4 $3.60
$2.25/share) Year 5 and beyond: g 6%
LG 3
LG 3
LG 3
LG 3
--Gitman2002.CH08.314-368.CTP 7/19/01 12:21 PM Page 361
Assume also that as the result of a strange set of circumstances, these three companies
all have the same required rate of return (k 10%).
a. Use the appropriate DVM to value each of these companies.
b. Comment briefly on the comparative values of these three companies. What is
the major cause of the differences among these three valuations?
Valuation using the DVM:
Intrinsic value 1 0 D D (1 ) g
kg kg
Buggies-Are-Us:
Intrinsic value $2.25(1 + 0) $22.50
0.10 0.06
Steady Freddie, Inc.:
Intrinsic value $2.25(1 0.06) $2.385 $59.63
0.10 0.06 0.04
Gang Buster Group:
Step 1: Present value of dividends using a required rate of return of 10%:
Year Dividends PVIF, 10% Present Value
1 $2.53 0.909 $2.30
2 2.85 0.826 2.35
3 3.20 0.751 2.40
4 3.60 0.683 2.46
Total: $9.51
Step 2: Price of stock at the end of year 4:
5 4
4 (1 )
$3.60(1 0.06) $3.82 $95.50
0.10 0.06 0.04
DDg P
kg kg
Step 3: Present value of the stock price:
Smart/Gitman/Joehnk, Fundamentals of Investing, 12/e Chapter 8
PV $95.50 PVIF10%, 4 YRS.
$95.50 .683
$65.23
Step 4: Value of stock $9.51 (Step 1) + $65.23 (Step 3) $74.74
b. The intrinsic value of Gang Busters is $74.74, compared to $59.63 for Steady Freddie and $22.50
for Buggies-Are-Us. The difference in the values is caused by the difference in dividend growth
rates. The Buggies-Are-Us dividends do not grow, resulting in a very low intrinsic value for its
stock. The dividends of Steady Freddie, Inc., grow at a constant rate of 6% forever, whereas
Gang Busters dividends grow at approximately 12% for the first four years and 6% from year 5
into the future. This higher growth in dividends in the earlier years causes Gang Buster Group to
be worth much more than Steady Freddie.
To value each of these companies, we can use the Dividend Valuation Model (DVM) formula:
DVM = D1 / (k - g)
Where:
DVM is the estimated value of the company
D1 is the dividend in the first year
k is the required rate of return
g is the growth rate of dividends
Let's calculate the values for each company:
For Buggies-Are-Us:
D1 = $2.53
k = 10%
g = 0% (as dividends are expected to remain at $2.25/share)
DVM = $2.53 / (0.10 - 0) = $2.53 / 0.10 = $25.30
For Steady Freddie, Inc.:
D1 = $2.85
k = 10%
g = 6%
DVM = $2.85 / (0.10 - 0.06) = $2.85 / 0.04 = $71.25
For Gang Buster Group:
D1 = $3.20
k = 10%
g = 6%
DVM = $3.20 / (0.10 - 0.06) = $3.20 / 0.04 = $80.00
Now let's comment on the comparative values of these three companies and the major cause of the differences among these three valuations:
The value of Buggies-Are-Us is $25.30, while Steady Freddie, Inc. and Gang Buster Group have values of $71.25 and $80.00, respectively. The major cause of the differences among these valuations is the growth rate of dividends. Buggies-Are-Us has a growth rate of 0%, meaning its dividends are expected to remain constant. Steady Freddie, Inc. and Gang Buster Group have a growth rate of 6%, indicating that their dividends are expected to increase over time. This higher growth rate leads to a higher valuation for both Steady Freddie, Inc. and Gang Buster Group compared to Buggies-Are-Us.