Streetbites from the media perspective
The Dow-Jones Industrial Average
Streetbites from the media perspective
 The Dow-Jones Industrial Average
Videos for Module 8, Unit 1-of-2
o DJIA overview (6:24)
o DJIA average price change (4:04) [TQ11]
o DJIA divisor (8:40)
TQ11 DJIA average price move required to reach a new milepost
A recent newspaper article says that the DJIA is 350 points away from reaching the
17,000 point milepost. You check the Wall Street Journal tables and see that the divisor
equals 0.1480. Find how much the average price of the thirty stocks in the DJIA must
change to reach the milepost. ANSWER: $1.73
From http://www.djindexes.com/
Lessons about the Structure of Finance
From http://finance.yahoo.com/q/cp?s=%5EDJI
Lessons about the Structure of Finance
Lessons about the Structure of Finance
Chapter 8, Unit 2 of 2
Dividend growth, intrinsic value, and the
total ROR
Lessons about the Structure of Finance
 The search for intrinsic value!
 See textbook pages 386 - 408 for relevant readings.
Videos for Module 8, Unit 2-of-2
o DJIA overview (6:24)
o DJIA average price change (4:04) [TQ11]
o DJIA divisor (8:40)
o Estimating g with data (11:13) [Example 8]
o Common stock intrinsic value (3:30)
o Plotting actual and expected dividends (4:59)
o Constant growth valuation model (6:42) [ST19]
o Find V and ROR on counteroffer (8:54) [ST2am]
o Components of total stock ROR (1:35) [Table 8.4]
o Partition total stock ROR (9:36) [ST16]
o Changes in intrinsic value over time (8:08) [SV2a]
o Changes in intrinsic value over time - ROR (7:16)
o Converge to V and find ROR (7:46) [ST8]
o ROR given sustainable growth (16:09) [SV4dm]
o Price multiples (5:19)
o Intrinsic PE ratio (13:25)
o Compare multiples and infer (2:37) [ST10]
Lessons about the Structure of Finance
FORMULA 8.7 Constant growth rate for dividends
dividends  dividends t 1  g 
t
Smooth dividend growth occurs when one period’s dividend always is g percent bigger
than the previous period’s dividend. Even though that never really happens, we still can
learn a lot from what it would mean….
Formula 8.8 shows the discounted sum of the infinite dividend stream when g < r :
Lessons about the Structure of Finance
FORMULA 8.8 Intrinsic value, constant growth dividend valuation model
 stock 
dividend1

 
r -g
 value 0

dividend0 (1  g )
r -g
BUT DIVIDENDS NEVER REALLY GROW SMOOTHLY
–DIVIDENDS ARE STICKY!
year
t
-11
2
3
4
5
6
7
annual
dividendt
% change from
year t-1
-2-3$1.80
...
$1.80
0.00%
$2.60
44.44%
$2.20
15.38%
$2.70
22.73%
$3.20
18.52%
$3.30
3.12%
TABLE 8.3 A typical dividend history
g
from time t to
time 7
-410.63%
12.89%
6.14%
14.47%
10.55%
3.12%
...
EXAMPLE 8 Find the best estimate of the dividend growth rate from Table 8.3
Yesterday the company paid its annual dividend of $3.30 as shown in row 7 of Table
8.3. Assume that dividends grow smoothly in accordance with constant growth formula
8.7. Each year, however, there may be random white noise errors. Compute the best
estimate of the dividend growth rate and plot the function that shows dividends growing
smoothly. Also, find the best estimate for next year’s dividend (t = 8).
ANSWER:
Rewrite formula 8.4 as

log(dividendt ) log dividend0 1  g 
t

Apply simple math rules and add the white noise and find
log(dividendt )  logdividend0  t log1  g   noiset
Lessons about the Structure of Finance
The important point about the preceding formula is that our calculator uses the formula
to estimate the growth rate g!
div6
•
div3
•
div1
•
•
$3.76
$3.38
•
•
•
div4
div5
div7 = $3.30
noise7 = -8 cents
div2
Growth rate g = 11.34% defines the exponential
line that best fits through the actual dividend data.
time
FIGURE 8.2: Plot of the dividend history from table 8.3 and the line of best fit for Example 8
INSTEAD OF DOING THESE ALTERNATES CONSIDER THE
LECTURE PROBLEMS HANDOUT, return after ST16
TR18 T/F, intrinsic value in dividend growth when g>r
The dividend growth valuation model equates intrinsic value to the discounted sum of
the perpetual and smoothly growing dividend stream. When the dividend growth rate
(g) exceeds the discount rate (r) the formula gives an intrinsic value that is a negative
number. Determine whether the following interpretation of the preceding fact is TRUE
or FALSE: the stock has an infinite intrinsic value when number of growth periods = ∞.
ANSWER: A
a. True
b. False
Lessons about the Structure of Finance
TR40 Relation between g, r and V in the constant growth model
The dividend growth valuation model equates a stock’s intrinsic value to the discounted
sum of the perpetual and smoothly growing dividend stream. The relation between the
dividend growth rate (g) and the discount rate (r) is very important. Which statement
accurately describes that relation?
ANSWER: C
a. When g equals zero percent then the stock’s intrinsic value is less than div/r.
b. When g exceeds r then the stock’s intrinsic value is negative, meaning the stock is
worthless.
c. The stock’s intrinsic value is an increasing function of the dividend growth rate g.
d. Two choices, B and C, are correct
e. The three A-B-C choices are all correct
EXERCISES 8.2B
4. The Company dividend appears to grow smoothly at a constant exponential rate of
5.5%. Analysts forecast that next year’s dividend should equal $3.80. For you to
receive a 14% average annual rate of return, how much should you offer for the stock?
©ST19 .
ANSWER Use formula 8.8 to find that intrinsic value equals $44.71 ( = $3.80 / ( 0.14 –
0.055). The stock is a buy if actual price is less than $44.71.
Set the typically unknown left-hand-side slot for intrinsic value
equal to observable market supply price and solve for the
instantaneous discount rate, aka the equity capitalization rate.
The equity capitalization rate (total rate of return) from a stock investment has two
sources. A current income component provides immediate cash flow in the form of
dividends, a changing price component causes capital gains or losses.
FORMULA 8.9 Components for stocks of the total rate of return
r 
dividend1
 stock 


 value 0

g
 expected   capital 

 

  dividend    gains 
 yield
  yield 

 

Lessons about the Structure of Finance
Expected dividend yield
( dividend1 / price0 )
realized cash flow
immediately taxable
relatively predictable & more
certain
relatively small, averaging 1 to
4%
Capital gains yield
(g)
accrued cash flow
taxes are deferred
very unpredictable & more
uncertain
relatively large, averaging 8 to
12%
TABLE 8.4 Component characteristics for the total rate of return
TR22 Describe partitioning of stock ROR
According to the constant growth dividend valuation model, the total rate of return
partitions into the expected dividend yield and the capital gains yield. Which statement
is the most accurate description of the partition?
ANSWER: B
a. the dividends are usually tax exempt whereas capital gains are immediately taxable
b. usually the dividend component is a realized cash flow whereas the capital gains
yield is an accrued cash flow
c. the long-run average dividend yield is bigger than the capital gains yield
d. the dividend yield is less predictable and riskier than the capital gains yield
e. the capital gains yield minus the expected dividend yield equals the total rate of
return
View the alternate version of ST16 on the class handout.
EXERCISES 8.2C
1. A share of company stock just paid its annual dividend of $1.45. Exactly 4 years ago
the dividend was $0.90. Your analyst tells you the stock's expected dividend yield is
5%. You believe the constant growth dividend valuation model applies perfectly to this
properly valued stock. Find (i) the expected total rate of return and (ii) the stock’s
current intrinsic value. ©ST16
ANSWER Find the dividend growth rate as g = ($1.45  $0.90)1/4; g = 12.66%. The
total rate of return equals, according to formula 8.9, the sum of the growth rate (12.66%)
and the expected dividend yield (5%). Thus, r equals 17.66 percent. All numbers
required by formula 8.8 to find intrinsic value are known: V0 = div0(1+g)/(r-g); =
$1.45(1.1266)/(.1766  .1266); V0 = $32.67.
EXERCISES 8.2B
5. The Company is expected to announce their annual dividend tomorrow. One year
ago they paid a dividend of $2.40, and 4 years ago they paid $2.12. You believe that
future dividends will grow by the same rate as past ones. You are aware that riskless
government securities are yielding 3.5%, and you make an offer to purchase the stock
so that you earn 7.2% above the risk-free rate. How much is your offer price? ©ST2a.
Lessons about the Structure of Finance
ANSWER: Find that g = 4.22% [=($2.40 / $2.12) 1/3 – 1. Then find that r = 10.7% (=
0.035 + 0.072). Then use formula 8.8 to find that intrinsic value equals $40.24 [ =
$2.40(1 + 0.0422)2 / ( 0.1070 – 0.0422); = $2.61 / 0.0648 ].
7 modified. Due to market conditions, you must purchase the stock for $1.50 above
your offer price. Find your expected total rate of return at this higher purchase price.
©ST2b .
Company (ticker)
Air T, Inc. (AIRT)
Airborne, Inc. (ABF)
AirNet Systems, Inc.
(ANS)
Atlas Air, Inc. (CGO)
FedEx Corporation
(FDX)
TNT Post Group N.V.
(TP)
stock price-to- price-toprice earnings book
-1-2-3$ 4.00 10.0
1.18
12.65 45.2
0.69
price-tocash price-toflow
sales
-3-55.5
0.17
2.5
0.19
4.25
35.47
7.1
15.6
0.60
2.60
2.3
7.4
0.34
1.71
44.29
17.8
2.45
6.7
0.66
25.94
51.9
5.78
17.3
1.42
TABLE 8.5 Snapshot of multiples for a peer group of air courier companies
ST10 Comparison to peer group
Suppose the company stock price is $56 , earnings per share is $1.56 , operating cash
flow per share is $3.19 , and book value per share is $24.78 . For a carefully
constructed peer group you find the following average multiples: the price-to-earnings
ratio is 30, the price-to-cash flow ratio is 15; the price-to-book is 2. Compare the
company and peer group multiples and, assuming the peers are virtual clones of the
company, make inferences about the company share price.
ANSWER: comparison of price-to-cash flow ratios makes the company seem relatively
overvalued AND comparison of price-to-book ratios makes the company seem
relatively overvalued
Lessons about the Structure of Finance
FORMULA 8.12 The intrinsic P/E ratio, general version
 stock 


 value 0
where
earnings1


1 
payout

r 1 -  (1 - payout)
(ROE)   r
TR10 PE ratio and dividend growth dynamics
You observe the following for companies A and B:
price per share: $14.80 for company A, and $24.10 for company B
earnings per share: $0.86 for company A, and $1.65 for company B
In an equilibrium setting where prices are consistent with the dividend growth model,
which statement is supported best by the above data?
ANSWER: E ; PE_A = 17.2 ;PE_B = 14.6
a. company A probably has fewer growth opportunities than company B
b. company A probably is undervalued relative to company B
c. company A probably has riskier dividends than company B
d. company A probably is overvalued relative to company B
e. company A probably has less risky dividends than company B
Lessons about the Structure of Finance