6.2 Valuations using Multipliers, Transactions, and the Dividend Discount Model

Overview

In the last module, you forecast the firm’s income statement and balance sheet. This forecast gave us the firm’s free cash flows (FCF), which you discounted to get the enterprise value (EV). From the EV, you subtracted debt and added the cash balances to get the firm’s equity value. You took this equity value and divided it by the shares outstanding to get an estimate of the firm’s price per share.

With a calculated price per share, you could compare the firm’s traded price per share with our value and determine if the share price was priced too high, just right, or too low. In a way, you were the Goldilocks of share price analysts!

In this module, you will continue with the valuation of firms, but this time using multipliers, transactions, and the dividend discount model (DDM). These methodologies yield approximations to the company’s share price. So, you may ask what is the advantage of that? After all, the free cash flows gave us a much more accurate valuation.

The truth is that the estimation of share prices using multipliers, transactions, and the DDM make for quick and dirty estimates of what the share price is. Most firms do not calculate their own share price using FCFs; instead, they rely on equity analysts to do that. The problem that arises then is that many firms do not believe in the assumptions made by equity analysts; after all, the firm’s insiders have access to all the data that can be used to forecast prices and the equity analysts have only limited access. So, the firm can calculate its share prices quickly using these methods.

Valuations Using Multipliers, Transactions,
and the Dividend Discount Model
Alfonso F. Canella Higuera
October 19, 2021
When firms do not have the time, staffing, expertise, or the inclination to calculate their price
per share, they use shortcuts to estimate this number. These shortcuts can be summarized using the
following:
Multipliers (EPS, Sales, Book Value, EBITDA)
Transactions (premium, synergy)
Dividend discount model (DDM)
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In this document, we will go over each of these in detail and weigh the pros and cons of each.
Multipliers
This methodology looks at the prices paid for firms in the same industry and relates the prices
paid to different metrics for the firm.
One example of this is earnings per share (EPS). EPS is one of the favorite metrics used by
firm managers and equity analysts to summarize a firm’s financial performance. The problem with
EPS is that it can be gamed. For example, something that corporations have been doing for quite a
few years is to take excess cash and buy back shares of stock. In doing this they accomplish the
following:
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they reduce cash balances which, in the event of an acquisition, represent a discount to
the buyer; no one wants to sell anything at a discount!
high cash balances are a drag on performance because the firm’s weighed average cost
of capital (WACC) must fund these balances. Cash accounts, in general, earn little to no
interest while the WACC’s value is much higher. So, in net terms, the firm is funding
basically idle assets
buying back shares of stock props up the value of these shares
finally, buying back shares reduces the number of shares outstanding. The EPS is the
firm’s net earnings divided by number of shares so if the number of shares is smaller, the
denominator in the division is smaller and the EPS is higher
While equity analysts readily adjust for changes in the number of shares outstanding when
they calculate EPS, this number tends not to be asterisked so everyone just goes along with the latest
value. As the number of shares outstanding drops, everything else equal, the EPS must go up. So,
it can be a misleading number.
To use EPS as a multiplier, we start with the average price per share paid for an acquired
firm. This purchase price is a marker that the markets use to price firms in a given industrial sector.
Let’s say, for example, that five firms were acquired in the last 3 years in the aviation parts
sector. If the average price paid for these firms was 18x their average yearly EPS, that gives us
something to work with in coming up with a price estimate for our own firm.
For this example, we will assume that our firm’s EPS for the last four quarters (trailing twelve
months or TTM for short) of 4Q19 was $4.00. If we multiply the $4.00 by the 18x multiplier to
EPS, we get that one estimate of the price per share of our firm, were it to be acquired at prices along
the lines of those paid in the last 3 years, would be $72.
The formula is as follows:
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝒑𝒑𝒑𝒑𝒑𝒑 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 = 𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨 𝑬𝑬𝑬𝑬𝑬𝑬 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 𝒙𝒙 𝟒𝟒𝟒𝟒𝟒𝟒𝟒𝟒 𝑬𝑬𝑬𝑬𝑬𝑬 = 𝟏𝟏𝟏𝟏 𝒙𝒙 $𝟒𝟒. 𝟎𝟎𝟎𝟎 = $𝟕𝟕𝟕𝟕. 𝟎𝟎𝟎𝟎
The above methodology works for the last four quarters, the next four quarters (4Q, which
are the next twelve months or NTM) forecast, and the 4Q after that. So, conceivably, we can have
multiple price per share estimates using one single EPS multiplier for our firm’s forecast EPS for
2020 and 2021:
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝒑𝒑𝒑𝒑𝒑𝒑 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 = 𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨 𝑬𝑬𝑬𝑬𝑬𝑬 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 𝒙𝒙 𝟒𝟒𝟒𝟒𝟒𝟒𝟒𝟒 𝑬𝑬𝑬𝑬𝑬𝑬 = 𝟏𝟏𝟏𝟏 𝒙𝒙 $𝟒𝟒. 𝟐𝟐𝟐𝟐 = $𝟕𝟕𝟕𝟕. 𝟔𝟔𝟔𝟔
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝒑𝒑𝒑𝒑𝒑𝒑 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 = 𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨 𝑬𝑬𝑬𝑬𝑬𝑬 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 𝒙𝒙 𝟒𝟒𝟒𝟒𝟒𝟒𝟒𝟒 𝑬𝑬𝑬𝑬𝑬𝑬 = 𝟏𝟏𝟏𝟏 𝒙𝒙 $𝟒𝟒. 𝟓𝟓𝟓𝟓 = $𝟖𝟖𝟖𝟖. 𝟎𝟎𝟎𝟎
As you can see, which year’s EPS you use makes a big difference on price. Which one is
chosen, as with beauty, depends on the observer. In general, the best option is to go with the TTM
as it reflects actual results and not some forecast of dubious accuracy. After all, one does not want
to overpay and the NTM and 4Q21 values show significant increases over 4Q19.
Now that we have covered EPS, we can look at another metric that may be used to value a
company’s share price and that is Book Value (BV). The company’s BV is the value of the equity
in the balance sheet. Mind you, BV is not the market value of the equity (which is the number of
shares outstanding times the market price per share), it is the value of the equity as represented by
the sum of share paid-in capital plus retained earnings.
The calculation for valuing a firm’s share price using BV is very similar to the formula we
used for EPS:
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝒑𝒑𝒑𝒑𝒑𝒑 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 = 𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨 𝑩𝑩𝑩𝑩 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 𝒙𝒙 𝟒𝟒𝟒𝟒𝟒𝟒𝟒𝟒 𝑩𝑩𝑩𝑩 = 𝟑𝟑. 𝟏𝟏 𝒙𝒙 $𝟐𝟐𝟐𝟐. 𝟐𝟐𝟐𝟐 = $𝟖𝟖𝟖𝟖. 𝟑𝟑𝟑𝟑
Something that you will notice when you work with multipliers is that they give different,
sometimes wildly different, answers. These must be consolidated into a coherent number that will
be applied to the firm. This consolidation requires that the multipliers be ranked in terms of
reliability.
For example, we already stated that EPS can be gamed (on the con side) but it’s used
constantly to show the firm’s performance (on the pro side). With BV, it’s an accounting figure that
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is used as the reference – the equity account in the balance sheet – so it is not strictly a figure that
sheds much light on the firm’s profitability, liquidity, or leverage, all of which are key for any firm.
One alternative is to use the Sales multiplier. The use of this multiplier is a bit more
cumbersome that the two just discussed. This is because the value for our firm that we would get
using the Sales multiplier is the enterprise value (EV).
Let’s run an example with an average Sales multiplier of 2.1, TTM Sales of $3,750 Million
and interest-bearing debt of $2,100 Million. The calculations are:
𝑬𝑬𝑬𝑬 = 𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨 𝑺𝑺𝑺𝑺𝑺𝑺𝑺𝑺𝑺𝑺 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 𝒙𝒙 𝟒𝟒𝟒𝟒𝟒𝟒𝟒𝟒 𝑺𝑺𝑺𝑺𝑺𝑺𝑺𝑺𝑺𝑺 = 𝟐𝟐. 𝟏𝟏 𝒙𝒙 $𝟑𝟑𝟑𝟑𝟑𝟑𝟑𝟑 = $𝟕𝟕, 𝟖𝟖𝟕𝟕𝟓𝟓
𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬 𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽 = 𝑬𝑬𝑬𝑬 − 𝑫𝑫𝑫𝑫𝑫𝑫𝑫𝑫 = $𝟕𝟕, 𝟖𝟖𝟖𝟖𝟖𝟖 − $𝟐𝟐, 𝟏𝟏𝟏𝟏𝟏𝟏 = $𝟓𝟓, 𝟕𝟕𝟕𝟕𝟕𝟕
If we assume that the firm has, say, 71 million shares outstanding, the price per share, based
on the calculations above, is:
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝒑𝒑𝒑𝒑𝒑𝒑 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 =
$𝟓𝟓, 𝟕𝟕𝟕𝟕𝟕𝟕
= $𝟖𝟖𝟖𝟖. 𝟑𝟑𝟑𝟑
𝟕𝟕𝟕𝟕
Note that the division above works because the numerator and the denominator are both in
millions. Had they not been, you would have to adjust the units for either one or both to make sure
they are apples to apples.
So, based on our Sales multiplier, the firm’s share price should be around $81, which is not
that different from the values obtained by the EPS and BV multipliers. As we noted with EPS and
BV, these multipliers have flaws and while they are not fatal flaws, they are significant. The fact
that they yield similar numbers should not distract the observer from these flaws.
At this juncture, we reach into our financial metrics for the one true financial metric that any
firm should rely on to give it an honest answer to how well it is performing. That metric is EBITDA
– earnings before interest, taxes, depreciation, and amortization. The beauty of EBITDA is that it
strips away all the externalities, as it were, that are contained in some financial metrics:
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the exclusion of interest eliminates the leveraging of the firm. Firms leverage to gain
returns on equity. The problem with leverage is that as firms lever, they increase their
risk to equity holders, so these raise their target ROE to account for that risk
the exclusion of taxes eliminates the vagaries of changes to the tax code. These changes
have nothing to do with the firm’s efficiency and everything to do with political
calculations at the national level, something that most firms should not rely on
the exclusion of depreciation and amortization eliminates changes to accounting rules
and tax laws that are meant to increase investment in capital goods. Policies that
encourage investments in capital goods have nothing to do with a firm’s efficiency and
profitability and by excluding it, EBITDA provides the purest essence of the firm’s
operations
As with the Sales multiplier, the value that one obtains using EBITDA is the firm’s EV. So,
as with Sales, we must run the same set of formulas. In this case, we will use the following
assumptions – EBITDA multiplier = 10.6x, TTM EBITDA = $810 Million, interest-bearing debt =
$2,100 Million, and shares outstanding = 71 Million:
𝑬𝑬𝑬𝑬 = 𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨𝑨 𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬 𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴𝑴 𝒙𝒙 𝟒𝟒𝟒𝟒𝟒𝟒𝟒𝟒 𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬 = 𝟏𝟏𝟏𝟏. 𝟔𝟔 𝒙𝒙 $𝟖𝟖𝟖𝟖𝟖𝟖 = $𝟖𝟖, 𝟓𝟓𝟓𝟓𝟓𝟓
𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬𝑬 𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽 = 𝑬𝑬𝑬𝑬 − 𝑫𝑫𝑫𝑫𝑫𝑫𝑫𝑫 = $𝟖𝟖, 𝟓𝟓𝟓𝟓𝟓𝟓 − $𝟐𝟐, 𝟏𝟏𝟏𝟏𝟏𝟏 = $𝟔𝟔, 𝟒𝟒𝟒𝟒𝟒𝟒
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝒑𝒑𝒑𝒑𝒑𝒑 𝒔𝒔𝒉𝒉𝒂𝒂𝒂𝒂𝒂𝒂 =
$𝟔𝟔, 𝟒𝟒𝟒𝟒𝟒𝟒
= $𝟗𝟗𝟗𝟗. 𝟑𝟑𝟑𝟑
𝟕𝟕𝟕𝟕
The EBITDA calculation shows a higher price per share for the firm than the other three
multipliers do. This leaves in a bit of a quandary. Which of the multipliers should be overweighed,
if at all? Which ones should be underweighed, if at all? Should all be weighed equally? Should
some multipliers be excluded?
To analyze this situation, perhaps the starting point should be to show all four per share prices
side by side and compare them. We do this below:
Multiplier
Calculated $ per share
Index to EPS
EPS
$72.00
100%
Book Value
$84.32
117%
Sales
$81.34
113%
EBITDA
$91.35
127%
We can take the data above and make some assumptions on how we will weigh the values
per share. Before we do, though, we introduce two new factors that are not multipliers per se but
still provide value in the calculations.
Transactions
The first is premium paid over pre-announcement share price. This figure is fairly easy to
calculate. The share price of the acquired firm trades at what is considered an equilibrium price (that
is, the equilibrium between demand for the stock by investors and supply of the stock by sellers).
That share price is compared to the final price paid once the acquisition was finalized. This premium
percent is then applied to the current share price of our firm to come up with what its purchase price
might be:
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝒑𝒑𝒑𝒑𝒑𝒑 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 = 𝑷𝑷𝒓𝒓𝒓𝒓 − 𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑𝒑 𝒙𝒙 (𝟏𝟏 + 𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷)
Assuming a pre-announcement share price of, say $71.00 and a premium paid of 21% over
the pre-announcement price, we get:
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𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝒑𝒑𝒑𝒑𝒑𝒑 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 = $𝟕𝟕𝟕𝟕. 𝟎𝟎𝟎𝟎 𝒙𝒙 (𝟏𝟏 + 𝟐𝟐𝟐𝟐%) = $𝟖𝟖𝟖𝟖. 𝟗𝟗𝟗𝟗
The second factor we can bring in is synergies. Synergies are a catch-all term for scale
benefits that the two combined firms can obtain that could not be obtained had the two been operating
independently. So, synergies are a significant factor in the price premium paid because they assume
that the acquired firm is more valuable once it has been combined with the acquiring firm, thus
yielding economies of scale.
Synergies are only relevant and should only be included in the calculations if and only if the
acquiring firm will adjust its budgets to include these forecast savings. Many firms do not do this
and as a result, the synergies that were forecast do not pan out. Still, hope springs eternal and firms
pay over the trading value for a firm.
Synergy-related share prices use the same formula as the price premium paid over the preannouncement share price:
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝒑𝒑𝒑𝒑𝒑𝒑 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 = $𝟕𝟕𝟕𝟕. 𝟎𝟎𝟎𝟎 𝒙𝒙 (𝟏𝟏 + 𝟏𝟏𝟏𝟏%) = $𝟖𝟖𝟖𝟖. 𝟔𝟔𝟔𝟔
One example of synergies is the projected salary savings from redundant staff. When two
firms merge (or when one is acquired), there will likely be areas where staff are redundant. For
example, the various departments of the two firms combined have a total staff of, say, one thousand.
In the combined firm, only 650 staff may be needed. This means that 350 staff are redundant. (It is
cruel to consider this perhaps, but it is a calculation that is made during mergers and acquisitions so
we must understand the mechanics of it.)
Some firms do make staff redundant and cut jobs after an acquisition or a merger in order to
collect these synergies. Let’s do the math with the 350 staff cuts. For this example, let’s assume
the following: average staff salary = $65,000, average cost of benefits = 30% of salary, yearly salary
growth rate = 3%, WACC = 7%, shares outstanding = 71 million:
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽 𝒐𝒐𝒐𝒐 𝑺𝑺𝑺𝑺𝑺𝑺𝒇𝒇𝒇𝒇 𝑪𝑪𝑪𝑪𝑪𝑪𝑪𝑪 =
𝟑𝟑𝟑𝟑𝟑𝟑 𝒙𝒙 $𝟔𝟔𝟔𝟔, 𝟎𝟎𝟎𝟎𝟎𝟎 𝒙𝒙 (𝟏𝟏+. 𝟑𝟑𝟑𝟑%)
= $𝟕𝟕𝟕𝟕𝟕𝟕, 𝟑𝟑𝟑𝟑𝟑𝟑, 𝟎𝟎𝟎𝟎𝟎𝟎
(𝟕𝟕% − 𝟑𝟑%)
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽 𝒑𝒑𝒑𝒑𝒑𝒑 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 =
$𝟕𝟕𝟕𝟕𝟕𝟕, 𝟑𝟑𝟑𝟑𝟑𝟑, 𝟎𝟎𝟎𝟎𝟎𝟎
= $𝟏𝟏𝟏𝟏. 𝟒𝟒𝟒𝟒
𝟕𝟕𝟕𝟕, 𝟎𝟎𝟎𝟎𝟎𝟎, 𝟎𝟎𝟎𝟎𝟎𝟎
Just the estimated staffing cuts are estimated to provide $10.41 per share in gains to the
combined firm. This compares well with the premium dollar paid over pre-announcement of $10.65
($81.65 minus $71).
So, when you read about mergers and acquisitions and the job cuts that follow, what you are
actually reading is the implementation of synergy projections that informed the final price paid for
the acquired firm. As we said, this is a cruel concept in business but it is a calculation that is made
all the time during mergers and acquisitions.
In fact, it is very likely that one of the key drivers in mergers and acquisitions is the gain of
synergies (read scale) to the acquiring firm. The reality, though, is a bit messier. Too often, and this
Page 5 of 7
has been explained extensively in the press, the culture of the acquiring firm clashes with the culture
of the acquired firm to create a less than optimal combination.
One example of this is the merger between McDonnell-Douglas and Boeing in 1997. To
many in Boeing, the philosophy of McDonnell-Douglas executives did not mesh well with the
philosophy of Boeing as a whole.
Continuing with our example, we can now put the complete table of values for the
multipliers, including the stock premium and synergy values:
Multiplier
EPS
Book Value
Sales
EBITDA
Premium
Synergy
Price/share
$72.00
$84.32
$81.34
$91.35
$85.91
$81.65
Weight
10%
10%
10%
50%
10%
10%
100%
Weighed Price/share
$7.20
$8.43
$8.13
$45.68
$8.59
$8.17
$86.20
Interestingly, the $86.20 weighed average share price we just calculated is 21% above the
$71.00 pre-announcement share price. This is the same number as the premium paid by other firms
that acquired firms in past years.
Dividend Discount Model (DDM)
The DDM mimics the methodology used by the free cash flow (FCF) valuation but instead
of calculating the income statement, balance sheet, and FCF, it just uses the dividends paid out by
the firm as a proxy for the cash flows.
While this makes quick work of the valuation, it is of course a very rough estimate of what
the price per share should be for our firm. To calculate the share price using the DDM, we start with
the firm’s last yearly dividend payments – in other words, we use the TTM dividend stream paid by
the firm.
Let’s say that for the purposes of our calculation, the firm has the following values:
•
•
•
dividends paid out TTM (2019) = $2.30
projected yearly growth in dividend payments = 4.0%
WACC for the firm = 7.0%
The formula for the present value of the dividend stream is as follows:
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽𝑽 =
$𝟐𝟐.𝟑𝟑𝟑𝟑 𝒙𝒙 (𝟏𝟏 + 𝟎𝟎.𝟒𝟒)
(𝟏𝟏 + .𝟎𝟎𝟎𝟎)
+
$𝟐𝟐.𝟑𝟑𝟑𝟑 𝒙𝒙 (𝟏𝟏 + .𝟎𝟎𝟎𝟎)𝟐𝟐
(𝟏𝟏 + .𝟎𝟎𝟎𝟎)𝟐𝟐
+
$𝟐𝟐.𝟑𝟑𝟑𝟑 𝒙𝒙 (𝟏𝟏+.𝟎𝟎𝟎𝟎)𝟒𝟒
(.𝟎𝟎𝟎𝟎 − .𝟎𝟎𝟎𝟎)
= $𝟖𝟖𝟖𝟖. 𝟖𝟖𝟖𝟖
The DDM model gives an answer that is lower than what we calculated using the various
weighed multipliers but still not far off. Still, it’s an estimate of what the actual value of the firm’s
stock price is and a very rough one at that.
Page 6 of 7
The reason why it’s such a rough estimate is that dividends are not a reliable proxy for FCF.
Some firms pay more in dividends than they should and some pay no dividends when they should.
In the first case, firms pay too much in dividends because in the past they performed well
and paid solid dividends but the present doesn’t offer such halcyon times. So, while they should
reduce their dividend payouts and keep cash in the firm for internal projects and overall liquidity,
they pay dividends in order not to trigger the wrath of shareholders, who would sell their shares and
crater the stock price.
In the second case, some companies don’t pay dividends (think tech here) and won’t pay
them because they haven’t done so in the past. So, their cash balances build up to very high levels
until they become rather untenable (remember the cost of funding those cash balances is the WACC
and the cash balances are earning paltry returns compared to the firm’s WACC). When these become
untenable, some firms make special dividend payouts to shareholders.
One example of a special dividend is Costco’s $10/share special dividend paid out in
December, 2020. This compares with an annual average divided paid out of $2.80/share.
Case Questions
Use the template provided to:
•
•
•
calculate share price estimates using EPS, Sales, BV, EBITDA, premiums, and synergies
apply the weights used in this document to the six factors above to come up with a
weighed price per share
use the dividend payments and projected growth rates provided to calculate the DDMbased prices per share for three firms
The template contains all the data you need to complete the assignment.
Page 7 of 7
FINANCIAL ANALYSIS
Source: Bloomberg, Capital IQ
Beat Estimates
Missed Estimates
Stock Buybacks
Source: Company filings and team estimates
Source: Bloomberg Pricing & Estimates
Ex. 25a – TJX Historic ROE and Payout Ratio
60%
13.5%
13.0%
50%
12.5%
40%
12.0%
30%
11.5%
11.0%
20%
10.5%
10%
FYE11
FYE12
FYE13
Capital Appreciation
Operating Margins
Source: Bloomberg
FYE14
FYE15
9.5%
Dividend yield
Ex. 25 b – Rev/SF and SF/Store
500
10.0%
23.3
Amount ($ K)
400
23.6
300
23.0
200
22.7
100
22.4
–
22.1
Revenue/SF
Source: Company filings and team estimates
SF per store
Ex. 26 – Current and Target Number of Stores
Target
Current (3Q ’16)
Marmaxx
0
Homegoods
2000
TJX Canada
4000
TJX Europe
6000
Stable existing store sales and robust new store growth drive organic topline
revenues. We expect existing store revenues to grow at a 6% CAGR during the next
5 years. This assumes a continuation of the constant increases in revenues for samestores of the past 27 quarters. Adding to these will be new, smaller stores, which we
assume will be growing at a rate of 180 per year over the next 5 years. Revenues from
these new stores will grow at a 3.9% CAGR until FY2020. Margins will improve as
TJX opens more, smaller stores near urban areas, where it should sell higher-margin
products (seasonal, beauty, and jewelry) at higher volumes per square foot (Ex. 25b,
26). Overall, we project a 5.9% annual revenue growth rate that will allow TJX to reach
$40B in top-line revenues by FY21 (for more detail, see Appendices 2 through 5.)
Sq.ft. (K)
0%
TJX’s ROE has increased 8.6% from 43.3% (FY11) to 51.9% (FY15). This
increase is mainly due to increased dividend pay-outs (4%, Ex. 25a), share buybacks (2.7%, Appendix 16) and increases in operating margins (1.9%, Ex. 25a),
which are the result of higher revenues per square foot (Ex. 25b). The share buybacks drove leverage (as measured in avg. assets/avg. equity) from 2.58 (FY11) to 2.51
(FY15). These share buy-backs, by virtue of increasing leverage, will drive
shareholders to require higher ROEs. TJX has been able to exceed these higher
expectations due to much higher than average performance. We attribute TJX’s
delivery of higher ROEs over time to its ability to controls costs – viz. as a percent of
sales, COGS fell from 73.1% (FY11) to 71.5% (FY15) and SG&A from 16.4% (FY11)
to 16.1% (FY11) – and asset utilization, as inventory turns increased from 6.1x (FY11)
to 6.7x (FY15).
Trade Secret
As a primarily brick-and-mortar retailer, TJX relies on leased space rather than
owned stores which allow them to optimize store size to changes in demographics
and consumer preferences. We estimate that revenues per square foot (RSF) will
increase at a 1.7% CAGR from $380.5K (FY15) to $414.6K (FY20) while the average
footprint of new stores will fall from 22,500 square feet to 22,000.
TJX will improve margins from 28.5% to 30% as it uses its increasing purchasing
power and an atomized supplier base to drive COGS lower. As a result, we project
EBITDA to grow at a 5-5.1% per year for the next 5 years (Ex. 27).
Source: Company filings and team estimates
50000
40000
Ex. 27 – Gross Margins
29.5%
29.3%
29.1%
30000
28.9%
20000
28.7%
10000
28.5%
0
28.3%
Revenue:
GP Margin
The metrics discussed above – revenue growth, efficient use of store space, and
improved margins- explain, in part, the relentless climb in TJX share prices, as
illustrated in the previous page’s chart. Over the past five years, TJX have beat
estimates fourteen times and missed estimates 5 times. Five times is also the amount
of times that TJX has gone to the markets to buy back shares. While the chart clearly
shows that the share buy-backs do not have an immediate impact on share price, they
do have a long term impact, which we estimate to be $5-6 per share. With a dividend
yield of 1.3%, TJX is out-performing all indices (see bottom of page 1), and according
to our analysis will continue to do so for the foreseeable future. We explain how in the
next section.
Source: Company filings and team estimates
VALUATION
Ex. 28 – Stock Price Football Field
We used a weighted average of discounted cash flows (DCF), comparables, and
leveraged recapitalization values to arrive at a target price of $83.40 – a 18.1% upside
over the current stock price of $70.56 (Ex. 29) We assigned a higher weight to the DCF
because we believe that TJX, a mature company in mature industry, will continue
growing by taking market share from its full price competitors and holding its own
against the online competition. We explain our assumptions in detail below.
Source: Team Estimates
Ex. 29 – Scenario Summary
DCF (55% weight) We used a 5-year DCF model to reflect TJX’s position as a mature
OP retailer. The Base Case, which has a 50% probability, assumes a 4.4% yearly samestore growth while the Bull Case (25% probability) and Bear Case (25% probability)
assume 5.5% and 2.7% growth rates respectively (Ex. 30):
Ex. 30 – Revenue Assumptions
Source: Team Estimates
Ex. 31 – Comparables Summary
Source: Team Estimates
Source: Team Estimates
Our discount rate of 7.8% reflects a beta of 0.8, and we did not modify it despite
TJX’s share buy-backs. We applied a 9.4% risk premium based on the equity market
premium observed during the past 10 years. For more detail, please see Appendix 6.
Source: Team Estimates
Ex. 32 – Peer Debt/EBITDA Multiples
Source: Team Estimates
Ex. 33 – Leveraged Recapitalization
Comparables (40% weight, Ex. 31) We weighed comparables as follows: OP
retailers – 55%, traditional retailers (Macy’s, Nordstrom, etc.) – 40%, and online
retailers (amazon, overstock, etc.) – 5%. The metrics used are EV/Revenue (30%),
EV/EBITDA (30%), Price/FCF (20%), and P/E (20%). For more detail, please see
Appendices 7 and 14.
Leveraged Recapitalization (5% weight, Ex. 32, 33) TJX’s current capital structure
has a 0.4x Debt to EBITDA is equivalent to a 3.4% of debt to market capitalization.
This figure is among the lowest in the industry where the median is 1.8x Debt to
EBITDA. Assuming that TJX may in the future look out for alternative methods to
stock buy-backs in order to increase shareholder wealth, we foresee the company
increasing its debt levels to 1.4x Debt to EBITDA. This would take its debt to about
$5.9B from the current $1.6B. In this case, we want to consider this potential
eventuality yet recognize that it is not a likely scenario, so we have assigned it a weight
of 5%. For more detail, please see Appendix 8.
Ex. 34 – Bootstrap Revenue Forecast
Source: Team Estimates
Ex. 34 – Bootstrap Model of Price per Share
Source: Team Estimates
Bootstrap Statistical Price Simulation (5% weight)
We used regressions to forecast revenues and their probability-based distributions. To
accomplish this, we related a future quarter’s revenue to a reference quarter (3Q10)
using a predictor function. As with all forecasts, there will be deviations, which are
quantified and assigned probabilities as they are normally distributed. We bounded our
confidence intervals at ± 2.5% to get a more granular view of TJX’s future
performance. After doing this exercise, we obtained a lower-bound share price of
$95.20 (blue line, Ex. 34), which is ~30% above the current share price of $70.56. We
also calculated a mean price of $98.70 (orange line), which is 34% above the current
share price. Thus, our model predicts that TJX share prices should rise by one third
over the next 5 years. We gave this scenario a 5% weight to arrive at our $83.40 target
price. We gave it this weight because, while we are confident of our methodology, we
believe that QoQ volatility may have been overstated in the past 5 years due to the
gains made by new online retailers during that period. For more detail on simulations,
please see Appendix 9 (Bootstrap) and 19 (Monte Carlo, which was not used).
APPENDIX 1 INCOME STATEMENT (GAAP)
APPENDIX 2: INCOME STATEMENT (COMMON SIZE)
APPENDIX 3: BALANCE SHEET (GAAP)
APPENDIX 4: CASH FLOW STATEMENT (GAAP)
APPENDIX 5: DCF SCENARIOS
APPENDIX 6: COMPARABLES
APPENDIX 7: LEVERAGED RECAPITALIZATION
APPENDIX 8: BOOTSTRAP STATISTICAL MODEL
We used a bootstrap simulation to forecast revenues from FY15 to FY24. In a bootstrap model, forecast revenues are based on actual
revenue growth rates between 1Q10 and 3Q15. To refine our calculations, we also used the total growth rate from our reference
quarter (3Q10) to 3Q15. Variations in growth rates are the residuals of QoQ revenue regressions. As with revenues, we ran similar
regressions on COGS and Sales and Marketing to determine variation residuals. We can say with 95% confidence that the price for
TJX should increase to $95.30 (up by 35%). Other assumptions used for our simulation are:
1) Future revenue fluctuations will be similar to those between 1Q10 to 3Q15 as consistent with the bootstrap method
2) All DCF assumptions are kept the same except, of course, for QoQ growth rates and their statistical fluctuations
3) The Weighted Average of Cost of Capital (WACC) is 7.8% and the Terminal Value growth rate is 2%.
Growth rate fluctuations are calculated using the function:
log
𝑅𝑅𝑅𝑅, 𝑞𝑞
= 𝜃𝜃 + 𝜀𝜀(𝑦𝑦,𝑞𝑞)
𝑅𝑅𝑅𝑅 − 1, 𝑞𝑞
where y = 2010 to 2014 and q = 1,2,3,4
𝜃𝜃 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓, 𝜀𝜀 = 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
The fluctuation multipliers are the expected value of the residuals ε. Thus, revenue is equal to the actual growth rate for that year
times a multiplier, which is a variation from the mean. We ran 1,000 iterations to get a distribution of the dispersion from the mean.
The results are outlined below as an implied stock price and present value of TJX.
Aggregate Forecast Revenue (M$)
2015
2016
Median
Mean
95th
Percentile
5th Percentile
2017
2018
2019
2020
2021
2022
2023
2024
$29,111
$31,391
$33,759
$36,355
$39,110
$42,089
$45,233
$48,672
$52,351
$56,392
$29,186
$31,415
$33,815
$36,402
$39,176
$42,138
$45,336
$48,812
$52,549
$56,535
$29,771
$32,859
$35,822
$39,241
$42,587
$46,612
$50,226
$54,428
$59,061
$63,561
$28,669
$30,205
$32,080
$34,041
$36,208
$38,681
$41,232
$43,863
$47,385
$50,558
Present Value (M$)
Price per Share (US $)
Median
71,820
98.50
Mean
71,870
98.60
95th Percentile
74,870
102.70
5th Percentile
69,492
95.30
Source: Team Estimates
Equity Valuations using Multiples and Transactions
Historical Multiples:
– Average
EPS
JTM EPS
Average
Book Value
JTM Book Value
Average
Sales
JTM Sales (Last 4Q)
Firm Value
Debt Value
Equity Value
Average
EBITDA
JTM EBITDA (Last 4Q)
Firm Value
Debt Value
Equity Value
Average
Premium
Pre-Announcement Stock Price
Average
Synergy
Pre-Announcement Stock Price
Average
EPS
BV
Sales
EBITDA
Premium
Synergy
16.4
3.9
3.5
13.0
35.0%
30.0%
Last 4Q
2.55
Est. 2021
2.85
Est. 2022
3.05
14.00
2,040
2,382
428
2,382
31.00
31.00
Shares outstanding (M)
80.20
Northern
Eastern
Central
2020 Dividends
Dividends Growth/yr.
2.60
2.2%
2.75
2.4%
2.80
1.9%
Dividend Stream
2021
2022
Northern
Eastern
Central
DDM Value of each Firm
$/share
Northern
Eastern
Central
WACC
7.5%
TV
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