FIN449
Valuation
Michael Dimond
Where are we going with all this?
Risk &
Cost of Capital
Forecast
Financials
Facts &
Information
Recasting &
Sustainable OCF
DCF Calculations
Comps
Value &
Perspective
Exam
Valuation #2
Valuation #3
Final Project
Valuation – The Big Picture
Why use Fundamental Analysis?
January 2000: Internet Capital Group was trading at $174.
“Valuation is often not a helpful tool in determining when to sell
hypergrowth stocks”, Henry Blodget, Merrill Lynch Equity
Research Analyst in January 2000, in a report on Internet Capital
Group.



There have always been investors in financial markets who have
argued that market prices are determined by the perceptions (and
misperceptions) of buyers and sellers (inefficiencies of the
market), and not by anything as prosaic as cash flows or earnings.
Perceptions do matter, but they are not everything.
Asset prices cannot be justified by merely using the “bigger fool”
theory.
“Irrational Exuberance”
January 2000: Internet Capital Group was trading at $174.
January 2001: Internet Capital Group was trading at $ 3.
How about mistaken notions of how the
market works?
January 2000: Internet Capital Group was trading at $174.
January 2001: Internet Capital Group was trading at $ 3.
Discounted Cash Flow Valuation



What is it: In discounted cash flow valuation, the
value of an asset is the present value of the
expected cash flows on the asset.
Philosophical Basis: Every asset has an intrinsic
value that can be estimated, based upon its
characteristics in terms of cash flows, growth and
risk.
Fundamental Analysis derives those cash flows
from the underlying, or fundamental, operations of
the business.
Discounted Cash Flow Valuation (cont’d)


Information Needed: To use discounted cash flow valuation,
you need to
 estimate the life of the asset
 estimate the cash flows during the life of the asset
 estimate the discount rate to apply to these cash flows to get
present value
Market Inefficiency: Markets are assumed to make mistakes
in pricing assets across time, and are assumed to correct
themselves over time, as new information comes out about
assets.
Advantages of DCF Valuation



Since DCF valuation, done right, is based upon an
asset’s fundamentals, it should be less exposed to
market moods and perceptions.
If good investors buy businesses, rather than stocks
(the Warren Buffett adage), discounted cash flow
valuation is the right way to think about what you
are getting when you buy an asset.
DCF valuation forces you to think about the
underlying characteristics of the firm (fundamentals)
and understand its business. If nothing else, it
brings you face to face with the assumptions you
are making when you pay a given price for an asset.
Disadvantages of DCF valuation


Since it is an attempt to estimate intrinsic value, it
requires far more inputs and information than other
valuation approaches
These inputs and information are not only noisy
(and difficult to estimate), but can be manipulated
by the savvy analyst to provide the conclusion he or
she wants.
Disadvantages of DCF Valuation (con’t)

In an intrinsic valuation model, there is no
guarantee that anything will emerge as under or
over valued. Thus, it is possible in a DCF valuation
model, to find every stock in a market to be over
valued. This can be a problem for
 equity research analysts, whose job it is to follow
sectors and make recommendations on the most
under and over valued stocks in that sector
 equity portfolio managers, who have to be fully
(or close to fully) invested in equities
When DCF Valuation works best

This approach is easiest to use for assets (firms)
whose




cashflows are currently positive and
can be estimated with some reliability for future periods, and
where a proxy for risk that can be used to obtain discount
rates is available.
It works best for investors who either


have a long time horizon, allowing the market time to correct
its valuation mistakes and for price to revert to “true” value or
are capable of providing the catalyst needed to move price
to value, as would be the case if you were an activist
investor or a potential acquirer of the whole firm
Discounted Cashflow Valuation
t = n CF
t
Value = 
t
t = 1 (1 + r)
where CFt is the cash flow in period t, r is the discount rate


appropriate given the riskiness of the cash flow and t is the life
of the asset.
For an asset to have value, the expected cash flows have to be
positive some time over the life of the asset.
Assets that generate cash flows early in their life will be worth
more than assets that generate cash flows later; the latter may
however have greater growth and higher cash flows to
compensate.
Equity Valuation versus Firm Valuation

Value just the equity stake in the business

Value the entire business, which includes, besides
equity, the other claimholders in the firm
Valuation

Value = Debt Value + Equity Value

Equity Value / Shares Outstanding
= “Correct” Price per Share

Context & perspective come from comparables
and other less robust methods

Publicly traded company can be declared to be
“overvalued” or “undervalued”
What is Free Cash Flow – Really?






Free Cash Flow is cash available to some relevant
entity.
OCF refers to cash from a firm’s ongoing operating
activities (NI = OCF + Accruals).
FCFF is OCF adjusted for investments and
divestments in operating assets, and is available to
debt holders and equity holders.
FCFE is FCFF adjusted for changes in the firm’s debt
levels, and is available to equity holders.
In both FCFF and FCFE, some or all of this amount
may be reinvested in the company.
Why is valuation using Dividends less realistic than
using Free Cash Flows?
First Principle of Valuation


Never mix and match cash flows and discount rates.
The key error to avoid is mismatching cashflows and discount
rates, since discounting cashflows to equity at the weighted
average cost of capital will lead to an upwardly biased
estimate of the value of equity, while discounting cashflows to
the firm at the cost of equity will yield a downward biased
estimate of the value of the firm.
Value of Equity =
t=n CF

t=1
to Equity t
(1+ k e )t
t= n
Value of Firm =
CF to Firm t
 (1+ WACC)
t =1
t
Equity Valuation

The value of equity is obtained by discounting expected
cashflows to equity, i.e., the residual cashflows after meeting all
expenses, tax obligations and interest and principal payments,
at the cost of equity, i.e., the rate of return required by equity
investors in the firm.
Value of Equity =
t=n CF

t=1
to Equity t
(1+ k e )t
where,
CF to Equityt = Expected Cashflow to Equity in period t
ke = Cost of Equity

The dividend discount model is a specialized case of equity
valuation, and the value of a stock is the present value of
expected future dividends.
Firm Valuation

The value of the firm is obtained by discounting expected
cashflows to the firm, i.e., the residual cashflows after
meeting all operating expenses and taxes, but prior to debt
payments, at the weighted average cost of capital, which is
the cost of the different components of financing used by the
firm, weighted by their market value proportions.
t= n
Value of Firm =
CF to Firm t
 (1+ WACC)
t
t =1
where,
CF to Firmt = Expected Cashflow to Firm in period t
WACC = Weighted Average Cost of Capital
Cash Flow Computation

Use the following data to compute OCF & FCF
EBIT =
Depreciation =
Interest =
Tax Expense =
t=
Net Income =
ΔFA =
ΔNWC =
ΔDebt =
Preferred Div =
1,671
633
123
599
0.3869509
949
896
385
286
3
OCF = NI + Int + Depr
949+123+633 =
OCF = EBIT(1-t) + Depr
1,705.0000
1671(1-0.3869509)+633 =
1,657.4050
FCF = OCF - ΔFA - ΔNWC
1705 - 896-385 =
FCF = OCF - ΔFA - ΔNWC
424.0000
1657.3230 - 896-385 =
376.4050
FCFE = FCF - ΔDebt - Interest - PfdDiv
424 - 286 - 123 - 3 =
FCFE = FCF - ΔDebt - Interest - PfdDiv
12.0000
376.3230 - 286 - 123 - 3 =
(35.5950)
We need to adjust for the tax shield used earlier
FCFE = FCF - ΔDebt - Interest(1-t) - PfdDiv
376.3230 - 286 - 123(1-0.3870) - 3 =
12.0000
Difference
(0.0000)
Which is more accurate?
Year
0
Growth Rate
Year
1
10%
Year
2
9%
Year
3
8%
Year
4
7%
Year
5
5%
FCFE 100.0000 110.0000 119.9000 129.4920 138.5564 145.4843
WACC
Ke
8%
12%
Beyond
4%
Year
0
Growth Rate
Year
1
10%
Year
2
9%
Year
3
8%
Year
4
7%
Year
5
5%
Beyond
4%
FCFE 100.0000 110.0000 119.9000 129.4920 138.5564 145.4843
WACC
Ke
8%
12%
Year 6 CF 151.3036
Terminal Value 1891.2954
Equity Value $1,529.75
Firm Value and Equity Value

To get from firm value to equity value, which of the following
would you need to do?





Subtract out the value of long term debt
Subtract out the value of all debt
Subtract the value of all non-equity claims in the firm, that are
included in the cost of capital calculation
Subtract out the value of all non-equity claims in the firm
Doing so, will give you a value for the equity which is



greater than the value you would have got in an equity valuation
lesser than the value you would have got in an equity valuation
equal to the value you would have got in an equity valuation
Cash Flows and Discount Rates
Assume that you are analyzing a company with the following
cashflows for the next five years.
Year
CF to Equity Int Exp (1-t) CF to Firm
1
$ 50
$ 40
$ 90
2
$ 60
$ 40
$ 100
3
$ 68
$ 40
$ 108
4
$ 76.2
$ 40
$ 116.2
5
$ 83.49
$ 40
$ 123.49
Terminal Value $ 1603.0
$ 2363.008
 Assume also that the cost of equity is 13.625% and the firm can
borrow long term at 10%. (The tax rate for the firm is 50%.)
 The current market value of equity is $1,073 and the value of debt
outstanding is $800.
 Calculate the Equity Value and the Firm Value.

Equity versus Firm Valuation
Method 1: Discount CF to Equity at Cost of Equity to get value of equity
 Cost of Equity = 13.625%
 PV of Equity = 50/1.13625 + 60/1.136252 + 68/1.136253 +
76.2/1.136254 + (83.49+1603)/1.136255
= $1073
Method 2: Discount CF to Firm at Cost of Capital to get value of firm
 Cost of Debt = Pre-tax rate (1- tax rate) = 10% (1-.5) = 5%
 WACC
= 13.625% (1073/1873) + 5% (800/1873) = 9.94%
 PV of Firm = 90/1.0994 + 100/1.09942 + 108/1.09943 + 116.2/1.09944
+ (123.49+2363)/1.09945
= $1873

PV of Equity = PV of Firm - Market Value of Debt
= $ 1873 - $ 800 = $1073
First Principle of Valuation


Never mix and match cash flows and discount rates.
The key error to avoid is mismatching cashflows and discount
rates, since discounting cashflows to equity at the weighted
average cost of capital will lead to an upwardly biased
estimate of the value of equity, while discounting cashflows to
the firm at the cost of equity will yield a downward biased
estimate of the value of the firm.
Value of Equity =
t=n CF

t=1
to Equity t
(1+ k e )t
t= n
Value of Firm =
CF to Firm t
 (1+ WACC)
t =1
t
The Effects of Mismatching
Error 1: Discount CF to Equity at Cost of Capital to get equity
value
PV of Equity = 50/1.0994 + 60/1.09942 + 68/1.09943 + 76.2/1.09944 +
(83.49+1603)/1.09945 = $1248
Value of equity is overstated by $175.
Error 2: Discount CF to Firm at Cost of Equity to get firm value
PV of Firm = 90/1.13625 + 100/1.136252 + 108/1.136253 +
116.2/1.136254 + (123.49+2363)/1.136255 = $1613
PV of Equity = $1612.86 - $800 = $813
Value of Equity is understated by $ 260.
Error 3: Discount CF to Firm at Cost of Equity, forget to subtract
out debt, and get too high a value for equity
Value of Equity = $ 1613
Value of Equity is overstated by $ 540
Supplementary Material
96 Common Errors in Company Valuations
by Pablo Fernandez & Jose Maria Carabias

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=895151
More About Cash Flows and Discount Rates
Assume that you are analyzing a company with the following
cashflows for the next five years.
Year
CF to Equity Int Exp (1-t) CF to Firm
1
$ 50
$ 40
$ 90
2
$ 60
$ 40
$ 100
3
$ 68
$ 40
$ 108
4
$ 76.2
$ 40
$ 116.2
5
$ 83.49
$ 40
$ 123.49
Terminal Value $ 1603.0
$ 2363.008





Assume also that the cost of equity is 13.625% and the firm can
borrow long term at 10%. (The tax rate for the firm is 50%.)
What is the growth rate for FCFE assumed for each year?
How is terminal value calculated?
What is the implied growth rate for the terminal value?
More About Cash Flows and Discount Rates
Assume that you are analyzing a company with the following
cashflows for the next five years.
Year
CF to Equity
1
$ 50
2
$ 60
20% growth
3
$ 68
13.3% growth
4
$ 76.2
12.1% growth
5
$ 83.49
9.6% growth
CAGR = 13.7%
Terminal Value $ 1603.0

TV = CFn x (1+ g) ÷ (Ke – g) = 1603.0
TV = 83.49 x (1 + g) ÷ ( 13.625% – g) = 1603.0
g=?
(83.49 ÷ 50)^(1/4) - 1
Terminal Growth Rate
TV = CFn x (1+ g) ÷ (Ke – g)
:. TV x (Ke – g) = CFn x (1+ g)
:. TV x (Ke – g) = CFn x (1+ g)
:. TV x Ke – TV x g = CFn + CFn x g
:. TV x Ke – TV x g – CFn = CFn x g
:. TV x Ke – CFn = CFn x g + TV x g
:. TV x Ke – CFn = g x (CFn + TV)
:. (TV x Ke – CFn) ÷ (CFn + TV) = g
Since g = (TV x Ke – CFn) ÷ (CFn + TV)
g = ((1603 x 13.625%) – 83.49) ÷ (83.49 + 1603) = 8.00%
More About Cash Flows and Discount Rates
Assume that you are analyzing a company with the following
cashflows for the next five years.
Year
CF to Equity
1
$ 50
2
$ 60
20% growth
3
$ 68
13.3% growth
4
$ 76.2
12.1% growth
5
$ 83.49
9.6% growth
CAGR = 13.7%
Terminal Value $ 1603.0

TV = CFn x (1+ g) ÷ (Ke – g) = 1603.0
TV = 83.49 x (1 + g) ÷ ( 13.625% – g) = 1603.0
(83.49 ÷ 50)^(1/4) - 1
g = ((1603 x 13.625%) – 83.49) ÷ (83.49 + 1603) = 8.00%
Calculating Free Cash Flow to Equity

FCFE = Net income – Net investment + Net debt issued
Net Investment

Net investment = (Capital expenditures – Depreciation) +
Increase in noncash working capital
CapEx

Line item on Statement of Cash Flows?

Calculate the changes (from year to year) of ALL long-term
assets shown on the balance sheet.

Find the total amount (for a given year) shown in the “Investing”
section of the Statement of Cash Flows.
Issues?
Depreciation

“Basic definition” of net cash flow = net income + depreciation

Non-cash expense

In the “balance sheet” approach to define capital expenditures,
depreciation is usually not incorporated explicitly. Why not?

If the “Statement of Cash Flows” approach is used, one must
explicitly subtract depreciation from capital expenditures
(shown in the “Operating” section of the Statement of Cash
Flows)
Non-cash Working Capital

Noncash working capital = (current assets – cash) – current
liabilities… what else?

Noncash working capital = (current assets – cash) – (current
liabilities – interest bearing debt included in current liabilities)
Why?

Why not include cash?
Net Debt Issued

“Net” debt issued implies that one must take both debt
issuances AND repayments into account

Discussion: Constant Debt Ratio



Suppose a firm always finances new investment with a fixed debt
ratio (say, 30% debt and 70% equity, for example). The general
equation for FCFE then may be expressed as follows:
FCFE = Net income – (1 – debt ratio)(Net investment)
OR
FCFE = Net income – (equity ratio)(Net investment)
Free Cash Flow to Equity

FCFE = Net income – Net investment + Net debt issued
Data Source: EDGAR

http://www.sec.gov