Valuation
FIN 449
Michael Dimond
Discounted Cash Flow Valuation
Michael Dimond
School of Business Administration
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.
• Information Needed: To use discounted cash flow valuation, you need
– to estimate the life of the asset
– to estimate the cash flows during the life of the asset
– to 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.
Michael Dimond
School of Business Administration
Valuation: Simplicity vs Clarity
Simplest DCF approach - constant growth model:
2013 FCFE
6,604.4 CF0
Ke
8.97%
Constant growth
5.0%
plus cash
40,979.0
Equity value
215,846.2
Number of shares
31,072.0
Intrinsic value/share $
6.95
•
Risk and long-term CF growth assumptions matter, but we could easily
build a table to model sensitivity to changes in growth and cost of capital.
Michael Dimond
School of Business Administration
Valuation: Simplicity vs Clarity
Simplest DCF approach - constant growth model:
2013 FCFE
6,604.4 CF0
Ke
8.97%
Constant growth
5.0%
plus cash
40,979.0
Equity value
215,846.2
Number of shares
31,072.0
Intrinsic value/share $
6.95
2-stage growth model:
2013 FCFE
Ke
Years 1-5 Growth
LT growth (after Y5)
plus cash
Equity value
Number of shares
Intrinsic value/share $
6,604.4 CF0
8.97%
10.0%
5.0%
40,979.0
258,279.2
31,072.0
8.31
FCFE
CF1 7,264.8
CF2 7,991.3
CF3 8,790.5
CF4 9,669.5
CF5 10,636.5
Michael Dimond
School of Business Administration
Valuation: Simplicity vs Clarity
2-stage growth model:
2013 FCFE
Ke
Years 1-5 Growth
LT growth (after Y5)
plus cash
Equity value
Number of shares
Intrinsic value/share $
6,604.4 CF0
8.97%
10.0%
5.0%
40,979.0
258,279.2
31,072.0
8.31
3-stage growth model:
2013 FCFE
Ke
Years 1-5 Growth
Years 6-10 Growth
LT growth (after Y10)
plus cash
Equity value
Number of shares
Intrinsic value/share $
6,604.4
8.97%
10.0%
7.0%
5.0%
40,979.0
275,120.1
31,072.0
8.85
FCFE
CF1 7,264.8
CF2 7,991.3
CF3 8,790.5
CF4 9,669.5
CF5 10,636.5
These models
are great and
you get an
answer quickly,
but they are
very high level.
FCFE
CF6 11,381.0
CF7 12,177.7
CF8 13,030.1
CF9 13,942.2
CF10 14,918.2
Michael Dimond
School of Business Administration
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.
Michael Dimond
School of Business Administration
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.
Michael Dimond
School of Business Administration
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
Michael Dimond
School of Business Administration
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
Michael Dimond
School of Business Administration
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.
Michael Dimond
School of Business Administration
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 =
where,
t=n
CF to Equity t
 (1+ k )t
t=1
e
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.
Michael Dimond
School of Business Administration
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.
CF to Firm t
 (1+ WACC) t
t =1
t= n
Value of Firm =
where,
CF to Firmt = Expected Cashflow to Firm in period t
WACC = Weighted Average Cost of Capital
• The difference between equity value and the value of the firm is
the value of claims on assets (e.g. Debt)
Michael Dimond
School of Business Administration
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.
Michael Dimond
School of Business Administration
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
Michael Dimond
School of Business Administration
First Principles 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.
t=n
CF to Equity t
Value of Equity = 
(1+ k e )t
t=1
CF to Firm t
Value of Firm = 
t
t =1 (1+ WACC)
t= n
Michael Dimond
School of Business Administration
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
Michael Dimond
School of Business Administration
DCF Methods Compared
• FCFE//Ke – Equity cash flow method
• FCFF//WACC – Corporate valuation method
• FCFF//Ku – Adjusted present value method (APV)
Michael Dimond
School of Business Administration
DCF: Equity cash flow method
UNROUNDED
FCFF
D
E
TC
wd
we
Terminal growth
Kd
Debt (n=-1)
Debt (n=0)
t
Rf
Rm
MRP
β
Ke
1000.0
5000.0
13417.7
18417.7
0.2715
0.7285
3.5%
5.0%
4830.9
5000.0
40%
3%
10%
7%
1.2
11.4%
Equity Cash Flow Method (FCFE//Ke)
FCFE (n=0)
1024.2
g
3.5%
Ke
11.4%
PV
13417.7
Equity Intrinsic Value
13417.7
Michael Dimond
School of Business Administration
DCF: Corporate valuation method
UNROUNDED
FCFF
D
E
TC
wd
we
Terminal growth
Kd
Debt (n=-1)
Debt (n=0)
t
Rf
Rm
MRP
β
Ke
1000.0
5000.0
13417.7
18417.7
0.2715
0.7285
3.5%
5.0%
4830.9
5000.0
40%
3%
10%
7%
1.2
11.4%
Corporate Valuation Method (FCFF//WACC)
FCFF (n=0)
1000.0
g
3.5%
WACC
9.1%
PV
18417.7
Debt (n=0)
5000.0
Equity Intrinsic Value
13417.7
Michael Dimond
School of Business Administration
DCF: Adjusted present value method (APV)
UNROUNDED
FCFF
D
E
TC
wd
we
Terminal growth
Kd
Debt (n=-1)
Debt (n=0)
t
Rf
Rm
MRP
β
Ke
1000.0
5000.0
13417.7
18417.7
0.2715
0.7285
3.5%
5.0%
4830.9
5000.0
40%
3%
10%
7%
1.2
11.4%
APV Method (FCFF//Ku)
FCFF (n=0)
g
Ku
PV
Int Exp (n=0)
t
Tax savings
g
Ku
PV
Total of PVs
Debt (n=0)
Equity Intrinsic Value
1000.0
3.5%
9.7%
16795.0
241.5
40%
96.6
3.5%
9.7%
1622.7
18417.7
5000.0
13417.7
Michael Dimond
School of Business Administration
DCF results compared
• In theory, the methods produce equivalent results
Method
Equity CF ->
Corp Val ->
APV ->
Intr. Value
13417.7
13417.7
13417.7
$ Diff
0.0
0.0
0.0
% Diff
0.0% vs Corp Val
0.0% vs APV
0.0% vs Equity CF
• This is rarely the case in the real world…
Michael Dimond
School of Business Administration
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.
Michael Dimond
School of Business Administration