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Introduction1.1 Fundamental terms
Summary
Lecture: Basic Elements
Lutz Kruschwitz & Andreas Loffler
Discounted Cash Flow, Section 1.1
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
Outline
IntroductionDCFThe predecessors
1.1 Fundamental terms1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Summary
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
DCFThe predecessors
DCF is short for 3
Deutsche CelluloidFabrik
Chemical factory in EastGermany, Eilenburg,founded 19th century,later acquired by IGFarben, nowECW-Compound GmbH
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
DCFThe predecessors
DCF is short for 4
Caribbean stateDominica with airport atCanef ield
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
DCFThe predecessors
DCF is short for 5
Dobermann Club deFrance
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
DCFThe predecessors
DCF is short for 6
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
DCFThe predecessors
Irving Fisher (1867–1947) 7
Fisher is one of the earliest AmericanNeoclassicals. He studiedMathematics, Social Science andPhilosophy. 1892 Professor at Yale.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
DCFThe predecessors
Franco Modigliani (1918–2003) 8
Modigliani was born in Italy, movedto USA in 1939. 1962 Professor atMassachusetts Institute ofTechnology. 1985 Nobel Laureate inEconomics.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
DCFThe predecessors
Merton H. Miller (1923–2000) 9
1961 Professor at University ofChicago. 1990 Nobel Laureate inEconomics.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Aims of the book 10
1. To put taxes and uncertainty togetherinto one model and
2. To give precise formal definitions ofseveral concepts such as
I cash flows (gross, net, free, . . . ?)I taxes (firm income, personal income
or both, . . . ?)I cost of capital (discount rates,
returns, . . . ?)
3. While maintaining the following principles:
I no free lunch (goes back toModigliani–Miller!)
I no revelation of stochasticstructure of future cash flows.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
The model 11
Copeland/Koller/Murrin
Valuation based on discounted cash flow (DCF)involves discounting
I of future payment surpluses
I after consideration of taxes
I using appropriate cost of capital.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Future cash flows 12
CF forecast
What matters are future cash flows.
But, the question of how to forecast cash flowswill not be considered here,
nor the question of how to derive cash flowsfrom balance sheets.
Furthermore, the investment policy (expansionand replacement investments) will be given.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
EBIT, gross and free cash flows 13
International
accounting standards
EBIT+ Accruals
= Gross cash flows before taxes− Corporate income taxes− Investment expenses
= Free cash flow− Interest, debt service− dividends, capital reduction
= Zero
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Taxes 14
US Tax
Authority
We consider two different types of income tax:
– Corporate income tax (Chapter 2).
– Personal income tax (chapter 3).
Value-based and sales taxes are ignored.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
The characteristics of a tax 15
German tax file
Characteristics are
– the tax subject (who?)
– the tax object (why?)
– the tax due (how much?), which isa product of the tax base and alinear tax scale.
Notice that in our model the tax rate isdeterministic.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Cost of capital 16
Reuters monitor
It is obvious what the cost of capital is in aone-period context. In a multi-periodcontext there are at least three differentnotions of this concept: cost of capital canbe
I returns,
I discount rates, or
I yields.
How now?
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Cost of capital: notation 17
Notation:
FCF firm’s free cash flowV value of the firm
Idea:
cost of capital is used fordiscounting (we are very loosehere), hence
V0 =FCF1
1 + k0+
FCF2
(1 + k0)(1 + k1)+ . . .
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Cost of capital: main idea 18
This idea shall also be applied in the future: at t = 1 we want tohave
V1 =FCF2
1 + k1+
FCF3
(1 + k1)(1 + k2)+ . . .
where k1 is the same cost of capital from the last slide!
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Cost of capital: a rough definition 19
First, let us ignore uncertainty. Then the definition of cost ofcapital should run
kt =DefFCFt+1 + Vt+1
Vt− 1
Implication: Costs of capital are inevitably (expected) returns.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Cost of capital: another concept 20
A different approach could be
V0 =FCF1
1 + k0+
FCF2
(1 + k1)2+ . . .
but then =⇒ V1 6=FCF2
1 + k1+
FCF3
(1 + k2)2+ . . .
Here the costs of capital are yields. We do not think much alongthis course (this is a different concept), because it is difficult toobserve yields empirically.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Cost of capital: discount rates 21
You pay at time t a price Pt,s for cash flow FCFs due at s:
-
t s
Pt,s FCFs� �?
We would then define a discount rate as
Pt,s =DefFCFs
(1 + κt,s)s−t
What relation exists between these discount rates and (expected)returns (=cost of capital)?
We will see later: without further assumptions not much. . .Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time
Time 22Different notions of time
discrete (easy tohandle)
continuous (elegant, butlaborious)
Time horizon
I finite
I infinite: Here we assume transversality, which is equivalent tosaying ‘nothing strange happens when T →∞’.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements
Introduction1.1 Fundamental terms
Summary
Summary 23
Valuation requires knowledge of
– free cash flows,
– taxes,
– cost of capital.
Costs of capital are returns, not yields.
Lutz Kruschwitz & Andreas Loffler Lecture: Basic Elements