lecture: basic elements - wiley€¦ · lutz kruschwitz & andreas l¨oﬄer lecture: basic...

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


Summary

Outline

IntroductionDCFThe predecessors

1.1 Fundamental terms1.1.1 Cash flows1.1.2 Taxes1.1.3 Cost of capital1.1.4 Time

Summary



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



Summary

DCFThe predecessors

DCF is short for 4

Caribbean stateDominica with airport atCanef ield



Summary

DCFThe predecessors

DCF is short for 5

Dobermann Club deFrance



Summary

DCFThe predecessors

DCF is short for 6



Summary

DCFThe predecessors

Irving Fisher (1867–1947) 7

Fisher is one of the earliest AmericanNeoclassicals. He studiedMathematics, Social Science andPhilosophy. 1892 Professor at Yale.



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.



Summary

DCFThe predecessors

Merton H. Miller (1923–2000) 9

1961 Professor at University ofChicago. 1990 Nobel Laureate inEconomics.



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.



Summary


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.



Summary


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.



Summary


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



Summary


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.



Summary


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.



Summary


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?



Summary


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)+ . . .



Summary


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!



Summary


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.



Summary


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.



Summary


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


Summary


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 →∞’.



Summary

Summary 23

Valuation requires knowledge of

– free cash flows,

– taxes,

– cost of capital.

Costs of capital are returns, not yields.


lecture: basic elements - wiley€¦ · lutz kruschwitz & andreas l¨oﬄer lecture: basic...

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