Betriebswirtschaftliche Bewertungsmethoden Studiengänge B.A. Business Administration

slide no.: 1Prof. Dr. Rainer Stachuletz – Berlin School of Economics

Betriebswirtschaftliche Bewertungsmethoden

Studiengänge B.A. Business Administration

Prof. Dr.Rainer StachuletzCorporate Finance

Fachhochschule für Wirtschaft BerlinBerlin School of Economics

Winter 2006/2007


Fisher - SeparationNeanderthalian Consumption Patterns

Some people prefer to consume now, some to invest now and consume later.

Without investment opportunities, consumers can only decide whether to consume now or later.

0

20

40

60

80

100

120

0 20 40 60 80 100 120


0

10

20

30

40

50

60

70

80

90

100

110

120

0 10 20 30 40 50 60 70 80 90 100 110

Fisher - SeparationConsumption Patterns and Financial

Markets

If there were financial investment opportuni-ties, a household can decide to lend a part of his income to financial markets. At an interest rate of i.e. 20% p.a. and a consumption pattern of (40:60), the household will then enjoy 72 in t 1.

Financial markets increase wealth.


Fisher - SeparationConsumption and Real Asset Investments

GE0

V0A Y0

PA

Y1

GE1

b1A

a0A

To invest always means a decision between consumption (V0A) and investment (a0A). What you invest in to, you will earn one period later. (b1A).

Given an income (Y0), the graph shows all possible combinations of consumption and investment-plans). This „transformation - function“ is convex shaped, because of the generally declining marginal prod-uctivity of real - asset investments. From Y0 each unit of invested money will first lead to a relatively higher future income, later (when investing your money in less profitable projects) it will lead to a lower future income.


Fisher SeparationConsumption and Real Investments

GE0

V0A Y0

PA

Y1

GE1

b1A

a0A

UA

T

The individual combination of consumption/investment depends on the individual utility function.

The utility - function UA describes all combinations, providing the same utility to a specific individual.

The optimum consumption/ investment-pattern is then given at (PA), where the utility function becomes tangent to the the transfor-mation function.


Fisher SeparationConsumption and Real Investments

a0B

GE0

Y0

V0B

PB

PA

U A(0)

U B(0)Y1

b1A

b1B

GE1

V0A a0A

T

The figure shows the invest-ment (a0) and consumption-budgets (V0) of two investors (A und B).

Investor A plans to invest (a0A) more than he wants to spend on immediate consumption (V0A). From his investment he can expect a future income of b1a.

Investor B prefers to consume (V0B) and to invest less (a0B). From his investment he can expect to get b1B. His future consumption budget may then be lower than that of Investor A.


Fisher SeparationConsumption, Financial + Real Asset

Investments

GE0Y0

PA

Y1

GE1

-1+ itg = - 1+ i

PAI

PAF

Real investments compete with financial investments. This compe-tition is shown by the combination of the two transformation– functions.The slope of the financial market line is determined by the interest rate, given by (1+i), i.e. each currency unit invested in financial assets (f0A) leads to a future income of f0A (1+i).Where the functions become tangent (that is PA), the profitability of real asset investments equal the profits from financial asset investments. Below PA, real asset investements are more attractive (i.e.PAI) , above PA financial assets become superior (i.e. PAF).


Fisher SeparationConsumption, Financial + Real Asset

Investments

a1

PA

GE0V0

Y0

Y1

GE1

UA

T

a0

P

b1

Z0

C0 = NPV

e1

r0

F0

The optimal real-investment pro-gramme is given at P. At an avai-lable income of Y0 and a given consumption plan of V0 without financial markets only a proportion of r0 would be invested, generating an income of e1 in t1. The economy would be underinvested.

As financial markets exist, it would be possible to borrow F0 to realize the optimal investment programme a0. This programme will generate a future income of b1 in t1. Subtrac-ting a1 (interest and repayment) the reamaining income in t1 will be higher than in a world without financial market.


GE0

Y0

U A

(0)

U B

(1)

GE1

P

U A

(1)

U B(0)

V 0B

(1)

V0A(1) F0A

F0B

Y1

a 0

(1)

Z1

Z0

b1

b1A

a1B

Consumpt.A

Financ. Inv.A

Real Invest.A

i1

b1

(1)

0 c

Fisher SeparationSeparability of Consumption and

InvestmentThe graph shows the theoretical independency of consumption and investment plans under ideal financial market conditions. Two investors, A and B, can realize the same programme a0 despite of their different consumption plans VOA resp. VOB.

While B has to borrow (F0B), A can realize the real-investment programme a0 and will invest a part (F0A) of her income at an interest rate of i in financial assets.


Term – Structure of Interest Rates Germany (2000 – 2005)

4,97%4,90% 4,88% 4,89% 4,92% 4,96% 5,00% 5,05% 5,09% 5,14%

3,12% 3,17%

3,39%

3,62%

3,82%

3,99%

4,14%4,27%

4,38%4,47%

2,41%

2,85%

3,23%

3,54%

3,81%

4,21%

4,37%4,50%

4,61%

2,22%

2,41%

2,64%

2,88%

3,10%

3,33%

3,48%

3,64%3,78%

3,90%

3,48%

4,03%

2,79%

2,62%

2,41%

2,93%

3,06%

3,17%3,26%

3,34%3,42%

2,00%

2,50%

3,00%

3,50%

4,00%

4,50%

5,00%

5,50%

1 2 3 4 5 6 7 8 9 10

1. November 2000

1. November 2001

1. November 2003

1. November 2004

1. November 2005


Valuation - Spot Rates (“Flat” Rate)

t t 1 t t

40.000,00 40.000,00 1.040.000,00

37.383,18

34.937,55

848.949,79

2-×1,0740.000

3-×1,071.040.000

0 2 3

921.270,52

Market Value

11,0740.000 -×


t 0 t 1 t 2 t 3

4 0 . 0 0 0 , 0 0 4 0 . 0 0 0 , 0 0 1 . 0 4 0 . 0 0 0 , 0 0

3 8 . 0 9 5 , 2 4

3 5 . 5 9 9 , 8 6

8 4 8 . 9 4 9 , 7 9

9 2 2 . 6 4 4 , 8 9

M a r k t w e r t ?

11,0540.000

2 1,0640.000

3 1,071.040.000

Valuation - Spot Rates (Yields)


t 0 t 1 t 2 t 3

40.000,00 40.000,00 1.040.000,00

Loan:

971962,62

-971.962,62 interest 7 % Interest 7 % interest 7 %

- 68.037,38

- 68.037,38

- 68.037,38

Difference: 0

Difference: - 28.037,38

Investment:

- 26.450,36

+ 26.450,36 interest 6 % interest 6 %

+ 1.587,02

+ 1.587,02

Difference: 0

Difference: - 26.450,36

Investment:

- 25.190,82

25.190,82

Interest: 5 %

1.259,54

Difference: 0

Market Value ?

920.321,44

Valuation - Spot RatesDuplication-Portfolio


Which Value is the Right One ?

Three approaches lead to three results:

But which is the right one ??????

Valuation Mode Result (P.V.)

3y Interest Rate flat (7%) 921.270,52 €

Term – Structure of Interest Rates (5,6,7%)

922.644,89 €

Duplication of Cash Flows 920.321,44 €


Always Use Spot Rates to Determinethe

Price of a Future Cash Flow 1 2 3

Yield 5% 6% 7%

Spot Rates 5% 6,03% 7,1%

00010711

0701

06031

70

051

70

40510021071

0701

061

70

051

70

32

32

.,

.

,,

,.,

.

,,

Proof :

(Bond, threeyears to matu-rity, 7% cou-pon rate.)


t r[t] q[s,t] r[s,t]

1 2,41% 1,0241 2,41%2 2,85% 1,028562975 2,86%3 3,23% 1,032472836 3,25%4 3,54% 1,03571334 3,57%5 3,81% 1,038588645 3,86%6 4,03% 1,040972195 4,10%7 4,21% 1,042955747 4,30%8 4,37% 1,044757588 4,48%9 4,50% 1,046243224 4,62%

10 4,61% 1,047521695 4,75%

t

1

1t

1i

it,st

tt,s

qr1

r1q

Term – Structure of Interest Rates and related Spot Rates (Calculation)

Example:

%,,,,,

,, 5731

03247102856102411035401

03541 4

1

3214

sr

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Betriebswirtschaftliche Bewertungsmethoden Studiengänge B.A. Business Administration