Betriebswirtschaftliche Bewertungsmethoden Studiengänge B.A. Business Administration

1. Betriebswirtschaftliche Bewertungsmethoden Studiengänge B.A. Business Administration Prof. Dr.Rainer Stachuletz Corporate Finance Fachhochschule für Wirtschaft Berlin Berlin School of Economics Winter 2006/2007

2. 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.

3. 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.

4. GE1 Y1 PA b1A Y0 V0A a0A GE0 Fisher - SeparationConsumption and Real Asset Investments 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.

5. GE1 UA Y1 PA b1A T V0A Y0 a0A GE0 Fisher SeparationConsumption and Real Investments 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.

6. (0) U A (0) U B Fisher Separation Consumption and Real Investments GE1 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. Y1 PA b1A PB b1B T Y0 V0A a0A GE0 a0B V0B

7. GE1 tg a = - 1+ i -1+ i Y1 PAF PA PAI GE0 Y0 Fisher SeparationConsumption, Financial + Real Asset Investments 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).

8. GE1 Y1 UA P a1 PA b1 e1 T r0 Y0 Z0 a0 GE0 C0 = NPV V0 F0 Fisher SeparationConsumption, Financial + Real Asset Investments The optimal real-investment pro-gramme is given at P. At an avai-lable income of Y0and a given consumption plan of V0 without financial markets only a proportion of r0would be invested, generating an income of e1 in t1. The economy would be underinvested. As financial markets exist, it would be possible to borrow F0to realizethe 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.

9. (0) U A (1) U B (0) U B (1) (1) V0A a 0 Fisher SeparationSeparability of Consumption and Investment GE1 The 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 a0despite 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. Z1 (1) U A Y1 b1A P a1B b1 Financ. Inv. A Real Invest. A Consumpt. A Y0 GE0 F0A Z0 (1) F0B V 0B

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

11. - 1 × 40.000 1,07 - 2 × 40.000 1,07 - 3 × 1.040.000 1,07 Valuation - Spot Rates (“Flat” Rate) t t t t 0 1 2 3 40.000,00 40.000,00 1.040.000,00 Market Value 37.383,18 34.937,55 848.949,79 921.270,52

12. Valuation - Spot Rates (Yields)

13. t t t t 0 1 2 3 40.000,00 40.000,00 1.040.000,00 Market Value ? 971.962,62 - Loan: interest 7 % Interest 7 % interest 7 % 971962,62 - 68.037,38 - 68.037,38 - 68.037,38 Difference: 0 Difference: - 28.037,38 + 26.450,36 Investment: interest 6 % interest 6 % - 26.450,36 + 1.587,02 + 1.587,02 Difference: 0 Difference: - 26.450,36 25.190,82 Investment: Interest: 5 % 1.259,54 - 25.190,82 Difference: 0 920.321,44 Valuation - Spot RatesDuplication-Portfolio

14. 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 € Which Value is the Right One ? Three approaches lead to three results: But which is the right one ??????

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

16. Term – Structure of Interest Rates and related Spot Rates (Calculation) Example: