fisher separation theorem

2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityChapter 2

Consumption, Investment and the Capital Market

Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National University

2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityLearning ObjectivesExplain how a companys managers can, in principle, make financial decisions that will be supported by all shareholders.Explain how the existence of a capital market makes this result possible.Identify the companys optimal investment/dividend policy under conditions of certainty.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem:A Simplified ExampleThe foundation for many fundamental results of finance theory:How a company deals with diverse preferences for dividends and investment when there is more than one shareholder.Assumptions under capital market:Certainty, frictionless, and interest rate for borrowers equals interest rate for lenders.Implication of theorem:A company can make dividend/investment decisions that are in the best interests of all shareholders, regardless of differences in the preferences of individual shareholders.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem:A Simplified Example (cont.)Example 1: Assume capital market does not existA company has only two shareholders (A and B), who hold equal shares of $800 each.Project Small involves $500 outlay now and $570 cash flow later. But Project Upgrade requires outlay of an additional $200 and incremental cash flow of $220.Project Upgrade can only be undertaken together with Project Small, forming Project Large.Projects Small and Large enable dividends, of $300 and $100 respectively, to be paid now.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem:A Simplified Example (cont.)Example 1: Assume capital market does not exist (cont.)Projects Small and Large enable dividends, of $570 and $790 respectively, to be paid later.Assume Shareholder A wishes to consume $150 now, and shareholder B wishes to consume only $50 now.Note: Given A and Bs consumption preferences, A will want the company to invest in Project Small, while B will prefer Project Large. Clearly, the company cannot make a decision that will satisfy both shareholders simultaneously. Therefore, it is impossible to say which investment is optimal.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem:A Simplified Example (cont.)Solution:Introduce a capital market (CM).Essentially, the shareholders can lend excess income (dividends) in the CM or borrow to satisfy current consumption if current dividends are insufficient.A resolution is possible because the CM enables:One of the shareholders to achieve a result that is better than the result the company alone could provide.Using the net present value (NPV) rule for optimal investment decision.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityAssume the interest rate is 12% in the CM, then calculate the rates of return for each project and compare.Project Small returns 14% while Project Upgrade returns 10%.Hence, only invest in Project Small, leaving $300 in dividends.Shareholder A gets $150 now, as desired.Shareholder B also gets $150 now, but only wants $50, so lends $100 in the capital market at 12%, receiving $112 later.Fishers Separation Theorem:A Simplified Example (cont.)


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal ApproachThe theorem attempts to provide a consistent set of rules to make investment, financing and dividend decisions. Although initially developed in a simplified setting, the rules are applicable even when more realistic assumptions are made.Assumptions in Fishers analysis:Only two points in time: present Time 1, future Time 2.There are no uncertainties or imperfections in the CM, and all decision makers are rational.The companys managers wish to use the companys resources according to the wishes of the shareholders.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)The company:Endowed with a fixed amount of resources at Time 1.Managers must decide how much to invest and pay as dividends.The level of investment at Time 1 determines:The residual resources at Time 1, available as a dividend at Time 1.The resources that will be available to be paid as dividends at Time 2.These opportunities can be summarised in a production possibilities curve (PPC).


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)PPC decisions (assuming 200 units of resources in Time 1) (Figure 2.1)Point (200, 0) whole 200 paid as dividend at Time 1, investment is zero, dividend at Time 2 is zero.Point (0, 250) no dividend at Time 1, whole of resources invested at Time 1, resources of 250 available for distribution at Time 2.Point Q (150, 160) intermediate case. Time 1 dividend of 150, 50 invested. Time 2 resources of 160 available.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)The shareholders:Forgo current consumption by investing in a company at Time 1 in order to earn a return that increases consumption opportunities at Time 2.A persons preference for consumption at Time 1 or 2 can be represented by indifference curves all combinations of Time 1 and Time 2 consumption on the same indifference curve make the consumer equally well off.Convex shape of indifference curves shows that a consumers desire to increase consumption at a given time decreases as the consumption level at that time increases (decreasing marginal utility). See Figure 2.2.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)The companys decision:Bringing the company and shareholders together what investment/dividend decision should be made?Assuming two shareholders, A and B, with indifference curves A1, A2, A3 and B1, B2, B3.As can be seen in the following diagram, Shareholder As utility is maximised at point A, while Shareholder Bs utility is maximised at point B. See Figure 2.3.For example: Shareholder A would be worse off at any point on indifference curve A1 than point A, on A2 and any point on the indifference curve A3 is not possible.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)Figure 2.3: There is no simple investment decision that can maximise both shareholders utility simultaneously:If we choose point A, Shareholder B is disappointed as he/she ends up on the lower indifference curve B1, rather than on B2 at point B (of course, this would disappoint Shareholder A). However, a solution exists if there is a capital market (CM).In capital market, current resources may be transformed into future resources and vice versa. Assume capital market is frictionless (interest rate is the same for borrowers and lenders).


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)The market opportunity line can be used to show the combinations of current and future consumption that an individual can achieve from a given wealth level, using capital market transactions:


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)Figure on next slide: Shows that an income stream of 140, 121 and a capital market with 10% interest can satisfy two investors (A, B) through borrowing and lending/investing by:Maximising their wealth.Maximising their utility.See pp. 202 for a more detailed interpretation of market opportunity line and company policy effect on shareholders wealth.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)Market Opportunity LineC A/B A C B140


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)Proving there is an optimal policy:Figure 2.7 combines preferences of shareholders A and B with companys optimal choice.Choices P1 and P2 provide shareholders with inferior utility to the choice of P.Shareholders do not consume at point P.The capital market allows them to consume at PA and PB respectively.This maximises shareholders wealth.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)Identifying the optimal policy:The following decision rule should be used:Accept the project if and only if:


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)The previous decision rule is called the net present value rule.The return next period is divided by the factor (1 + i) to convert the future return to present value. The investment outlay is then subtracted from the present value to give the net present value (NPV).If the NPV is positive, the project will increase the wealth of the shareholders and should, therefore, be accepted.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)Implications for financial decision-making:There are implications for investment, financing and dividend decisions:Implications hold where there are perfect markets for both capital and information.Implications unaffected by the introduction of uncertainty, provided all participants have the same expectations.Implications unaffected by extension to the multi-period case.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)The investment decision:The theorem means that a company can make investment decisions in the interests of every shareholder, regardless of differences between shareholders preferences.NPV analysis can be used to identify the optimal decision.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)The financing decision:Fishers analysis uses a single-market interest rate.No distinction between debt and equity securities, and cost to company of acquiring funds, is independent of the type of security issued.Value of company and wealth of shareholders are independent of the companys capital structure.Financing decision is irrelevant.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityFishers Separation Theorem: A Formal Approach (cont.)The dividend decision:Dividend decision is irrelevant, provided the company does not alter its investment decision.This is possible because, unlike the situation in Fishers analysis, companies can lend or borrow in the capital market themselves.For example, a company can pay a higher dividend and still maintain the optimal level of investment by borrowing in the capital market.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityInvestors Reactions to Managers Decisions supplies funds to transact in transmits information toFigure 2.11COMPANYmakes an investment, funding or dividend decisionCAPITAL MARKETThere is a consequent effect on the company's share priceINVESTORSadjust their expectations


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityInvestors Reactions to Managers Decisions (cont.)A companys managers make investment, financing and/or dividend decisions.The information of these decisions is transmitted to investors.Investors may adjust their expectations of future returns from an investment and revise their valuation of the companys shares.Investors compare the market price with their revised valuation and either buy or sell shares in the company.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversityInvestors Reactions to Managers Decisions (cont.)Certainty:If all investors knew an investments cash flows, they would know its NPV. Hence, share price of company would go up.Uncertainty:In practice, there is uncertainty.Effect of managers decisions on the share price is no longer predictable. A simplification is to assume that share price will adjust immediately to reflect the true value of the company.Empirical evidence suggests investors react quickly to the receipt of new information since information is reflected on security prices.


2-*Copyright 2009 McGraw-Hill Australia Pty Ltd PPTs t/a Business Finance 10e by PeirsonSlides prepared by Farida Akhtar and Barry Oliver, Australian National UniversitySummaryHow can diverse investors all be satisfied with the decisions of management?Fishers separation theorem tells us that if there is a capital market, managers are able to make decisions that will satisfy all shareholders.Companies should maximise shareholder wealth and let shareholders use the capital market to allocate this wealth over time.Company and shareholders decisions are separate.


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fisher separation theorem

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