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# Npv rule

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### Npv rule

1. 1. Investment Decision Rules We illustrated that the best strategy for our investor was to invest in real assets only if their rate of return exceeds that of the capital market. The decision rule is: Accept all projects that have an expected rate of return that is greater than the rate of return on the capital market.
2. 2. Many One-Period Investments Suppose that as well as investing in the market an individual could invest in several real assets offering the following payoffs. Rate of return on the capital market is 20%. This is the same example as in previous set of slides. Investment Outlay Payoff Return in t0 in t1 A 100 110 10% B 100 125 25% C 100 150 50% D 100 200 100%
3. 3. The objective of the investor is maximisehis wealth. Does the above decision rule achieve this? We showed that the present value of cash flows from investments when only those which have a higher rate return than the capital market are accepted is €496 (€495.83 rounded up). This cannot be bettered by any other combination of investments.
4. 4. A more Direct Method Why not directly compute the change in wealth from a project? Accept any project that adds to wealth and reject any project which reduces wealth. If all projects that add to wealth are accepted and all that reduce wealth are rejected then wealth will be maximised.
5. 5. NET PRESENT VALUE (NPV) NPV measures the additional amount that a project adds to an individual’s wealth. A project’s NPV is the Present Value of its future cash inflows discounted at the opportunity cost of capital (rate of return on the capital market) less its initial Cost. A project’s present value is the wealth that the project contributes. Its NPV is the incremental contribution to wealth of the project.
6. 6. Net Present Value (NPV) in Single PeriodCase.NPV = PV - required investment C1NPV = - C 0 + 1+ r
7. 7. NPV Decision Rule Invest in all projects where the PV of future cash flows is greater than the initial cost. That is where the NET PRESENT VALUE is greater than 0.
8. 8. The NPV rule applied to our Example Investment Outlay in Payoff in PV of NPV t0 t1 Payoff A 100 110 91.67 -8.33 B 100 125 104.17 4.16 C 100 150 125 25 D 100 200 166.67 66.67
9. 9. • Cleary project A will not be taken.• If 100 euro is invested in the capital Market with it hasan NPV of 0.• The total of the NPVs is (4.16+25+66.67= 95.83) Thisoverall NPV plus the capital of 400 euro the individualoriginally had comes to €495.83 which is the maximumwealth that this individual can attain Given theinvestment opportunities available to him.Note we have worked out the best strategy using todifferent decision rules. The (internal) rate of return ruleand the NPV decision rule. Both given exactly the sameanswer in this situation.
10. 10. The NPV and Corporations (Companies) The previous slides have illustrated how applying the NPV rule that an individual can make decisions to maximise his wealth. Does this also apply to companies in which the individual has shares?
11. 11. Maximisation of Company Value Since by increasing the value of the firm is the only way in which management can influence shareholders wealth, their objective must be to maximise the value of the firm. This objective is achieved by accepting all projects with an NPV > 0.
12. 12. Atours PLC Balance Sheet in Market ValuesFixed Assets 100,000 Shareholders 120,000 EquityCash 20,000Market Value 120,000 Market Value 120,000of Assets of Equity
13. 13. Suppose that Atours has an investment opportunitythat costs €20,000. Its balance sheet after taking onthe investment is outlined in table 2. Table 2 Atours PLC Balance Sheet in Market Values Fixed Assets 100,000 Shareholders 100,000 + PV Equity Project PV Market Value 100,000 + PV Market Value 100,000 + PV of Assets of Equity
14. 14. The project is worth the present value of its future cash flows (PV). Clearly the firm should take the project if: 100,000 + PV > 120,000 or PV - 20,000 > 0 i.e. NPV >0 Decision Rule: That is a firm should take every project that has a Net Present Value greater than zero.
15. 15. Arranging consumption patterns If we return to the original example where we have 4 projects which cost €100 each. However, our individual needs €200 euro to spend in t0. What should he do? Should he only take the projects with the highest NPVs?
16. 16. If the investor needed to spend €200 euroin t0 and just invests in C and D Present Value of Cash Flows T0 T1 Consumed Cash 400 0 Invest -200 Payoff 350 Consume 200 350 491.67
17. 17. If he uses the capital market Present Value of Cash Flows T0 T1 Consumed Cash 400 0 Invest -300 Borrow 100 Payoff 475 Repay 120Consume 200 355 495.83
18. 18. Lesson Regardless of the desired consumption pattern invest in ALL projects with a positive NPV: then use the capital market to adjust consumption to the desired level.
19. 19. But Different Shareholders have differentpreferences The firms’ cost of capital will be the same for all shareholders. However, some shareholders would like to consume more now and others are more willing to defer consumption. Can the firm keep both types of shareholder happy?
20. 20. Maximisation of Welfare AFTER an individual has maximised his wealth through investing in projects with positive NPVs he can then and only then maximise his welfare by using the capital market to spread the consumption of his wealth to suit himself. Borrowing and lending on the capital market do not change an individual’s wealth but it can make him better off.
21. 21. Separation of Ownership from Control When there is a perfect capital market the management of a company can make investment decisions independently of shareholders consumption requirements.
22. 22. Perfect Capital Market Borrowing rate equals lending rate Everyone can borrow and lend as much as they wish at these rates No transactions costs Information is freely available to all Instantaneous Access to the Market No TAXESNote- we have also assumed certainty
23. 23. Consider two individuals Consumpta Clubb and Prudence Paragon , each of whom owns 50% of Cash Bo Ltd. Cash Bo’s only asset is €3000 in cash so Consumpta and Prudence investments are worth €1500 each. The firm is faced with a choice of three projectsProject T0 T1 Initial InvestmentA 1000 1700B 1000 1300C 1000 1100
24. 24. The rate of interest in the capital market is 20%. NPV IRR (Rate of Return)A 417 70%B 83 30%C -83 10%
25. 25. The Shareholders have DifferentConsumption Requirements Using the NPV or IRR rule suggests taking A with B and rejecting C. However, Consumpta needs money straight away and asks the firm to pay a Dividend of €1500 each right now. Prudence does not need any money at the moment and suggests that the firm invest all its spare cash on her behalf.
26. 26. Firm’s Cash FlowsCash Flows if Projects A and B are takenAssume that spare cash is paid out as Dividends T0 T1Cash on Hand 3000Invest in A and B (2000) 3000Investment in -Capital MarketDividends for (1000) (3000)Shareholders
27. 27. The Spender’s Cash Flows Cash Flows and Consumption of Consumpta T0 T1 Dividends 500 1500 Borrow 1250 Repay (1500) Consumption 1750 0
28. 28. The Saver’s (Prudence) Cash Flows Cash Flows and Consumption of Prudence T0 T1 Dividends 500 1500 Lend (500) Payoff from 600 Lending Consumption 0 2100
29. 29. Separation Theorem Provided that there is a perfect capital market the firm makes the shareholders better off by maximising its own value. It achieves this by taking all projects with positive NPVs. The shareholders then maximise their own welfare by using the capital market as necessary. This separation of the investment and consumption decisions facilitates the separation of ownership from control