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    2. Internal Rate of Return (IRR) IRR is the rate of return or discount rate that makes the NPV = 0. Decision Rule: Accept the project if the IRR is greater than the required return

    3. Internal Rate of Return (IRR) This is the most important alternative to NPV. It is often used in practice and is intuitively appealing. It is based entirely on the estimated cashflows and is independent of interest rates found elsewhere. Without a financial calculator, this becomes a trial and error process.

    4. Internal Rate of Return (IRR) A critical thing to note is that there should be at least one change of sign in order to realise IRR. there should be a negative net cashflow among positive net cashflows or a positive cashflow among negative cashflows. The change in sign is crucial.

    5. Internal Rate of Return (IRR) Using a spreadsheet; Start with the cashflows. You first enter your range of cashflows, beginning with the initial cash outlay (negative).

    6. Internal Rate of Return (IRR) Call the IRR function Choose insert on the menu bar Select function Choose IRR from among the list Select the range of cashflows Enter a guess rate, but it is not necessary; Excel will start at 10% as a default The default format is a whole percent you will normally want to increase the decimal places to at least two to get the most accurate output.

    7. Internal Rate of Return (IRR) NPV and IRR will generally give us the same decision. There are however some exceptions. Non-conventional cashflows cashflow signs change more than once Mutually exclusive projects Initial investments are substantially different Timing of cashflows is substantially different

    8. Internal Rate of Return (IRR) When the cashflows change sign more than once, there is more than one IRR. When we solve for IRR it would be noticed that we are solving for the root of an equation and when we cross the x-axis more than once, there will be more than one return that solves the equation. Therefore, IRR may be unreliable if we have any negative cashflows after our original investment.

    9. Internal Rate of Return (IRR) Suppose an investment will cost 90,000 initially and will generate the following cashflows: Year 1: 132,000 Year 2: 100,000 Year 3: -150,000 The required return is 15%. Should we accept or reject the project?

    10. Internal Rate of Return (IRR)

    11. Internal Rate of Return (IRR) Mutually exclusive projects If you choose one, you cant choose the other Example: You can choose to attend graduate school next year at either Legon or Central, but not both

    12. Internal Rate of Return (IRR) Intuitively you would use the following decision rules: NPV choose the project with the higher NPV IRR choose the project with the higher IRR

    13. Internal Rate of Return (IRR)

    14. Internal Rate of Return (IRR) The required return for both projects is 10%. Which project should you accept and why? (Accept Project A because of NPV)

    15. Internal Rate of Return (IRR) Conflicts between NPV and IRR NPV directly measures the increase in value to the firm. Whenever there is a conflict between NPV and another decision rule, you should always use NPV. IRR is unreliable in the following situations Non-conventional cashflows Mutually exclusive projects

    16. Internal Rate of Return (IRR) Advantages of IRR It takes into account the time value of money, which is a good basis for decision-making. Results are expressed as a simple percentage, and are more easily understood than some other methods. It indicates how sensitive decisions are to a change in interest rates.

    17. Internal Rate of Return (IRR) Advantages of IRR It is a simple way to communicate the value of a project to someone who doesnt know all the estimation details. If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task.

    18. Internal Rate of Return (IRR) Advantages of IRR It is a simple way to communicate the value of a project to someone who doesnt know all the estimation details. If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task.

    19. Internal Rate of Return (IRR) Disadvantages For mutually exclusive projects: timing and scale differences. This may lead to incorrect decisions in comparisons of mutually exclusive investments. Assumes funds are re-invested at a rate equivalent to the IRR itself, which may be unrealistically high.

    20. Internal Rate of Return (IRR) IRR will produce more than one mathematically correct rate for each year in which inflows are followed by outflows and vice versa. This is common with projects with unconventional cashflows. This can create some confusion to the user.

    21. Choice of Discount Rate Cost of capital - weighted average and marginal (financing rate) Opportunity cost of capital - what could they earn if that money was elsewhere Current capital position and expected capital position over next few years The rates of return for alternative investments. Market sentiments.

    22. Sources of discount rate Banks Long term government papers Ministry of Finance Sponsors

    23. Suggestions For industrial projects use market rate or cost of borrowing funds. For public sector projects use social time preference rate. For public projects to be funded from international loans use the cost of borrowing.

    24. Suggestions Generally, in financial analysis, the market rate is used, whilst the social time preference rate is used for public sector projects. When funding comes from various sources or from the same source but at different rates, then, compute and use the weighted average.

    25. Choosing Year 0 or Year 1 World Bank World Bank believes that since investment is made and some returns may accrue from the first year, then discounting should start from 0 to first year. In this case, the initial year is Year 1.

    26. Choosing Year 0 or Year 1 Others Other international originations use Year 0. Their argument is that investment must take place before benefits accrue. Thus, discounting should start from the second year. Choose any convention but be consistent.

    27. Deciding on a Project We should consider several investment criteria when making decisions. NPV and IRR are the most commonly used primary investment criteria. Payback is a commonly used secondary investment criteria, but only because of its ease of use.

    28. Deciding on a Project For a single project, a positive NPV indicates acceptability. For multiple (competing) projects, the project(s) with the highest NPVs should receive highest priority.