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# Net Present Value and Other Investment Rules

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1. Key Concepts and Skills • Be able to compute payback and discounted payback and understand their shortcomings • Be able to compute the internal rate of return and profitability index, understanding the strengths and weaknesses of both approaches • Be able to compute net present value and understand why it is the best decision criterion

2. 1.Net Present Value • NPV is the difference between the market value of a project and its cost or how much value is created from undertaking an investment. • The first step is to estimate the expected future cash flows. • The second step is to estimate the required return for projects of this risk level. • The third step is to find the present value of the cash flows and subtract the initial investment, which is the NPV.

3. Why Use Net Present Value? • Accepting positive NPV projects benefits shareholders. • NPV uses cash flows • NPV uses all the cash flows of the project • NPV discounts the cash flows properly

4. n CFt ∑ PV = (1 + R)t t = 0 Net Present Value Sum of the PVs of all cash flows NOTE: t = 0 Initial cost often is CF0 and is an outflow. n CFt ∑ - CF0 NPV = (1 + R)t t = 1 Initial Outlay

5. NPV – Decision Rule If the NPV is positive, accept the project. Reject if negative. • A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. • Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.

6. Calculating NPV with Spreadsheets • Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well. • Using the NPV function: • The first component is the required return entered as a decimal. • The second component is the range of cash flows beginning with year 1. • Add the initial investment after computing the NPV.

7. 2. Payback Period • How long does it take to get the initial cost back in a nominal sense? • Computation • Estimate the cash flows • Subtract the future cash flows from the initial cost until the initial investment has been recovered • Decision Rule – Accept if the payback period is less than some preset limit

8. The Payback Period Method • Disadvantages: • Ignores the time value of money • Ignores cash flows after the payback period • Biased against long-term projects • Requires an arbitrary acceptance criteria • A project accepted based on the payback criteria may not have a positive NPV

9. The Payback Period Method • Disadvantages: • Ignores the time value of money • Ignores cash flows after the payback period • Biased against long-term projects • Requires an arbitrary acceptance criteria • A project accepted based on the payback criteria may not have a positive NPV • Advantages: • Easy to understand • Biased toward liquidity

10. 3.Discounted Payback Period • Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis • Compare to a specified required period • Decision Rule - Accept the project if it pays back on a discounted basis withinthe specified time

11. 4. Profitability Index • For conventional CF Projects: PV(Cash Inflows) Absolute Value of Initial Investment • PI is essentially a Benefit/Cost Ratio • Minimum Acceptance Criteria: • Accept if PI > 1

12. Advantages and Disadvantages of the Profitability Index • Advantages • Closely related to NPV, generally leading to identical decisions • Easy to understand and communicate • May be useful when available investment funds are limited • Disadvantages • May lead to incorrect decisions in comparisons of mutually exclusive investments PI = PV(future CF) | Initial Outlay |

13. 4 Internal Rate of Return • IRRis the most important alternative to NPV • It is often used in practice and is intuitively appealing • It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere

14. The Internal Rate of Return • IRR: the discount rate that sets NPV to zero • Minimum Acceptance Criteria: • Accept if the IRR exceeds the required return • Ranking Criteria: • Select alternative with the highest IRR

15. Similarity Between NPV & IRR Formulas NPV: Enter R and solve for NPV IRR: Enter NPV = 0, solve for IRR.

16. 5.5 Problems with IRR • Multiple IRRs • The Scale Problem • Mutually Exclusive Projects

17. \$200 \$800 0 1 2 3 100% = IRR2 - \$800 -\$200 0% = IRR1 Multiple IRRs There are two IRRs for this project: Which one should we use?

18. ModifiedInternal Rate of Return (MIRR) • Controls for some problems with IRR Three Methods: • DiscountingApproach • Reinvestment Approach • 3. Combination Approach • MIRRwill be different number for each method • For this reason, some of us call it the Meaningless IRR rather than the Modified IRR.

19. Best Method for MIRR MIRR Method 1DiscountingApproach Step 1: Discount future outflows (negative cash flows) to present and add to CF0 Step 2: Zero out negative cash flows which have been added to CF0. Step 3: Compute IRR normally

20. MIRR Method 2ReinvestmentApproach Step 1: Compound ALL cash flows (except CF0) to end of project’s life Step 2: Zero out all cash flows which have been added to the last year of the project’s life. Step 3: Compute IRR normally

21. MIRR Method 3CombinationApproach Step 1: Discount all outflows (except CF0) to present and add to CF0. Step 2: Compound all cash inflows to end of project’s life Step 3: Compute IRR normally

22. The Scale Problem How to deal with this issue? - Calculate incremental IRR or NPV of incremental cash flows

23. Dealing with The Scale Problem How to justify the large budget using the IRR approach?

24. Dealing with The Scale Problem • Formula for Calculating the Incremental IRR: • IRR=66.67% • NPV of Incremental Cash Flows:

25. IRR and Mutually Exclusive Projects • Mutually exclusive projects • If you choose one, you can’t choose the other • Example: You can choose pursue an MBA at • either the UWM or Marquette, but not both • Intuitively you would use the following decision rules: • NPV – choose the project with the higher NPV • IRR – choose the project with the higher IRR

26. Example With Mutually Exclusive Projects The required return for both projects is 10%. Which project should you accept and why?

27. NPV Profiles IRR for A = 19.43% IRR for B = 22.17% Crossover Point = 11.8%

28. With the cross– over in the NPV profiles, we find that the better project depends critically on the required return. When the required return is low (less than 11.8%), pick project A. When the required return is high (greater than 11.8%), pick project B. Mutually Exclusive

29. NPV vs. IRR • NPV and IRR will generally give us the same decision With Two Exceptions: • Non-conventional cash flows – cash flow signs change more than once • There can be multiple IRRs for the same project • Mutually exclusive projects • Initial investments are substantially different • Timing of cash flows is substantially different

30. 5.7 The Practice of Capital Budgeting • Varies by industry: • Some firms may use payback, while others choose an alternative approach. • The most frequently used technique for large corporations is either IRR or NPV.