Net present value is the difference between a project s value and its costs.

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2 2 Net present value is the difference between a project s value and its costs. We need to calculate the Present Value of future cash flows (discounted by the opportunity cost of capital) and subtract our initial investment.

3 3 Net present value measures each project's contribution to shareholder wealth. Companies can best help their shareholders by investing in projects with a positive net present value. While there are several long-term investment decision criteria, the net present value method is favored because it tends to focus on building shareholder value and has the fewest limiting assumptions

4 The bottom equation should look familiar it is a time value of money equation. Note the Co is an outflow. Other terms can also be negative, but in most of our examples we have an outflow followed by positive cash flows. 4

5 5

6 Note that the present value (sum of the discounted cash flows) is what the project is worth. We should not pay more than that amount for it. But if we can purchase this project for less, we will add value to the firm. 6

7 7

8 The Net Present Value tells us how much value (in dollars) we are adding to the firm by adopting this project. 8

9 If the NPV is negative or zero, we should reject the project. 9

10 10

11 If we are choosing between two (or more) competing projects called mutually exclusive projects because we will pick only one winner then you should pick the project with the highest NPV because it will add the most value to the firm. 11

12 12 Should I invest now or should I wait? When to make an investment is difficult in a dynamic world, where cost-saving technology is always improving and NPVs are greater if delayed until later. The right time to purchase an ever-increasing NPV investment is indicated by the highest present value of future NPVs, found by discounting the estimated NPV of projects made in future periods by the opportunity cost of capital. Remember to discount everything back to the current period. The decision rule for investment timing is that you chose the investment date that results in the highest NPV today.

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14 Note: here we are concerned only with expenses, the revenues generated would be the same. You can use your financial calculators to find Equivalent Annual Costs: (First find NPV of both projects: i = 10) Cfo= -500 Cfo= -600 Cf1= -120 Cf1= -100 Cf2= -120 Cf2= -100 Cf3= -120 Cf3= -100 Cf4= -100 Then treat as an annuity. PV=798.42, n=3, i = 10, FV =0 Calc PMT = PV=916.99, n=4, i = 10, FV =0 Calc PMT =

15 An alternative method. Assume that the projects can be renewed until they have a common expiration date. 15

16 IRR is first alternative to NPV. Many companies use IRR, but it must be used with caution. 16

17 17 IRR is the discount rate generated when we set the NPV equal to zero. The IRR is the hurdle rate, we must earn more than it to accept the project.

18 18

19 Notice at the IRR of 19.44% the NPV is zero. 19

20 Let s take a look at some pitfalls for the IRR. Lending or Borrowing: The IRR does not distinguish between the two. Example, if you spend 100 and get back 130 at the end of one year, your IRR is 30% and your is If you borrow 100 and pay back 130 then the IRR is still 30% but the NPV is The NPV clearly points out the negative aspects of this borrowing strategy. (assume 10% opportunity cost) 20

21 When your cash flows change signs more than once (-200, 200, 800, - 800) you will have more than one answer to the IRR. In the example, if our opportunity cost of capital is 25%, one IRR would tell us to accept, the other to reject. The NPV will always give you the proper choice. Another problem: with mutually exclusive projects the IRR may erroneously favor smaller projects. Example: Which would you chose: I ll give you 300% return on $1,000 in one year or only a 50% return on a million. Would you choose the higher IRR or the higher NPV. NPV at 8% would be 1778 and 388,888. You can calculate IRR of the difference between the cash flows of the large and small project. If the IRR of the difference is greater than the discount rate, go with the larger project. You don t have to worry about this when you use the NPV. 21

22 Here you have two mutually exclusive projects whose NPV s decline at different rates as the discount rate increases. If the discount rate is 8%, project B would be the best choice. If the discount rate is 12%, project A is best. You can calculate the cross-over rate is the IRR of project A-B. Again, this is not a problem when you use the NPV. 22

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24 Which would you pick? Project H has a higher IRR, but is short-lived. It adds less value to the firm. When the NPV and IRR differ, always go with the NPV. 24

25 Very dangerous to use. Used only by the uninformed. 25

26 The payback methods ignores all cash flows after some arbitrary cut-off date. In addition, it does not use discounted cash flows. Do not use except for insignificant projects. 26

27 Capital rationing exists if there is a limit on the amount of funds available for investment. There are two forms of capital rationing (6-28) Soft Rationing: exists if businesses themselves, or their senior managers, place limits on the capital budget. Soft rationing limits can be easily relaxed if added NPV investments are available. Financing is provided easily by financial markets. Hard Rationing: Limits set by the financial markets. With funding restraints, positive NPVs are foregone. With hard rationing, a firm must choose from among a list of projects with positive NPVs. 27

28 With a hard rationing constraint, choose the projects that have the highest profitability index to the limit of the financing budget. Your text uses an overly complicated formula you the profitability index. If you wish to replicate it you can take the NPV the add the initial investment to it and then divide by the initial cost. The profitability index is the ratio of the sum of the present values of the project (NPV) divided by the initial cost of the investment. It is a measure of the highest NPV per dollar of investment. PI = NPV/ Initial Investment. You would rank them and accept the highest. (Resources = 20 million, projects = 25 million. Which do you choose? The ones with the most bang per buck.) Pick N first at a cost of 7, then L and M for 3 and 6 respectively, and then P for 4. This will use up all your 20 million dollar budget. You would only use the profitability index in situations of capital rationing, or otherwise you would miss the opportunity to invest in projects that would add to shareholders wealth. 28

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