1、Advanced Corporate Finance Capital Budgeting Complications Finance 7330 Lecture 2.1 Ronald F. Singer,Making Investment Decisions,We have stated that we want the firm to take all projects that generate positive NPV and reject all projects that have a negative NPV. Capital budgeting complications aris
2、e when you cannot, either physically or financially undertake all positive NPV projects. Then we have to devise methods of choosing between alternative positive NPV projects.,Mutually Exclusive Projects,IF, AMONG A NUMBER OF PROJECTS, THE FIRM CAN ONLY CHOOSE ONE, THEN THE PROJECTS ARE SAID TO BE MU
3、TUALLY EXCLUSIVE. For example: Suppose you have the choice of modifying an existing machine, or replacing it with a brand new one. You could not do both and produce the desired amount of output. Thus, these projects are mutually exclusive. Given the cash flows below, which of these projects do you c
4、hoose?,Mutually Exclusive Projects,Time Modify Replace Difference0 -100,000 -250,000 -150,0001 105,000 130,000 25,0002 49,000 253,500 204,500IRR?,Mutually Exclusive Projects,Time Modify Replace Difference0 -100,000 -250,000 -150,0001 105,000 130,000 25,0002 49,000 253,500 204,500IRR .40 .30 .25Assum
5、e the hurdle rate is 10%,Mutually Exclusive Projects,Time Modify Replace Difference0 -100,000 -250,000 -150,0001 105,000 130,000 25,0002 49,000 253,500 204,500IRR .40 .30 .25NPV( 10%) 36,000 77,700 41,700Notice the conflict that can exist between NPV and IRR.,EXAMPLES OF CAPITAL BUDGETING COMPLICATI
6、ONS,1. Optimal Timing 2. Long versus Short Life 3. Replacement Problem 4. Excess Capacity 5. Peak Load Problem (Fluctuating Load) 6. Capital Constraints,EXAMPLES OF CAPITAL BUDGETING COMPLICATIONS,These Capital Budgeting Complications will stop the Firm from taking all possible positive NPV PROJECTS
7、. Thus, the firm is faced with the choice of two possibilities.Remember: Goal is still Max NPV of all possibilities,EXAMPLES OF CAPITAL BUDGETING COMPLICATIONS,We can divide these problems into three separate classes, each with their own method of solutions. (1) Once and for all deal.Choose the one
8、alternative having the highest NPV.(2) Repetitive Deal. Choose the one alternative having the highest equivalent annual cash flow.(3) Capital Budgeting ConstraintChoose the combination of projects having the highest NET PRESENT VALUE.,Once and For all Deals,INVESTMENT TIMING:When is the optimal time
9、 to take on an investment project? Consider T possible times, where, t = 1, .T. Then each “starting time“ can be considered a different project in a set of T mutually exclusive projects. Then find that t which Max: NPV(t) (1+r)t,Once and For all Deals,Example You are in the highly competitive area o
10、f producing laundry soap and detergents. You have a new product which you feel does a superior job in washing clothes, but you anticipate that the product will have difficulty being accepted by the consumer. Thus you expect that if you introduce the product now, you will have to suffer a few years o
11、f losses until the product is accepted by the consumer. A competitor is about to come out with a similar product. You feel that if you allow your competitor to come out with the product first, you can benefit from the time he spends acclimating your potential customers. However, you will then be giv
12、ing up your competitive edge.,Once and For all Deals,The initial investment in the product has already been spent, is a sunk cost and can be ignored for this problem. The anticipated life of the productive process is ten years from the time the product is first produced. Thereafter, there will be so
13、 much competition that any new investment in this product will have a zero NPV. The discount rate is 15%.,Once and For all Deals,Expected cash flows are:CASH FLOW ($ MILLIONS )year (fromstart of project 1 2 3 4-10 _immediately -4 -3 -2 20If introduced after one year -1 1 3.5 19.5If introduced aftert
14、wo years 0 2 4 19WHAT SHOULD YOU DO?,Once and For all Deals,NPV(0) (Introduced Immediately) is: 47.649 millionNPV(1) (Introduced in one years time) is: 55.531 millionNPV(2) (Introduced in two years time) is: 56.118 millionWHICH ONE OF THESE THREE OPTIONS SHOULD BE TAKEN?47.649 55.531 56.118 | | |0 1
15、 2 3 4 5 Calculate NPV from time 0.,Once and For all Deals,ShortcutCalculate the annualized rate of change of NPV. If delaying causes the NPV to increase by more than the discount rate, the project should be delayed. If not, the project should not be delayed.,Once and For all Deals,CautionThis metho
16、d assumes that the project cannot be reproduced at a positive NPV after the initial life of the project. Otherwise, you have to also account for the fact that the project that is started earlier can also be reproduced earlier. In that case, the alternatives look like:START IMMEDIATELY 0 10 20 30 _ON
17、E YEAR DELAY 0 1 11 21 31_ THIS LEADS TO THE SECOND CLASS OF PROBLEMS:,Repetitive Deals,Mutually exclusive projects with different Starting Times Mutually exclusive projects with different Economic Lives Replacement Decision Management of Excess of Peak Capacity,examples: Alternatives with Different
18、 Lives3 Little PigsBrick vs. Wood vs. Straw.,Alternatives with Different Lives,Example: YOU HAVE THE OPTION OF UNDERTAKING ONE OF TWO DIFFERENT WAYS OF ACHIEVING SOME GOAL. WHICH ONE SHOULD YOU TAKE? (A) A Bridge costing 5M lasts 15 years(B) A Bridge costing 4M lasts 10 yearsBoth generate $1 Million
19、 in net revenues per year. Let the Discount rate = 12% for each alternative. NPV (A) = $1.81 MillionNPV (B) = $1.65 Million,Alternatives with Different Lives,Conceptually The NPV rule would say, take the project with the highest Net Present Value. This may be wrong.Consider what happens after ten ye
20、ars. In particular by year 30.,Alternatives with Different Lives,A 1.81 1.81 1.81._0 5 10 15 20 25 30 35 B 1.65 1.65 1.65 1.65_0 5 10 15 20 25 30 35PV(A) over infinite horizon:PV(A) = 1.81 + 1.81 + 1.81 + = 2,214,900 (1.12)15 (1.1)30 PV(B) over infinite horizon:PV(B) = 1.65 + 1.65_ + 1.65_ + = 2,435
21、,700 (1.12)10 (1.12)20,Alternatives with Different Lives,ALTERNATIVE EQUIVALENT ANNUAL CASH FLOW (EACF) or (NUS in Hewlett Packard)Note: BMA talk about Equivalent Annual Cost, this is a more general concept. Consider the annuity having the same NPV and life of the project.EACF (A) = That annuity hav
22、ing a Present Value of 1.81, lasting 15 years at a discount rate of 12%. (A): PV(A) = Annuity x PVFA(r%, T)Annuity(A) = 265,700 = EACF(A)Annuity(B) = 292,000 = EACF(B),Alternatives with Different Lives,This “Equivalent Annual Cash Flow“ (or Cost) is a convenient way of examining the host of complica
23、ted, mutually exclusive capital budgeting problems listed above: These all involveA TIMING PROBLEM(1) When to start project(2) When to “cash in“ForestryWine(3) Replacement(4) Short vs. Long lived Project(5) When and how to increase capacityCan all be dealt with in a similar way?,Mutually exclusive p
24、rojects with different Starting Times,Instead of assuming that this is a once and for all deal, assume that the alternatives can be reproduced indefinitely. Note that this case differs from the Laundry Detergent Example treated above: 1. How?2. What impact will this have on the timing decision?,Mutu
25、ally exclusive projects with different Starting Times,Consider an example: The mutually exclusive decision, when to cut down a forest:In ten years with NCF of 47,000 In eleven years with NCF of 53,000In twelve years with NCF of 58,000If this were a one-time-only deal, you would simply calculate the
26、NPV of each alternative:NPV of cutting in ten years: 15,132.74NPV of cutting in eleven years: 15,236.23NPV of cutting in twelve years: 14,887.16,Mutually exclusive projects with different Starting Times,But, more realistically, you will be able to continue cutting down these trees every ten, eleven,
27、 or twelve years. Which is the best alternative as a repetitive procedure? The question is, what is better: (1) receiving an annuity of 47,000 every ten years(2) receiving an annuity of 53,000 every eleven years(3) receiving an annuity of 58,000 every twelve years,Mutually exclusive projects with di
28、fferent Starting Times,For any set of reproducible mutually exclusive projects with different lives, you can:Find the NPV of each project through one repetition, and then find its Equivalent Annual Cash Flow (EACF), and choose the one with the highest EACF.Where EACF is calculated as: that fixed pay
29、ment (annuity) having the same value and life of the project. So:EACF(10) = 2,678.12EACF(11) = 2,566.98EACF(12) You know this isnt the right one since it has a lower present value but takes longer to produceThus you want to take the shorter lived project now.,Replacement Decision,Return to the first
30、 example, you choose project (2), and now you are in the fifth year of that project. The project, as expected, is returning $19.5 million this year. But production difficulties have resulted in a machine which is wearing out faster than anticipated. So that your expected cash flow for the next five
31、years will be:0 1 2 3 4 5 Cash Flow 19.5 18 17 16 15 NPV of operating Cash Flows 62.54 50.54 38.61 26.24 13.39,Replacement Decision,A new production technology has been devised which will cost $100 million and generate $39 million for the next 7 years, with an anticipated scrap value of 3 million at
32、 the end of the seventh year. Should you replace the machine now, never, or plan to replace it some time in the future? It is assumed that the scrap value of the old machine will be 0 if not replaced during the next 5 years (the life of the old project), but can be sold for 3 million at any time dur
33、ing the next five years. The discount rate is assumed to be 12%.,Replacement Decision,Find the equivalent annual cash flow for the new machine, net of the current scrap value.Net Cash Flow of Replacement Machine 0 1 2 3 4 5 6 7-97 39 39 39 39 39 39 42 NET PRESENT VALUE 82.344 million EQUIVALENT ANNU
34、AL CASH FLOW: 18.043 million IRR 35.56%,Replacement Decision,Replace in the beginning of year 2. Note, simply comparing NPV will not give the right answer, neither will looking at incremental cash flow. This is because the replacement has a different life than the current process and they are obviou
35、sly mutually exclusive. Furthermore, and more important, the alternatives of replacing now versus not replacing now is not the appropriate alternatives. You can also replace next year, the year after, etc. The alternative which gives the greatest incremental value relative to all the other possible
36、alternatives could be calculated by looking at the incremental cash flows from each alternative. But it is easier to simply calculate the EACF and compare that to the current cash flow to see what to do.,Replacement Decision,In general, Equivalent Annual Cash Flow or Cost is used to consider a probl
37、em where the investment is considered ongoing and you have to examine what happens at the end of the projects life. All that EACF does is help you discover the decision which gives the highest NPV as a whole. STOP,Capital Rationing,In this situation, the decision maker is faced with a limited capita
38、l budget. As a result, it may not be possible to take all positive net present value projects. Under this scenario, the problem is to find that combination of projects (within the capital budgeting constraint) that leads to the highest Net Present Value. The problem here is that the number of possib
39、ilities become very large with a relatively small number of projects. Thus, in order to make the problem “manageable“, we can systematize the search.,Capital Rationing,Since we have a constraint, what we want to do is invest in those projects which gives us the highest BENEFIT per dollar invested. (
40、The highest bang per buck). What is the benefit?, it is the Present Value of the Cash Flows. So that we would want to choose that set of projects within the capital budgeting constraint that gives the highest:Net Present Value INVESTMENT This ratio is called the profitability Index.,Capital Rationin
41、g,For example, suppose we have a $13 million capital budgeting constraint, with 7 alternative capital budgeting projects with the following projections.Project NPV Investment A 10 15B 8 10C 4 2.5D 6 5E 5 2.5F 7 5G 4.5 3,Capital Rationing,Rank by Profitability Index (NPV/INV Project Profitability Ind
42、ex Investment Total E 2.0 2.5 2.5C 1.6 2.5 5.0 G 1.5 3 8.0F 1.4 5 13.0 D 1.2 5 B .8 10A .667 15COMBINATION WITH HIGHEST PROFITABILITY INDEX WITHIN THE CAPITAL BUDGET (E,C,G,F) has a NPV of $20.5 million, and a cost of $13 million.,Capital Rationing,However, if the budget were 15 million rather than
43、13 million we would have a problem. Adding D would go over the budget and be infeasible, but the combination CDEF has a higher NPV ($22 million) than the chosen combination of ECGF. This is because the amount spent was only 13 million leaving 2 million in unspent funds. In this case, we are better off choosing a combination which spends all the funds. THE ONLY WAY TO DO THIS RIGHT IS TO DO A FULL BLOWN LINEAR PROGRAMING PROBLEM WITH CONSTRAINTS.,
