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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 arise 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.
IF, AMONG A NUMBER OF PROJECTS, THE FIRM CAN ONLY CHOOSE ONE, THEN THE PROJECTS ARE SAID TO BE MUTUALLY 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 choose?
Example You are in the highly competitive area of 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 of 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 giving up your competitive edge.
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 much competition that any new investment in this product will have a zero NPV. The discount rate is 15%.
This method 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:
Return to the first 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 years will be:
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 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 during the next five years. The discount rate is assumed to be 12%.
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 obviously 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 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.
In general, Equivalent Annual Cash Flow or Cost is used to consider a problem where the investment is considered ongoing and you have to examine what happens at the end of the project's life. All that EACF does is help you discover the decision which gives the highest NPV as a whole.
In this situation, the decision maker is faced with a limited capital 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 possibilities become very large with a relatively small number of projects. Thus, in order to make the problem "manageable", we can systematize the search.
Since we have a constraint, what we want to do is invest in those projects which gives us the highest BENEFIT per dollar invested. (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:
However, if the budget were 15 million rather than 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.