The Phones Lines Example

Let’s start working on a slightly longer example and this will be a little bit more realistic, give you more time value of money material. It shows you really how present worth is supposed to work as an investment criteria. So let’s start with a simple problem, and this is called a basic service investment. These are things you must do, and what you’re trying to do is find the least cost way of doing them. Our particular service investment is to put in a bunch of phone lines. Here is the structure of the problem. You have to have in place right now 5,000 phone lines or something like that in an industrial park. You’re going to need another 5,000 phones lines in 5 years, but you don’t have to exactly have them immediately. In order to provide these 5,000 phones lines you have two plans that are available to you.

Plan A you should think of as the all now plan, it has the installation cost of the phone lines at $300,000. What happens is that after that, you have to maintain those phone lines. There is going to be a $15,000 per year maintenance cost over the life of the project. What we’re doing is we’re setting it up so that you only have to maintain the project for 20 years, 20 years is something that’s called our planning life. Now often times you’re going to find out that the planning horizon is given to you, that’s the end of the contract. That’s all we have to worry about. Often times you have your choice of a planning horizon. This ends up being a little bit difficult. A lot of people start thinking in terms of long planning horizons, but they forget that your certainty about what those costs are going to be in the future starts declining rapidly after about 3 years or so. 3 years is usually the limit of what you can do, but 5 is usually asked for. You should depend on choosing something reasonable. Choose exactly how long you want to do it. An example of a planning horizon that I had that was a little on the long side for me was that Portland development decided they needed to have a planning horizon of 60 years. They were using that for their buildings and materials.

So we have a 20-year planning horizon, so we’re going to have to take this maintenance cost the full 20 years. Now the other one is part now, part later as an option. What happens is you have line number 1, and this has a cost of $150,000 now and we’ll have a maintenance cost of $10,000 per year. Line 2, you’re going to install in 5 years, and that will cost you an additional $150,000 and that line will have an additional $10,000 per year maintenance. These are our two options. What we’re looking at here is an exclusive choice problem; you have to choose this one or this one. Because it’s exclusive choice, we’re going to be calculating the present worth of these two options and picking the one with the present worth nearest to positive infinity. The next stage of this is to go ahead and draw some cash flow diagrams because these cash flow diagrams help us figure out what the shape of the problem is, how to divide it, how to write it out in factor notation for us to do our calculations.

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