## Example

Suppose the leasing company of Example 2.1 has to choose between the following two proj ects:

1. Lease the car exactly as the case in Example 2.1 which had a net present worth of \$826.62

2. Buy a car at \$40,000, lease it for two years at \$12,000 per year with no maintenance cost, and sell it for \$24,000 at the end of two years.

Assuming an interest rate of 10%, which project should we choose? In this problem, n1=4 and n2=2, therefore, the least common multiplier of n1 and n2 is equal to four. That means project 1 is going on for two years after project 2 ends.

Can we make a fair comparison? What does the leasing company do with the money received from project 2? To solve this problem, we assume that they engage in project 2 for another two years. This is the same as assuming that we buy the same car and lease it under the same condition for another two years. The procedure is as follows.

Step 1:

Draw the cash flow diagram of the project with the smaller initial investment (in this case project 1) and check it against the null alternative. If NPW was not positive, we would disregard this project and would check project 2 to see if its NPW is greater than zero. In this case, we have already done the analysis and know that the NPW of project 1 is positive.

Step 2:

Since n1=4 and n2=2, then their common multiplier is 4 so we draw the cash flow diagram of both projects for n=4 years.

We repeat the netted cash flow diagram of project 2 as in Fig. 2.5b to get a four-year life for this project and, hence, equalize both lives. Step 3: Draw the netted cash flow diagram of project 1 and that of extended life project 2, as show in Figs. 2.5c and 2.5d.

Now calculate the respective NPW of the two proj ects. Fig. 2.5c Step 4:

NPW 1 was calculated before and is equal to \$826.58. NPW 2 is calculated using expressions 2.2b:

= -40000 + 12000 (P/F, 10,1) - 4000 (P/F,10,2) + 12000 (P/F,10,3) + 36000 (P/F,10,4) = -40000 + 12000 (0.9091) -4000 (0.8264) + 12000 (0.7513) + 36000 (0.6830) = 1,207.2

Since project 2 has a higher NPW, it would be the project to choose.

Chapter 2 Present Worth 33

The spreadsheet calculation is shown below in Example 2.3:

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<><><><><><><><><><><><> ## Project Management Made Easy

What you need to know about… Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.

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