## Benefit Cost Ratio and Payback Methods Benefit Cost Ratio

Another method of assessing the viability of a system or comparing several systems is to calculate the net present value of the costs and the benefits and obtain the benefit-cost ratio (B/C). If this ratio is greater than one, then the project is profitable.

### Example 6.1

A car leasing company buys a car from a wholesaler for \$24,000 and leases it to a customer for four years at \$5,000 per year. Since the maintenance is not included in the lease, the leasing company has to spend \$400 per year in servicing the car. At the end of the four years, the leasing company takes back the car and sells it to a secondhand car dealer for \$ 15,000. For the moment, in constructing the cash flow diagram, we will not consider tax, inflation, and depreciation.

Step 1:

The cash flow diagram is

Step 2:

Calculate the net present value of the benefits and the costs. Ne[ PrcssM Benefii NPB = 5000 (P/A,]0,4) + 15000 (P/F, 10,4)

Net Present Cost = NPC = 24,000 + 400 (P/,A, 10,41 = 25.268 Hence, B/C = 26095/25268 -1,033 The project is Htccptable.

The spreadsheet solution of this example is exactly as in the case of the NPW (Chapter 2). Equalizing Lives and Incremental Analysis

If two or more projects have to be compared with the B/C method, then the lives should be equalized as in the case of the present worth method. We also have to calculate the B/C of their differential cash flows in pairs and perform incremental analysis to ensure that the extra initial cost justifies the extra benefit. We can see that the B/C ratio is a difficult comparison method when more than one alternative is considered. Example 6.2

Suppose the leasing company of Example 6.1 has to choose between the following two proj ects:

1. Lease the car exactly as in Example 6.1.

2. Buy a car at \$25,000, lease it for two years at \$10,000 per year with no maintenance cost and sell it for \$18,000 at the end of two years.

Assuming an interest rate of 10%, which proj ect should we choose?

In this problem, n= and n2=2; therefore, the least common multiplier of n and n2 is equal to 4. That means that project 1 continues for 2 years after project 2 ends.

Step 1:

Start with the project that has the lowest initial investment. Perform the B/C analysis to see if the project is acceptable (i.e., B/C>1).

This is checking against the null alternative. We know from Example 6.1 that B/C= 1.033, hence the proj ect is economically acceptable.

Step 2:

Construct the netted cash flow diagram of the two projects at equalized lives. In this case, the common denominator of the lives of the two projects is four years; therefore, the cash flow diagram is constructed for four years. Step 3:

Construct the incremental cash flow diagram. Step 4:

Perform the incremental analysis, i.e., calculate the B/C of the differential. NPB = 5400 (P/F,lO,l) t MOO (P/PJ0,3) + 8400 (P/F, 10.4)

= 5400 (0 9091) + 5400 (0 7513) + 8400 (0.6830) = 14,703 36 NPC m 1000 + 1600 {P/F, 10,2)" 1000+1600 (0.8264) = 2322 24

Therefore,

B/C = 6.33 Henct, project 2 is preferred.

If a choice has to be made between several proj ects, rank them by increasing initial investment. Compare them two by two in the same manner as we did for the above two projects, pick the best one, and compare it with the next in the ranking. ## 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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