Page 307 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

this point it is not clear how to select the most attractive option with this information. We will see later
that the choice of the project with the highest NPV will be the most attractive. However, let us consider
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the following alternative analysis. If Project B is selected, a total of $120 × 10 is invested and yields
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12.9%, whereas the selection of Project A yields 14.3% on the $60 × 10 invested. To compare these two
options, we would have to consider a situation in which the same amount is invested in both cases. In
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Project A, this would mean that $60 × 10 is invested in the project and the remaining $60 × 10 is
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invested elsewhere, whereas in Project B, a total of $120 × 10 is invested in the project.

It is necessary in our analysis that we are sure that the last dollar invested earns at least 10%. To do this
we must perform an incremental analysis on the cash flows and establish that at least 10% is made on
each additional increment of money invested in the project.

Example 10.5

This is a continuation of Example 10.4.
a. Determine the NPV and the DCFROR for each increment of investment.
b. Recommend the best option.

Solution

a. Project A to Project C:
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Incremental investment is $40 × 10 = ($100 – $60) × 10 .
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Incremental cash flow for i = 1 is $2 × 10 /yr = ($12/yr – $10/yr) × 10 .
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Incremental cash flow for i = 2 to 10 is $8 × 10 /yr = ($20/yr – $12/yr) × 10 .
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NPV = –$40 × 10 + ($2 × 10 )(P/F, 0.10, 1) + ($8 × 10 )(P/A, 0.10, 9)(P/F, 0.10, 1)
NPV = $3.7 × 10 6
Setting NPV = 0 yields DCFROR = 0.119 (11.9%).
Project C to Project B:
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Incremental investment is $20 × 10 = ($120 – $100) × 10 .
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Incremental cash flow for i = 1 is $10 × 10 /yr = ($22/yr – $12/yr) × 10 .
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Incremental cash flow for i = 2 to 10 is $2 × 10 /yr = ($22/yr – $20/yr) × 10 .

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NPV = –$0.4 × 10 and DCFROR = 0.094 (9.4%)

b. It is recommended that we move ahead on Project C.

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From Example 10.5, it is clear that the rate of return on the $20 × 10 incremental investment required to
go from Project C to Project B did not return the 10% required, and gave a negative NPV.

The information from Example 10.4 shows that an overall return on investment of more than 10% is
obtained for each of the three projects. However, the correct choice, Project C, also has the highest NPV

using a discount rate of 10%, and it is this criterion that should be used to compare alternatives.