The general format to determine the PW is P PV i n A F 44 It is important to

# The general format to determine the pw is p pv i n a

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The general format to determine the PW is P PV( i %, n , A , F ) [4.4] It is important to pay attention to the sign placed on the PV function in order to get the correct answer for the alternative’s PW value. Excel returns the opposite sign of the A series because it interprets cash flows in the manner explained in Chapter 1, that is, costs are negative and the PV function value is a positive equivalent at time 0. Therefore, to retain the negative sense of a cost series A , place a minus sign immediately in front of the PV function. This is illustrated in the next example. b. Use the steps for a budget-constrained selection with b \$15,000. 1 and 2. Of the 2 4 16 possible bundles, Table 4.1 indicates that 6 are acceptable. These bundles involve all four projects plus do-nothing with PW DN \$0. 3. The PW value for a bundle is obtained by adding the respective project PW values. For example, PW 5 6646 973 \$7619. 4. Select projects F and H, since their PW is the largest and both projects exceed the MARR, as indicated by PW 0 at i 15%. Comment: Budget-constrained selection from independent projects is commonly called the capital rationing or capital budgeting problem. It may be worked effi- ciently using a variety of techniques, one being the integer linear programming tech- nique. Excel and its optimizing tool SOLVER handle this type of problem rather nicely. TABLE 4.1 Present Worth Analysis of Independent Projects with Investment Limited to \$15,000, Example 4.7 Total Initial PW of Bundle Bundle Projects Investment at 15% 1 F \$ 8,000 \$ 6646 2 G 15,000 1019 3 H 6,000 973 4 J 10,000 1553 5 FH 14,000 7619 6 Do-nothing 0 0 bLa01293_ch04_080-106 8/24/07 1:01 PM Page 96
4.6 Using Spreadsheets for PW Analysis 97 FIGURE 4.4 Equal-life alternatives evaluated using the PV function, Example 4.8. Cesar, a petroleum engineer, has identified two equivalent diesel-powered genera- tors to be purchased for an offshore platform. Use i 12% per year to determine which is the more economic. Generator 1 Generator 2 P , \$ 80,000 120,000 S , \$ 15,000 40,000 n , years 3 3 AOC, \$/year 30,000 8,000 Solution Follow the format in Equation [4.4] in a single cell for each alternative. Figure 4.4 cell tags show the details. Note the use of minus signs on P , the PV func- tion, and AOC value. Generator 2 is selected with the smaller PW of costs (numerically larger value). EXAMPLE 4.8 Continuing with the previous example, once Cesar had selected generator 2 to purchase, he approached the manufacturer with the concerns that the first cost was too high and the expected life was too short. He was offered a lease arrange- ment for 6 years with a \$20,000 annual cost and an extra \$20,000 payment in the first and last years to cover installation and removal costs. Determine if generator 2 or the lease arrangement is better at 12% per year. EXAMPLE 4.9 When different-life alternatives are evaluated, using the LCM basis, it is neces- sary to input all the cash flows for the LCM of the lives to ensure an equal-service evaluation. Develop the NPV function to find PW. If cash flow is identified by CF, the general format is [4.5] It is very important that the initial cost P not be included in the cash flow series identified in the NPV function. Unlike the PV function, the NPV function returns

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