EXAMPLES - Uniform Series That Are Shifted


The offshore design group at Bechtel just purchased upgraded CAD software for $5000 now and annual payments of $500 per year for 6 years starting 3 years from now for annual upgrades. What is the present worth in year 0 of the payments if the interest rate is 8% per year?


The cash flow diagram is shown in Figure 3–4. The symbol PA is used throughout this chapter to represent the present worth of a uniform annual series   A , and   P'A    represents the present worth at a time other than period 0. Similarly,   P  T    represents the total present worth at time 0. The correct placement of   P'A    and the diagram renumbering to obtain   n  are also indicated.   Note that P'A is located in actual year 2, not year 3. Also,  n = 6, not 8, for the P/A factor.  First find the value of   P'A of the shifted series.


Recalibration of sensitive measuring devices costs $8000 per year. If the machine will be reca-
librated for each of 6 years starting 3 years after purchase, calculate the 8-year equivalent
uniform series at 16% per year. Show hand and spreadsheet solutions.

Solution by Hand

Figure  3–5  a  and   b  shows the original cash fl  ows and the desired equivalent diagram. To convert the $8000 shifted series to an equivalent uniform series over all periods,  first convert the uniform series into a present worth or future worth amount. Then either the A/P factor or the A/F  factor can be used. Both methods are illustrated here.

Present worth method.  (Refer to Figure 3–5  a .) Calculate   P'A for the shifted series in year 2,  followed by   PT in year 0. There are 6 years in the A series.

Future worth method.  (Refer to Figure 3–5  a .) First calculate the future worth   F  in year 8.


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