Calculations Involving Uniform Series and Randomly Placed Single Amounts

When a cash flow includes both a uniform series and randomly placed single amounts, the procedures are applied to the uniform series and the single-amount formulas are applied to the one-time cash flows. This approach, illustrated in Examples 3.3, is merely a combination of previous ones. For spreadsheet solutions, it is necessary to enter the net cash flows before using the NPV and other functions.

EXAMPLE 3.3

An engineering company in Wyoming that owns 50 hectares of valuable land has decided to lease the mineral rights to a mining company. The primary objective is to obtain long-term income to finance ongoing projects 6 and 16 years from the present time. The engineering company makes a proposal to the mining company that it pay $20,000 per year for 20 years beginning 1 year from now, plus $10,000 six years from now and $15,000 sixteen years from now. If the mining company wants to pay off its lease immediately, how much should it pay now if the investment is to make 16% per year?

Solution

The cash flow diagram is shown in Figure 3–6 from the owner’s perspective. Find the present worth of the 20-year uniform series and add it to the present worth of the two one-time amounts to determine   PT,

Note that the $20,000 uniform series starts at the end of year 1, so the   P/A  factor determines the  present worth at year 0. 

When you calculate the   A  value for a cash fl ow series that includes randomly placed single amounts and uniform series,   fi  rst convert everything to a present worth or a future worth. Then you obtain the   A  value by multiplying   P  or   F  by the appropriate   A/P  or   A/F   factor.