### Calculations Involving Uniform Series and Randomly Placed Single Amounts

**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.

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