A build-to-operate (BTO) company signed a contract to operate Alamosa County industrial wastewater treatment plants for the next 20 years. The contract will pay the company $2.5 million now and amounts increasing by $200,000 each year through year 20. At an interest rate of 10% per year, what is the present worth now? Solve using (a) tabulated factors, and (b) a spreadsheet.

What will be an ideal response?


(a) Factors: Find P in year –1 using gradient factor and then move forward 1 year

P -1 = 2,500,000(P/A,10%,21) + 200,000(P/G,10%,21)
= 2,500,000(8.6487) + 200,000(58.1095)
= $33,243,650

F = P 0 = 33,243,650(F/P,10%,1)
= 33,243,650 (1.1000)
= $36,568,015
(b) Spreadsheet: If entries are in cells B2 through B22, the function
= NPV(10%,B3:B22)+B2 displays $36,568,004, which is the
present worth in year 0.

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