A regional municipality is studying a water supply plan for its tri-city and surrounding area to the end of year 2070. Tosatisfy the water demand, one suggestion is to construct a pipeline from a major lake some distance away. Constructionwould start at the beginning of 2030 and take five years at a cost of $30 million per year. The cost of maintenance andrepairs starts after completion of construction and for the first year is $3 million, increasing by 2 percent per yearthereafter. At an interest rate of 7 percent, what is the present worth of this project? Assume all cash flows take placeat year-end. Consider the present to be the end of 2025/beginning of 2026. Assume there is no salvage value at the endof year 2070.Click the icon to view the table of compound interest factors for discrete compounding periods when i = 7%.The present worth of this project is $(Round to two decimal places as needed.)million.

Present worth at year 2030Hence, present worth at year 2030 will be $158.147096 million

Answered: A regional municipality is studying a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A regional municipality is studying a water supply plan for its tri-city and surrounding area to the end of year 2070. To
satisfy the water demand, one suggestion is to construct a pipeline from a major lake some distance away. Construction
would start at the beginning of 2030 and take five years at a cost of $30 million per year. The cost of maintenance and
repairs starts after completion of construction and for the first year is $3 million, increasing by 2 percent per year
thereafter. At an interest rate of 7 percent, what is the present worth of this project? Assume all cash flows take place
at year-end. Consider the present to be the end of 2025/beginning of 2026. Assume there is no salvage value at the end
of year 2070.
Click the icon to view the table of compound interest factors for discrete compounding periods when i = 7%.
The present worth of this project is $
(Round to two decimal places as needed.)
million.

Expert Solution

Step 1: Evaluation of Present worth at year 2030

Present worth at year 2030 $equals C o n s t r u c t i o n space cos t open parentheses P divided by A comma i comma 5 close parentheses plus M a i n t e n a n c e space cos t open parentheses P divided by A comma g comma i comma 36 close parentheses open parentheses P divided by F comma i comma 5 close parentheses$

$equals $ 30 space open parentheses P divided by A comma 7 percent sign comma 5 close parentheses plus $ 3 space open parentheses P divided by A comma 2 percent sign comma 7 percent sign comma 36 close parentheses space open parentheses P divided by F comma 7 percent sign comma 5 close parentheses$

$equals $ 30 space cross times fraction numerator open parentheses 1 plus 0.07 close parentheses to the power of 5 minus 1 over denominator 0.07 open parentheses 1 plus 0.07 close parentheses to the power of 5 end fraction plus $ 3 cross times space fraction numerator 1 minus open parentheses fraction numerator 1 plus 0.02 over denominator 1 plus 0.07 end fraction close parentheses to the power of 36 over denominator 0.07 minus 0.02 end fraction cross times 1 over open parentheses 1 plus 0.07 close parentheses to the power of 5$

$equals $ 30 cross times 4.10020 plus $ 3 cross times 16.42875 cross times 0.7130$

$equals bold 158 bold. bold 147096$

Hence, present worth at year 2030 will be $158.147096 million