document.write( "Question 1165581: How long must a temporary warehouse last to be desirable investment if it costs $ 16,000 to build, has annual maintenance and
\n" ); document.write( "operating cost of $ 360, provides storage space-value at $ 3,600 per year and if the company MARR is 10%? Hint: Treat MARR
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\n" ); document.write( "a. 8 years b. 9 years c.7 years d. 6 years \n" ); document.write( "

Algebra.Com's Answer #852155 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "How long must a temporary warehouse last to be desirable investment if it costs $ 16,000 to build,
\n" ); document.write( "has annual maintenance and operating cost of $ 360, provides storage space-value at $ 3,600 per year
\n" ); document.write( "and if the company MARR is 10%?
\n" ); document.write( "Hint: Treat MARR as interest rate, i.
\n" ); document.write( "a. 8 years b. 9 years c.7 years d. 6 years
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\n" ); document.write( "\n" ); document.write( "First, the definition of the MARR conception from Google AI:\r
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document.write( "    In finance, MARR stands for Minimum Acceptable Rate of Return, also known as the hurdle rate \r\n" );
document.write( "    or minimum attractive rate of return. It is the minimal profit that an investor or company \r\n" );
document.write( "    is willing to accept from an investment or project, considering the project's risk and \r\n" );
document.write( "    the opportunity cost of other available investments. \r\n" );
document.write( "    A project must exceed its MARR to be considered financially viable and worthwhile for investment.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now we can re-phrase the problem in more accessible Math terms, that are understandable
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document.write( "    A company \"Warehouse, Inc\" is going to loan $16,000 to construct a warehouse.\r\n" );
document.write( "    The warehouse will provide the storage space-value at $ 3,600 per year.  It will have the annual \r\n" );
document.write( "    maintenance and operating cost of $360 per year. The loan interest is 10% compounded yearly.\r\n" );
document.write( "    How long the warehouse must function to recoup the cost of the loan and other relevant costs?\r\n" );
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document.write( "Let PMT be the annual payment for the loan (which is some constant value over the years).\r\n" );
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document.write( "Then the inequality for the project to be profitable is\r\n" );
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document.write( "    PMT + 360 <= 3600,           (1)\r\n" );
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document.write( "which implies\r\n" );
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document.write( "    PMT <= 3600 - 360 = 3240.    (2)\r\n" );
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document.write( "Now, let's calculate PMT for 6, 7, 8 and 9 years with the interest rate r = 10% = 0.1.\r\n" );
document.write( "Use the standard formula\r\n" );
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document.write( "    for n = 6 years  PMT =  =  = 3673.72;\r\n" );
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document.write( "    for n = 7 years  PMT =  =  = 3286.49;\r\n" );
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document.write( "    for n = 8 years  PMT =  =  = 2999.10;\r\n" );
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document.write( "    for n = 9 years  PMT =  =  = 2778.25.\r\n" );
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document.write( "Comparing these numbers with 3240 in the right side of (2), you see that to be profitable, \r\n" );
document.write( "the warehouse should function at least 8 years.    <<<---===  ANSWER\r\n" );
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