Based on your financial expertise, provide your response or viewpoint on the given financial question or topic. The response format is open.

Given a certain yearly savings, how much can I spend on a capital improvement? NPV of future cash flow
The question states :- Our insurance company is offering a 30% discount on an $8200/year   commercial policy, if we install sprinklers. The insurance is paid in   two installments. ... This appears to mean six-monthly payments, so I'll make some comparison calculations using six-monthly loan repayments to keep things simple. Without the loan or sprinklers the insurance costs $4100 every six months. Using this loan payment formula, the calculation below shows, with the 30% discounted insurance, sprinkler maintenance and loan repayment, you would be paying $4655.28 every six months.  The discount required to break even is 43.5%.  I.e. rearranging the equation :-  Alternatively, with the discount of 30% you would break even if the six-monthly repayment amount was $1030.  Solving the payment equation for s gives an equation for the loan :-  So with the 30% discount you would break even if the loan required was $25989. Checking by back-calculating the periodic payment amount, a :-  Likewise we can keep the loan at $40000 and solve for t to find the break-even loan term :-  (Note, in this formula Log denotes the natural logarithm.)  Now we can set some values :-  So with break-even payments the $40000 loan is paid off in just under 65.5 years.  I.e. checking :-  This just beats the $4100 cost of proceeding without the sprinklers. Notes If your loan repayment was monthly it would reduce the cost of the loan slightly.  The periodic interest rate is calculated from the APR according to the method used in the EU and in some cases in US.  The calculations above were run using Mathematica.