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November 9th, 2013, 05:01 PM  #1 
Newbie Joined: Oct 2013 Posts: 6 Thanks: 0  Question on benefit cost analysis
Hi all, I have a question regarding benefit cost analysis that I'm hoping someone could help me with. A taxexempt municipality is considering the construction of an impoundment for city water supplies. Two different sites have been selected as technically, politically, socially, and financially feasible. The city council has asked you to do a benefit cost analysis of the alternatives and recommend the best site. The city uses a 6% rate in all analysis of this type. Which should you recommend? Year Rattlesnake Canyon Blue Basin 0 $15,000,000 $27,000,000 175 +$2,000,000 +$3,000,000 Thank you 
November 9th, 2013, 05:45 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,412 Thanks: 1024  Re: Question on benefit cost analysis
Rattlesnake: (PV of 75 annual payments of $2million @ 6%)  $15million Blue Basin: (PV of 75 annual payments of $3million @ 6%)  $27million 
November 9th, 2013, 10:56 PM  #3 
Newbie Joined: Oct 2013 Posts: 6 Thanks: 0  Re: Question on benefit cost analysis
(1.06 x $2 million x 75)  $15 million = 144,000,000 (1.06 x $3 million x 75)  $27 million = 211,500,000 therefore Rattlesnake Canyon is the best site as it costs the least at 75 years? 
November 10th, 2013, 04:47 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Question on benefit cost analysis Quote:
Second, what you get is the PV of the project, so you want to maximize not minimize the number. The essential question you need to answer: is it worthwhile to pay an extra $12 million upfront to get $1 million extra cash flow for the next 75 years? (You might be tempted to say "yes" without calculating, but this is not obvious. The present value of annual payments of a half million dollars each year forever is only $7.8 million, so you wouldn't trade $12 million for that.)  

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