My Math Forum Question on benefit cost analysis

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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 tax-exempt 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 1-75 +$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: 14,597 Thanks: 1038 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
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Re: Question on benefit cost analysis

Quote:
 Originally Posted by Kaiso (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?
Hmm. You added one years' interest to the total amount that would be collected, and give it as a lump sum. This is much more valuable than getting it in 75 annual payments. (What would you rather have: $106,000 or fifty payments of$2000 each year starting from next year?) You need to look up your PV formula. (I know how I would compute this but probably it is different from what you've learned so I won't confuse you there.)

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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