There are two mutually exclusive proposals for a for a flood control project in
ID: 2762899 • Letter: T
Question
There are two mutually exclusive proposals for a for a flood control project in Illinois. The first proposal involves an initial outlay of $1,350,000 and annual expenses of $110,000. This plan is assumed to be permanent. The second proposal requires an initial outlay of $700,000, followed by $200,000 every 12 years thereafter. Annual expenses for the second proposal are estimated to be $95,000 for the first 12 years and $150,000 each year thereafter. Annual benefits are identical for both projects, and terminal salvage values are negligible. The interest rate is 6% per year. Which proposal should be recommended? (6.5 and 10.9)Explanation / Answer
Proposal 1 - The inital cost = 1,350,000
The present value of the annual expenses to perpetuity = Cash flow annually/Interest rate = 110,000/0.06 = 1,833,333.33
Hence Total Cost = 1,350,000 + 1,833,333.33 = $3,183,333.33
Proposal 2 - The Inital Cost = 700,000
The expenses for 12 years =95,000. The present value of this annuity is given by PV formula in excel wherein =PV(rate,nper,pmt) wnere rate = 0.06, nper = 12 and pmt = 95,000
Hence PV of costs of 95,000 for 12 years = pmt(0.06,12,95000) = $796,465.17
Hence PV of costs and expeses upto year 12 = $700,000 + $796,465.17 = $1,496,465.17
The Costs from year 12 + 150,000/0.06 = 277,777.78 + 2,500,000 = 2,777,777.78
This is to be discounted to today. So PV = 2,777,777.78/1.06^12 = $1,380,470.46
Hence total costs for propsal 2 = $1,496,465.17 +1,380,470.46 = $2,876,935.63
Since the PV of proposal 2 ($2,876,935.63) is lower than than of propsal 1 ($3,183,333.33)
Hence propsal 2 or second proposal should be recommended