NAME: Problem 3 (30pts) SHOW ALL WORK Cash flows for three ironmentally-friendly

Question

NAME: Problem 3 (30pts) SHOW ALL WORK Cash flows for three ironmentally-friendly, while others sacrifice environmentalism for profits. Assuming an expectied project life of 50 years and a MARR of 6%, determine the most acceptable project. Use the incremental Conventional B-C Method with PW (no credit will be given to alternative methods). Plan A Plan B $85,000 $60,000$90,000 $40,000 $30,000 $90,000 $105,000$120,000 Plan C Capital Investment Annual O&M; Annual Revenues Market Value ( yr 50) $150,000 $250,000 $ Annual Environmental $10,000 -$40,000 (loss) $60,000 $90,000 $100,000 Benefit

Explanation / Answer

Conventional Benefit - Cost (B/C) ratio = PW ( B) / [I - PW (Market Value) + PW (O & M) ]

where B is the benefit, O & M is the operating and maintenance cost, I is the investment

Here we are asked to do an incremental conventional BC method with PW

Plan A

First we calculate present worth of cost for Plan A :

PW(C,Plan A) = $85,000 + $40,000 ( P/A, 6%, 50) - 150,000 ( P/F, 6%, 50) .......(1)

So, we are converting the annual costs into a present worth of costs. Referencing the compound interest table for 6% because that is our MARR. We look at N = 50 because that is our project life of 50 years. We look at the column Present worth (P/A,6%,50) = 15.762

Next we find ( P/F, 6%, 50) again by looking at the compound interest table at 6 % at n = 50 years

( P/F, 6%, 50) = 0.0543

Substituting the values in eqn(1), we get :

PW(C,Plan A) = $85,000 + $40,000 ( P/A, 6%, 50) - 150,000 ( P/F, 6%, 50) = 85,000 + 40,000*15.762

                                                                                                                        - 150,000 *0.0543 = $ 707,335

Next, we calculate Present Worth of Benefit for Plan A

PW(B,Plan A) = 90,000(P/A, 6%, 50)+10,000 (P/A, 6%, 50) =90,000*15.762 + 10,000 * 15.762 = $ 1,576,200

(P/A, 6%, 50) = 15. 762 (which we got from table earlier)

Thus, B- C ratio for Plan A = PW(B,Plan A) / PW(C,Plan A) = $1,576,200 / $707,335 = 2.228

Since B - C ratio for Plan A = 2.228 > 1 hence Plan A is acceptable.

Plan B

PW(C,Plan B) = $60,000 + $30,000 ( P/A, 6%, 50) - 250,000 ( P/F, 6%, 50) = 60,000 + 30,000*15.762

                                                                                                                        - 250,000 *0.0543 = $ 519,285

PW(B,Plan B) = 105,000(P/A, 6%, 50) - 40,000 (P/A, 6%, 50) = 105,000 * 15.762 - 40,000 * 15.762 = $ 1,024,530

B- C ratio for Plan B = PW(B,Plan B) / PW(C,Plan B) = $1,024,530 / $519,285 = 1.972

Since B - C ratio for Plan B = 1.972 > 1 hence Plan B is acceptable.

Plan C

PW(C,Plan C) = $90,000 + $90,000 ( P/A, 6%, 50) + 100,000 ( P/F, 6%, 50) = 90,000 + 90,000*15.762

                                                                                                                        + 100,000 *0.0543 = $ 1,514,010

PW(B,Plan C) = 120,000 (P/A, 6%, 50)+60,000 (P/A, 6%, 50) =120,000* 15.762+ 60,000 * 15.762 = $ 2,837,160

B- C ratio for Plan C = PW(B,Plan C) / PW(C,Plan C) = $ 2,837,160 / $ 1,514,010 = 1.873

Since B - C ratio for Plan C = 1.873 > 1 hence Plan C is acceptable.

Since the B - C ratio of Plan A is 2. 228 is higher than the other 2 plans hence Plan A is the most acceptable project.

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