Question

Potable water is in short supply in many countries. To address this​ need, two mutually exclusive water purification systems are being considered for implementation in China. Doing nothing is not an option. Assume the repeatability of cash flows for alternative 1.

a. Use the PW method to determine which system should be selected when MARR = 7% per year.

b. Which system should be selected when MARR = 15​% per​ year?

a. The PW of system 1 is $_______. (Round to the nearest​ dollar.)

The PW of system 2 is ​$_______.(Round to the nearest​ dollar.)

Which system should be​ selected? Choose the correct answer below.

System 1 orSystem 2

b. The PW of system 1 is $_____.​(Round to the nearest​ dollar.)

The PW of system 2 is $_______. (Round to the nearest​ dollar.)

Which system should be​ selected? Choose the correct answer below.

System 2 or System 1

System 1 $100,000 50,000 25,000 21,000 5 years 12.7% System 2 $150,000 70,000 40,000 0 10 years 15.1% Capital investment Annual revenues Annual expenses MV at end of us Useful life IRR Discrete Compounding; i-7 Single Payment Uniform Series Compound Amount Factor To Find F Given P FIP 1.0700 1.1449 1.2250 1.3108 1.4026 1.5007 1.6058 1.7182 1.8385 1.9672 Compound Amount Factor To Find F Given A F/A 1.0000 2.0700 3.2149 4.4399 5.7507 7.1533 8.6540 10.2598 11.9780 13.8164 Sinking Capital Fund Factor To Find A Given F A/F 1.0000 0.4831 0.3111 0.2252 0.1739 0.1398 0.1156 0.0975 0.0835 0.0724 Present Worth Factor To Find P Given A PIA 0.9346 1.8080 2.6243 3.3872 4.1002 4.7665 5.3893 5.9713 6.5152 7.0236 Present Worth Factor To Find P Given F P/F 0.9346 0.8734 0.8163 0.7629 0.7130 0.6663 0.6227 0.5820 0.5439 0.5083 Recovery Factor To Find A Given P 1.0700 0.5531 0.3811 0.2952 0.2439 0.2098 0.1856 0.1675 0.1535 0.1424 4 5 10

Answer 1

a. Use the PW method to determine which system should be selected when MARR = 7% per year

The life of the alternative is different. Hence using the common multiple method we have to convert the unequal life into equal life. The LCM 5 years and 10 years is 10. So the system 1 is to be repeated 2 times. But system 2 needs not to be repeated.

System 1	System 2
Capital investment = 100,000 Annual revenue = 50,000 Annual expenses = 25,000 MV at the end of life = 21,000 Life = 5years Calculate the Net Cash Flow NCF = 50,000 – 25,000 = 25,000 PW = -100,000 – 100,000 (P/F, 7%, 5) + 25,000 (P/A, 7%, 10) + 21,000 (P/F, 7%, 5) + 21,000 (P/F, 7%, 10) PW = -100,000 – 100,000 (0.7130) + 25,000 (7.0236) + 21,000 (0.7130) + 21,000 (0.5083) PW = 29,937	Capital investment = 150,000 Annual revenue = 70,000 Annual expenses = 40,000 MV at the end of life = Nil Life = 10years Calculate the Net Cash Flow NCF = 70,000 – 40,000 = 30,000 PW = -150,000 + 30,000 (P/A, 7%, 10) PW = -150,000 + 30,000 (7.0236) = 60,708

a. The PW of system 1 is $29,937. (Round to the nearest​ dollar.)

The PW of system 2 is ​$60,708. (Round to the nearest​ dollar.)

Which system should be​ selected? Choose the correct answer below.

System 2 is to be selected because of highest PW.

b. Which system should be selected when MARR = 15​% per​year?

System 1	System 2
Capital investment = 100,000 Annual revenue = 50,000 Annual expenses = 25,000 MV at the end of life = 21,000 Life = 5years Calculate the Net Cash Flow NCF = 50,000 – 25,000 = 25,000 PW = -100,000 – 100,000 (P/F, 15%, 5) + 25,000 (P/A, 15%, 10) + 21,000 (P/F, 15%, 5) + 21,000 (P/F, 15%, 10) PW = -100,000 – 100,000 (0.4972) + 25,000 (5.0188) + 21,000 (0.4972) + 21,000 (0.2472) PW = -8,618	Capital investment = 150,000 Annual revenue = 70,000 Annual expenses = 40,000 MV at the end of life = Nil Life = 10years Calculate the Net Cash Flow NCF = 70,000 – 40,000 = 30,000 PW = -150,000 + 30,000 (P/A, 15%, 10) PW = -150,000 + 30,000 (5.0188) = 564

b. The PW of system 1 is $-8618.​(Round to the nearest​ dollar.)

The PW of system 2 is $564. (Round to the nearest​ dollar.)

Which system should be​ selected? Choose the correct answer below.

System 2 is to be selected because of highest positive PW.