Two mutually exclusive water purification systems are being considered for imple

Question

Two mutually exclusive water purification systems are being considered for implementation overseas. Refer to the data below:

System 1

System 2

Capital investment

Annual revenues

Annual expenses

MV at end of useful life

Useful life

$100,000

$50,000

$15,000

$20,000

12 years

$150,000

$75,000

$20,000

0

24 years

If MARR = 25 % per year, determine the present worth (PW) of the most profitable water purification system to use. Use the repeatability assumption.

System 1

System 2

Capital investment

Annual revenues

Annual expenses

MV at end of useful life

Useful life

$100,000

$50,000

$15,000

$20,000

12 years

$150,000

$75,000

$20,000

0

24 years

Explanation / Answer

Hi,

Please find the detailed answer as follows:

Step 1: Calculate IRR for both the Projects

System 1:

To calculate IRR, you need to put the value of NPV as 0 and solve for r as follows:

NPV = 0 = -100000 + (50000 - 15000)/(1+r)^1 + (50000 - 15000)/(1+r)^2 + (50000 - 15000)/(1+r)^3 + (50000 - 15000)/(1+r)^4 + (50000 - 15000)/(1+r)^5 + (50000 - 15000)/(1+r)^6 + (50000 - 15000)/(1+r)^7 + (50000 - 15000)/(1+r)^8 + (50000 - 15000)/(1+r)^9 + (50000 - 15000)/(1+r)^10 + (50000 - 15000)/(1+r)^11 + (50000 - 15000 +20000)/(1+r)^12

Solving for r, we get IRR as 34.17%

IRR (System A) = 33.95%

System 2:

NPV = 0 = -150000 + (75000 - 20000)/(1+r)^1 + (75000 - 20000)/(1+r)^2 + (75000 - 20000)/(1+r)^3 + (75000 - 20000)/(1+r)^4 + (75000 - 20000)/(1+r)^5 + (75000 - 20000)/(1+r)^6 + (75000 - 20000)/(1+r)^7 + (75000 - 20000)/(1+r)^8 + (75000 - 20000)/(1+r)^9 + (75000 - 20000)/(1+r)^10 + (75000 - 20000)/(1+r)^11 + (75000 - 20000)/(1+r)^12 + (75000 - 20000)/(1+r)^13 + (75000 - 20000)/(1+r)^14 + (75000 - 20000)/(1+r)^15 + (75000 - 20000)/(1+r)^16 + (75000 - 20000)/(1+r)^17 + (75000 - 20000)/(1+r)^18 + (75000 - 20000)/(1+r)^19 + (75000 - 20000)/(1+r)^20 + (75000 - 20000)/(1+r)^21 + (75000 - 20000)/(1+r)^22 + (75000 - 20000)/(1+r)^23 + (75000 - 20000)/(1+r)^24

Solving for r, we get IRR as 36.65%

Since, IRR of System 2 is higher, we conclude that System 2 is more profitable and we will calculate NPV for System 2.

Step 2: Calculate NPV of System 2:

NPV = -150000 + (75000 - 20000)/(1+.25)^1 + (75000 - 20000)/(1+.25)^2 + (75000 - 20000)/(1+.25)^3 + (75000 - 20000)/(1+.25)^4 + (75000 - 20000)/(1+.25)^5 + (75000 - 20000)/(1+.25)^6 + (75000 - 20000)/(1+.25)^7 + (75000 - 20000)/(1+.25)^8 + (75000 - 20000)/(1+.25)^9 + (75000 - 20000)/(1+.25)^10 + (75000 - 20000)/(1+.25)^11 + (75000 - 20000)/(1+.25)^12 + (75000 - 20000)/(1+.25)^13 + (75000 - 20000)/(1+.25)^14 + (75000 - 20000)/(1+.25)^15 + (75000 - 20000)/(1+.25)^16 + (75000 - 20000)/(1+.25)^17 + (75000 - 20000)/(1+.25)^18 + (75000 - 20000)/(1+.25)^19 + (75000 - 20000)/(1+.25)^20 + (75000 - 20000)/(1+.25)^21 + (75000 - 20000)/(1+.25)^22 + (75000 - 20000)/(1+.25)^23 + (75000 - 20000)/(1+.25)^24 = $68961.08

Answer is $68961.08.

Thanks.

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