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As an engineer for a consulting company, you are tasked with analyzing and evaluating two wastewater treatment facilities, with each facility having a life expectancy of 10 years. The cash flows in the table. Alternative A Alternative B First cost $ 915,000 $ 800,000 Maintenance and 20,000 30,000 Operating cost (Annual annual benefits 298,000 270,000 Salvage value 130,000 50,000 Table 1: Cash flow for Alternative A and Alternative B I Calculate the internal rate of return, IRR for each option B) According to the IRR, which option should you recommend? Explain.
Using interpolation,
Internal Rate of Return : RL + [NPVL / (NPVL - NPVH)] * (RH - RL) that is
RL: Lowest discount rate = 5% (assumed)
RH: Highest discount rate = 10% (assumed)
NPVL: 5% NPV
NPVH: VPN at 10%
For alternative A:
NPV = - 915,000 + (298,000 - 20,000) x P / A (5%, 10) + 130,000 x P / F (5%, 10)
= - 915,000 + 278,000 x 7.7217 + 130,000 x 0.6139
= - 915,000 + 2,146,633 + 79,807
= 1,311,440
NPV = - 915,000 + (298,000 - 20,000) x P / A (10%, 10) + 130,000 x P / F (10%, 10)
= - 915,000 + 278,000 x 6.1446 + 130,000 x 0.3855
= - 915,000 + 1,708,199 + 50,115
= 843,314
And therefore,
IRR = 5% + (1,311,440 / (1,311,440 + 843,314)) x (10-5)%
= 5% + (1,311,440 / 2,154,754) x 5%
= 5% + 3.04 x 5%
= 5% + 15.2%
= 20.2%
For alternative B:
NPV = 800,000 + (270,000 - 30,000) x Price / Price (5%, 10) + 50,000 x P / F (5%, 10)
= - 800,000 + 240,000 x 7.7217 + 50,000 x 0.6139
= - 800,000 + 1,853,208 + 30,695
= 1,083,903
NPVH = - 800,000 + (270,000 - 30,000) x P / A (10%, 10) + 50,000 x P / F (10%, 10)
= - 800,000 + 240,000 x 6.1446 + 50,000 x 0.3855
= - 800,000 + 1,474,704 + 19,275
= 693979
And therefore,
IRR = 5% + (1,083,903 / (1,083,903 + 693,979)) x (5-10)%
= 5% + (1,083,903 / 1,777,882) x 5%
= 5% + 0.61 x 5%
= 5% + 3.05%
= 8.05%
Since Alt-A has a higher IRR, Alt-A is preferred.
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Internal Rate of Return : RL + [NPVL / (NPVL - NPVH)] * (RH - RL) that is
RL: Lowest discount rate = 5% (assumed)
RH: Highest discount rate = 10% (assumed)
NPVL: 5% NPV
NPVH: VPN at 10%
For alternative A:
NPV = - 915,000 + (298,000 - 20,000) x P / A (5%, 10) + 130,000 x P / F (5%, 10)
= - 915,000 + 278,000 x 7.7217 + 130,000 x 0.6139
= - 915,000 + 2,146,633 + 79,807
= 1,311,440
NPV = - 915,000 + (298,000 - 20,000) x P / A (10%, 10) + 130,000 x P / F (10%, 10)
= - 915,000 + 278,000 x 6.1446 + 130,000 x 0.3855
= - 915,000 + 1,708,199 + 50,115
= 843,314
And therefore,
IRR = 5% + (1,311,440 / (1,311,440 + 843,314)) x (10-5)%
= 5% + (1,311,440 / 2,154,754) x 5%
= 5% + 3.04 x 5%
= 5% + 15.2%
= 20.2%
For alternative B:
NPV = 800,000 + (270,000 - 30,000) x Price / Price (5%, 10) + 50,000 x P / F (5%, 10)
= - 800,000 + 240,000 x 7.7217 + 50,000 x 0.6139
= - 800,000 + 1,853,208 + 30,695
= 1,083,903
NPVH = - 800,000 + (270,000 - 30,000) x P / A (10%, 10) + 50,000 x P / F (10%, 10)
= - 800,000 + 240,000 x 6.1446 + 50,000 x 0.3855
= - 800,000 + 1,474,704 + 19,275
= 693979
And therefore,
IRR = 5% + (1,083,903 / (1,083,903 + 693,979)) x (5-10)%
= 5% + (1,083,903 / 1,777,882) x 5%
= 5% + 0.61 x 5%
= 5% + 3.05%
= 8.05%
Since Alt-A has a higher IRR, Alt-A is preferred.
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