Question

Two mutually exclusive diesel generators are considered for purchase by a power generation company. Information relevant to compare the alternatives is summarized below:

Generator A | Generator B | |

Capital investment | $100,000 | $80,000 |

Market value at the end of service life | $35,000 | $10,000 |

Annual fuel and maintenance expenses | $3,000 | $5,000 |

Service life | 10 years | 10 years |

Use the IRR method to determine the better machine to be purchased. The MARR is 10% per year.

Answer #1

Incremental initial cost (A-B) = 100000 - 80000 = 20000

Incremental Salvage (A-B) = 35000 - 10000 = 25000

Incremental Fuel expenses (A-B) = 3000 - 5000 = -2000 (Annual savings)

let incremental IRR be i%, then

2000*(P/A,i%,10) + 25000*(P/F,i%,10) = 20000

dividing by 1000

2*(P/A,i%,10) + 25*(P/F,i%,10) = 20

using trail and error method

When i = 11%, value of 2*(P/A,i%,10) + 25*(P/F,i%,10) = 2*5.889232 + 25*0.352184 = 20.583076

When i = 12%, value of 2*(P/A,i%,10) + 25*(P/F,i%,10) = 2*5.650223 + 25*0.321973 = 19.349777

using interpolation

i = 11% + (20.583076-20) /(20.583076-19.349777)*(12%-11%)

i = 11% + 0.47% = 11.47% (Approx)

As incremental IRR > MARR, option A should be selected

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