Question

The City of Omniville has two options for a viaduct. One is a permanent cement canal and the other a cast iron (CI) pipe. If details for the options are as shown, at what rate of interest should the city be indifferent to either choice?

Cement Canal | CI PIPE | ||

Initial cost | ($6,000,000) | ($5,500,000) | |

Life | Perpetual | 30 | years |

Annual maintenance cost | $700,000 | $875,000 | |

Salvage | $0 | $770,000 | |

Initial Rate | 14.0% | p. y. |

Group of answer choices

6.9%

10.66%

16.31%

35.04%

Answer #1

Cement Canal

PV of annual maintenance cost = Annual maintenance cost/ Initial rate = 700000/0.14 = 5000000

Total NPV of cash outflow = Initial cost + PV of annual maintenance cost

= 6000000 + 5000000 = 11000000$ (cash outflow)

CI Pipe

PV of annual maintenance cost for 30 years = Annual maintenance cost * (PVIFA 30 years , X%)

PV of residual income at year 30 = Residual income / (1+ X%)

NPV = 5500000 + PV of annual maintenance cost for 30 years - PV of residual income at year 30 = 11000000

Now solve for X by computing equation

You can also use trail and error method

X= 16.31%

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