Question

# The City of Omniville has two options for a viaduct. One is a permanent cement canal...

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.

6.9%

10.66%

16.31%

35.04%

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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