Question

To increase the water supply in a city, there are several alternatives to building waterways. Build tunnels through the mountain or use pipes around the mountain. To build the tunnels it takes an initial investment value of $5.5 million but can operate forever without maintenance costs. As for installing the pipeline, it costs an initial investment of $5 million, with no maintenance costs, but a useful lifespan of only up to 50 years with a salvage value of 0. Which alternatives should be selected when viewed from the annual fee (AW)? Assume an interest rate of 6%.

Answer 1

Alternative 1: Tunnel.

Initial Investment = I = $5.5 Million

Useful life = N = ∞ years

Interest rate = I = 6%

Annual worth (AW) = ?

AW = 5500000(A/P,I%,N)

AW = 5500000(A/P,6%,∞)

We have (P/A,I%,∞) = 1/I, similarly (A/P,I%,∞) = I

AW = 5500000*(0.06)

AW = $ 330000

Alternative 2: Pipeline.

Initial Investment = I = $5 Million

Useful life = N = 50 years

Interest rate = I = 6%

Annual worth (AW) = ?

AW = 5000000(A/P,I%,N)

AW = 5000000(A/P,6%,50)

Using DCIF Tables

AW = 5000000(0.0634)

AW = $317000

Based on the Annual worth computations pipeline alternative may be selected, as it has a lower Annual worth.