Question

For the following exercise, use as many as appropriate the methods of: annual worth, present worth, benefit:cost ratio, payback period or internal rate of return. And compare the outcomes of any methods that you use.

Consider the determination of whether a worthwhile enterprise should be developed now, or at a later date. Consider a hydro-electric scheme, which if fully developed now will cost $70,000,000, and will have annual operating and maintenance costs averaging $3,500,000. However, if a first stage only is built now for $40,000,000, and the balance in 20 years time, the cost of the latter would then be $39,000,000; and the annual operation and maintenance will be $2,400,000 for the first 20 years and $4,000,000 thereafter. If the interest rate is 6% and the total life 40 years, which is the better alternative?

Answer 1

Annual worth (AW) method is used for comparison

Alternative 01

Given Data

Initial cost = $70000000

Annual O & M cost = $3500000

Interest rate = 6%

Life = 40 years

AW = 70000000(A/P,6%,40) + 3500000

Using DCIF Tables

AW = 70000000(0.0665) + 3500000

AW = $8155000

Alternative 02

Given Data

First Investment cost (First stage – Year 0) = $40000000

Second Investment cost (Second stage – Year 20) = $39000000

Annual O & M cost (First 20 years) = $2400000

Annual O & M cost (Next 20 years) = $4000000

AW = [40000000 + 39000000(P/F,6%,20) + 2400000(P/A,6%,20) + 4000000(P/A,6%,20) (P/F,6%,20)](A/P,6%,40)

Using DCIF Tables

AW = (40000000 + 39000000(0.3118) + 2400000(11.470) + 4000000(11.470) (0.3118))(0.0665)

AW = 6250573.3

Based on the annual worth it is evident that Alternative 02 has a lessor annual worth in comparison to Alternative 01. Therefore, the same may be selected.