Bab 8

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Incremental Analysis

Minggu 8

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Graphical Solutions Graphical review of an economic’s situation

will help to introduce incremental analysis.. example 1:

There were 3 mutually exclusive alternatives :A B C

Investment $2000 $4000 $5000Saving/year 410 639 700

Each alternative has a twenty-year life and no salvage value. If the MARR is 6%, which alternative should be selected?

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Graphical Solutions(2)

PWbenefit for alternative A = $410(P/A,6%,20) = $ 4703

PWbenefit for alternative B = $639(P/A,6%,20) = $ 7329

PWbenefit for alternative C = $700(P/A,6%,20) = $ 8029 Plotted graphically:

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Graphical Solutions(3) From the figure, we can see that the slope of the line from origin O to

A is greater than 6% line (NPW = 0). Thus the rate of return for A is greater than 6%.

Slope of line B – A is also greater than the 6% line, indicates that the rate of return on the increment of investement also exceeds 6%, thus desirable.

But the slope B-C indicates its rate of return is less than 6%, hence, undersirable.

We conclude that the A investment is satisfactory as well as the B-A therefore, B is satisfactory. C-B increment is unsatisfactory, so C is undesirable compared to B.

Our decision is to select Alternative B.

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Incremental Rate of Return Analysis

Using example 1, Incremental Rate of Return Analysis :alternative A : 2000 = 410 (P/A,i,20)

(P/A,i,20) = 4,878 ; i = 20%

alternative B : 4000 = 639 (P/A,i,20) (P/A,i,20) = 6,259 ; i = 15%

alternative C : 5000 = 700 (P/A,i,20) (P/A,i,20) = 7,143 ; i = 12,8 %

Each i from the three alternatives > MARR

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Incremental Rate of Return Analysis(2)Then we can examine the increments between the

alternatives by first arranging the alternatives in order of increasing initial cost :

IncrementB-A C-B

Incremental cost $ 2000 $ 1000

Incremental uniform annual benefit 229 61

Incremental rate of return :- for B-A : 2000 = 229(P/A,i,20)

(P/A,i,20) = 8,733 ; ΔROR = 9,6%- for C-B : 1000 = 61(P/A,i,20)

(P/A,i,20) = 16,393 ; ΔROR = 2%

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Incremental Rate of Return Analysis(3)

Δ ROR for B-A > MARR B is better than A

Δ ROR for C-B < MARR B is better than C

Thus, best alternative chosen is B.

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Elements In Incremental Rate of Return Analysis

1. Be sure all the alternatives are identified

2. (Optional) Compute the rate of return for each alternative

3. Arrange the remaining alternatives in ascending order of investment

4. Make a two-alternatives analysis of the first two alternatives

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Elements In Incremental Rate of Return Analysis(2)

5 Take the preferred alternative from step 4, and the next alternative from the list created in step 3

6 Continue until all alternatives have been examined and the best of the multiple alternatives has been identified

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Present Worth Analysis With Benefit-Cost Graphs Example :

Tahun Alt.1 Alt.2

0 -$10 -$20

1 + 15 + 28

PWbiaya $10 $20

Pwuntung 14,15 26,42

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Present Worth Analysis With Benefit-Cost Graphs(2)Based on the data, we can build Benefit-Cost Graphs:

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Present Worth Analysis With Benefit-Cost Graphs(3)

By looking at the graphs, we can see alternative 2’s NPW (line 2-4) is bigger than alternative 1’s NPW (line 1-3). So, we prefer alternative 2 than alternative 1

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Choosing An Analysis Method

Factor that may affect the decision in choosing analysis method :

Unless the MARR is known, neither present worth analysis nor annual cash flow analysis can be done

Present worth analysis and annual cash analysis often require far less computation than rate of return analysis

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Choosing An Analysis Method(2)

In some situation, a rate of return analysis is easier to explain to people unfamiliar with economic analysis. At other time, an annual cash flow analysis may be easier to explain

Business enterprise generally adopt one, or most two, analysis techniques for broad categories of problem.