Question

16. Use incremental analysis to select the best alternatives using Benefit-Cost ration 4000 2000 6000 7330 470008730 GO0D 1000 9000 10000 Cost Pw(benefits) 90009500 Useful life is 20years Interest 6%

Answer 1

USE BEST ALTERNATIVE USING INCREMENTAL ANALYSIS AND BENEFIT-COST RATIO:

Incremental analysis, also referred as differential or marginal analysis, is the simplest approach to solving complex business decisions. It uses the ‘cost-behavior concept’ to analyze how each cost (fixed or variable) will affect the different alternatives of future income. Incremental analysis is an effective tool to determine the best alternative that can yield the highest revenues with the least costs. Gathering the required financial information on all the options is as important as carrying out the actual analysis. The quality and reliability of the information also contributes to the success of using this tool in business decisions. Incremental analysis is also a critical and time saving tool that leads to an efficient method in identifying the possible results of decisions on future earnings in making better decisions regarding the productivity of the company. Incremental analysis helps companies decide whether or not to accept a special order, which is typically lower than its normal selling price. It also assists with allocating limited resources among several product lines to ensure the scarce asset is utilized to return the greatest benefit. Incremental analysis entails decisions on whether to produce or buy goods, scrap a project, or rebuild an asset. Finally, incremental analysis provides insight into whether to produce a good further or sell at a certain point during the manufacturing process. The focus of incremental analysis is to examine what differs between the alternatives. Incremental analysis utilizes up to four major components:
1. Revenue differences.
2. Cost differences.
3. Cost savings differences.
4. Opportunity costs.

Incremental amounts are often called differential or relevant, however thinking of incremental amounts as what 'differs between alternatives' will help you identify incremental amounts from a practical standpoint. Many of the costs that will 'differ' are variable costs because variable costs change in total when activity changes. As such, total variable costs will differ between most decisions. Fixed costs differ only in specified situations. Identifying the behavior of costs enables managers to anticipate how each cost will behave under alternative situations.

The benefit/cost method of analysis is a procedure wherein the magnitude of the benefits (B) associated with an alternative is compared with the magnitude of the cost (C). In dividing the benefits by the costs, a number equal to or greater than one would obviously mean that benefits exceed costs, indicating economic attractiveness. A benefit-cost ratio (BCR) is an indicator used in cost-benefit analysis, to show the relationship between the costs and benefits of a proposed project, in monetary or qualitative terms. Benefit-cost ratios (BCRs) are most often used in capital budgeting, to analyze the overall value for money of undertaking a new project. However, the cost-benefit analysis for large projects can be hard to get right because there are so many assumptions and uncertainties that are hard to quantify. This is why there are usually a wide range of potential BCR outcomes, so the BCR is usually used to get a rough idea about the viability of a project and how much the internal rate of return exceeds the discount rate, which is the company’s weighted average cost of capital — the opportunity cost of that capital. The BCR is calculated by dividing the proposed total cash benefits of a project by the proposed total cash costs of the project. Prior to dividing the numbers, the net present value (NPV) of the respective cash flows over the proposed lifetime of the project are calculated.

To calculate the net present values, we use the (NPV) formula, in which the values are divided by the sum of 1 and the discount rate raised to the number of periods:

NPV = Present Worth Revenue or Saving @i* - Present Worth Costs @i*

If the calculated NPV for a project is positive, then the project is satisfactory, and if NPV is negative then the project is not satisfactory.

A conventional B/C analysis is used almost exclusively for government projects. As such, the following terms apply:

Benefits (B) - Favorable consequences to the public
Disbenefits (D) - Unfavorable consequences to the public
Costs (C) - Consequences to the government (savings to the government are regarded as negative costs)

The last item reflects the loss caused to a part of the public.
In particular, let us denote
B: benefits of the project;
I: initial capital investment;
CR: capital recovery;
O&M: operating and maintenance costs.

The sign convention treats benefits and costs as positive values and disbenefits as negatives. Thus, a conventional benefit-to-cost ratio is calculated as B/C = (B - D) / C

In non-government evaluations, some analysts place maintenance and operation (M&O) costs in the numerator as disbenefits, in which case the resulting ratio is known as a modified B/C ratio.

A B/C ratio can be conducted in terms of PW, AW, or FW values, as long as all values are expressed in the same units.

Conventional B-C Ratio: PW (B) I + PW (O&M) or AW (B) CR + AW (O&M)

Modified B-C Ratio: PW (B) − PW (O&M) I or AW (B) − AW (O&M) CR

If the market residual value is also included, then
Conventional B-C Ratio: PW(B)/ I − PW (MV ) + PW (O&M)

Modified B-C Ratio: PW(B) − PW(O&M)/ I − PW(MV )

In any case, if the B-C ratio exceeds 1, then the project is justified. If B/C >1 then project(s) is economically satisfactory. If B/C =1 then project(s) the economic break even of the project is similar to other projects (with same discount rate or rate of return). If B/C <1 then project(s) is not economically satisfactory

Taking the above example, let us now calculate the correct way to do an incremental analysis:

	A	B	C	D	E	F
Costs	4000	2000	6000	1000	9000	10000
PW (Benefits)	7330	47000	8730	1340	9000	9500
Useful life is 20 years
Interest 6%

PW (Benefit; A, B,C,D,E,F) = 7330+47000+8730+1340+9000+9500

= 82900

PW (Cost; A, B,C,D,E,F) = 4000 + 2000+6000+1000+9000+10000

=32000 (A/P, 6%, 20)

=32000 - 0.0200

= 31800

B/C = 82900-31800

=0.051100

If a project has a BCR that is greater than 1, the project will deliver a positive NPV and will have an internal rate of return (IRR) above the discount rate used in the DCF calculations. This suggests that the NPV of the project’s cash flows outweighs the NPV of the costs, and the project should be considered. If the BCR is equal to 1, the ratio indicates that the NPV of expected profits equal the costs. If a project's BCR is less than 1, the project's costs outweigh the benefits then it should not be considered.