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Tommy and Angelica have to divide a dozen cookies between themselves. Tommy’s parents have given Angelica the responsibility of choosing how to split them. The catch: if Tommy doesn’t like the offer, he can reject it and leave both children with nothing. How do they rationally work through their situation? This video also serves as a soft introduction to forward introduction–note that we must guess what sort of offers the first player will make and then check to see how the second player will respond.

In this tutorial you are shown how to calculate the mean and standard deviation from a normal distribution using the following example. A high jumper knows from experience that she can clear a height of at least 1.78m once in 5 attempts. She also knows that she can clear a height of at least 1.65m on 7 out of 10 attempts. Find to 3 dp the mean and standard deviation of the heights the jumper can reach

When dealing with decisions using Cost Benefit techniques it is very important to follow the proven principles. The health of your company and your reputation depend on it. If these rules are not followed then your decisions could be flawed.

Let’s start, shall we?

Question #1. Is this technique suitable for the small business owner?

Yes. The theory works equally as well for small business as it does for big business and government.

Cost Benefit Analysis is a decision-making technique that assesses the positive outcomes (benefits) as well as the negative outcomes (costs) of different decision alternatives. The trick is to make its implementation easy for the small businessperson.

Once you have basic knowledge of the theory and can enter data into a spreadsheet then the rest is not too difficult.

Question #2. Is this all I need to make better decisions?

No. Cost Benefit Analysis is a tool to assist in making better financial decisions. It is not an end in itself. However, part of the Cost Benefit process requires that you think widely on all options before making a final decision. This is often where most people fail in their decision-making attempts.

Cost Benefit Analysis is also very skilful at providing a single viability output for each competing option, making comparisons objective and easy.

Question #3. What do I include as the Costs and the Benefits?

Costs. All costs attributable to the project are to be included. Some of these are listed below:

- Asset Costs (both Capital and ongoing)

- Supply costs for purchased items

- Extra administrative effort required to manage project

- Delivery costs if to your account

- Replacement of assets in future years

- Tender preparation costs

- Any specialised tooling associated with the project

Revenue. Revenue can only be attributed to a project if it were not received were the project not to go ahead.

Asset Disposal and Residual Values. Some assets may be retired prior to the end of their useful lives or may be salvaged at the end of the project. This value is to be included in the cash flows (less the costs associated with their sale or disposal).

Cost Savings. All cost savings attributable to the project are to be included. Wage and salary cost savings must include their overheads and on-costs.

Question #4. How do I treat non-financial costs and benefits?

Since only cash transactions (both costs and benefits) are included in Cost Benefit models, non-financial costs and benefits are usually described by way of notes.

If the Benefit Cost Ratio is = to 1 or > 1 then the use of non-financial costs and benefits would not be required since the project is already VIABLE. Normally these non-financial costs and benefits would be included when comparing competing options whose Benefit Cost Ratio is close to each other.

Question #5. How can I test my assumptions?

You are best placed to make assumptions based on your own experience and judgement. However, you can use a technique to show others how robust your assumptions really are. This technique is called Sensitivity Analysis.

This technique is important to understand because you have made many assumptions in your analysis. These could have been, for instance, the level of new income generated, the savings generated or the residual value of the asset at the end of the project life. These assumptions are at the heart of your analysis and have contributed to your final Benefit Cost Ratio outcome.

Since the future cannot be accurately predicted there is a high probability that some of your assumptions may prove incorrect.

Using this technique will add conviction and weight to your proposal by showing how changes to costs and benefits affect the Benefit Cost Ratio. Do small changes move the project from VIABLE to UNVIABLE?

Question #6. How can I be sure that the project is VIABLE?

You have made your assumptions based on your project knowledge and experience. You have constructed the model that shows the project to be VIABLE. If you have followed the proven principles it should work out OK. Once the project has been authorised it is important to ensure that the assumptions are correct and in fact are deliverable.

To ensure this happens follow up on these items:

- Any labour savings must be delivered – re-assign affected resources

- Cost savings due to process changes must be acted upon swiftly

- Increased revenue from price rises must be implemented urgently

A Post Completion Review undertaken a year from the project’s implementation will show you if all or some of your assumptions proved correct. It will also teach lessons on how this could done more successfully next time rather than making the same mistakes again.

Question #7. How can I implement this technique in my company?

There are a number of ways as follows:

- Use Cost Benefit Analysis yourself in a pilot project

- Convince the CEO of its benefits to the company and use that authority

- Use Cost Benefit Analysis in a specific business unit

All of these ways require a thorough understanding of the theory, the reasons for its implementation and the expected payoffs.

A training program would need to be undertaken so that all those involved understood the technique.

Question #8. Why does it have to include NPV to account for the time value of money?

Typically the life of the assets, or the decision being made, will have a financial impact over more than 1 year. This is usually 3 – 5 years (computers, software, factory machinery), 20 years for some large electrical equipment and even up to 100 years for underground pipes as used in water and sewer reticulation.

Inflation, year by year, reduces the buying power of the dollar causing us to spend more each year in dollar terms to purchase the same item. So it is with projects whose life span is more than one year.

Costs and benefits that occur in year 3 or 4 of the project would not have the same impact as if they occurred in year one.

The Benefit Cost Ratio and the final decision regarding VIABILITY could be completely wrong if NPV is not used in the model.

Question #9. Are there any limits to its applicability?

Not really, as long as you are dealing with financial costs and benefits. It has application to large and small decisions, complex and simple, long lived and short lived assets, also profit based and government and charities.

There are some general limitations:

Subjectivity – It is quite unlikely that two analysts working separately will estimate exactly the same Cost Benefit Ratio number. There are many variables that can be treated slightly differently, some of which are listed below:

- Estimation of physical and/or economic life of the asset/project

- Estimates of costs/benefits of environmental protection

- The choice of discount rates (the rates illustrated above are indicative of a range which could be applicable)

- The value of benefits can be different for different groups in society (i.e. the value of a $ to the poor section of the community is different to that of the affluent class)

Political Decision Making – The necessity of making political judgements on the viability of the project (timing of elections, regional loyalties) can sway an outcome. Also decision-makers are not consistent over space and time.

First Round Effects – We would normally only include the effects that are directly attributable to the project going ahead. We would not, for instance, include the increased community agricultural output generally due to a project going ahead. This would only be justified if the sector was originally under-employed.

Question #10. How can this technique actually help me?

There are many ways – some are listed below:

- Increases your confidence knowing you have used a proven reliable method.

- Having thought of all the options for solving the problem you can present your proposal knowing you have the answers.

- Using this technique will ensure you gain recognition and more opportunities for advancement

- Once the company sees the benefits of this technique it may wish you to be the trainer of other staff or the implementation champion – more opportunities for you.

- This technique will you save time in project assessment and ranking of competing proposals.

Traditionally, to find the standard normal probability distribution, you must convert the normal random variable x to the standard normal distribution using the z-value formula, and then find the area under the standard normal distribution function below z. The normal probability distribution functions described earlier in this chapter shortens this process. The Standard Normal Probability Distribution has a mean of 0 and a standard deviation of 1.

NORMSDIST

If you already have a z value, or if you’ve used the z-value formula STANDARDIZE described below to find a z-value, you can use the NORMSDIST function to find the probability that a random variable x is below z standard deviations from the mean. The NORMSDIST function uses the following syntax:

=NORMSDIST (z-value)

For example, if you create furniture that needs to fit people of various heights and know that the average American adult is 5’8″ tall, and the heights are normally distributed around this mean with a standard deviation of 4″, you can find the probability that one of your customers is less than 6’2″.

To use this function, you must first convert the data to the standard normal distribution as described below under “STANDARDIZE.” Doing so returns a z value of 1.5, meaning that 6’2″ is 1.5 standard deviations above the mean. When you enter 1.5 as the z-value parameter of the NORMSDIST function, the function returns the value 0.9331.

If you want to find the probability that a person is greater than 6’2″ tall, you just subtract this value from 1. If you want to find the probability that a person is between 5’4″ and 6′, you must make a few calculations. The probability that a person is less than 6′ tall is 0.8413. This means that the probability that a person is between the mean (5’8″) and 6′ is .3413 (because the probability that a person is less than 5’8″ is 0.5). Likewise, the probability that a person is between 5’4″ and 5’8″ is .34134474. Add these together to get 0.6826.

NORMSINV

If instead of having a value and needing to find the probability that a random variable falls below it, you know the probability for the range into which a random variable must fall and need to find the value defining this range, you can use the NORMSINV function.

To use the NORMSINV function, just enter the probability (between 0 and 1, of course) and the function returns the z-value below which the probability area you entered falls. If you choose a probability less than 0.5, the function returns a negative z-value. If you enter a probability greater than 0.5, the function returns a positive z-value. The NORMSINV function uses the following syntax:

=NORMSINV (probability)

STANDARDIZE

Traditionally, to answer probability questions about a normal distribution, you first convert the distribution to the standard normal distribution. The standard normal distribution has a mean of zero and a standard deviation of 1. To convert to the standard normal distribution, you find a z value using the STANDARDIZE function in Excel. The STANDARDIZE function uses the following syntax:

=STANDARDIZE(x, mean, standard deviation)

For example, if you have a product that costs an average of $6,000 to produce and a standard deviation of $800, what percentage of the items should you expect to cost more than $6,600?

To find out, enter the function as follows:

=STANDARDIZE (6600,6000,800)

The function returns the value .75. You can then use the NORMSDIST function to find the probability or area under the curve between 0 and .75.

The z-value tells you how far (in terms of the number of standard deviations) an individual observation is from the mean. It therefore also allows you to determine whether an observation

is an outlier (unusually large or small) and therefore suspect. Z-values of less than –3 or greater than +3 are generally treated as outliers and call for closer inspection.

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Project Economics and Decision Analysis: Volume 1: Deterministic Models

Statistical Methods

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Good financial decisions are the life-blood of a vibrant business. The 9 ways listed below will help you to improve the way you make financial decisions, guaranteed. Let’s list them out shall we?

1.Forces more options

It is pointless doing this analysis if you do not investigate ALL the available options. More options will mean a better outcome. What is the use of just hoping that your decision is best if you haven’t spent the time to ensure you have canvassed ALL the feasible ways of solving your problem?

Maybe the ‘Do Nothing’ option is the best way. Unless you test it out you won’t know.

There are resources to assist in thinking more creatively thereby allowing you to generate more ideas and options. Search the Internet under “creative thinking”, you will find many to choose from.

Thinking through all the options lays a good foundation for the analysis that follows.

2.Puts $s to costs and benefits

Placing a $ figure against all the costs and benefits provides a standardized way of looking at the answer. The answer is termed the Benefit Cost Ratio. There are certain costs and benefits that must be included and there are some that must be excluded.

Follow the proven guidelines and you can’t go wrong.

Some costs and benefits that must be included are:

- purchase price

- set up costs

- on-going maintenance costs

- resale price

- savings in labor, input resources, increased safety,

Some costs and benefits that must be excluded are:

- sunk costs

- depreciation and other accounting arbitrary allocations

- loan interest and repayments

- price changes due to inflation

This method provides a clear analysis of the option so that the best option stands out.

3.Takes account of inflation/time value of money

Typically the life of the assets or the decisions being made, have an impact over more than 1 year. This is usually 3–5 years (computers, software, factory machinery), 20 years for some large electrical equipment and even up to 100 years for underground pipes as used in water and sewer reticulation.

As you would know, inflation, year by year, reduces the buying power of the dollar, causing us to spend more each year to purchase the same item. So it is with projects whose life span is more than one year. Costs and benefits that occur in year 3 or 4 of the project would not have the same impact as if they occurred in year 1. Agreed?

This is a very important aspect of Cost Benefit Analysis-one you cannot discard. If you want to make the best decision this needs to be taken into account.

Cost Benefit Analysis models clearly outline the assumptions, the costs, benefits and the method of adjusting for changes in purchasing power over time.

4.“Cradle to Grave view of assets

When making decisions regarding asset purchases it is critical that ALL the costs relating to the asset are included in the proposal. How can you make a valid comparisons between competing proposals unless all the costs are thought through and included?

Some costs that are commonly missed are:

- installation costs

- initial transport costs

- tender preparation costs

- de-commissioning of old plant

- de-commissioning of this plant at the end of its life

- extra administrative effort

- labor on-costs

5.Clearly shows assumptions

Cost Benefit Analysis offers the ability to clearly outline all assumptions and how they were arrived at. This is especially important when discussing the merits, or otherwise, of each competing proposal. It also provides a firm foundation for discussing the lessons learnt once the successful proposal has been implemented.

6.Clearly shows which projects are VIABLE and which are UNVIABLE

The Cost Benefit Analysis model clearly shows which option is worthwhile adopting and which is not. If the Benefit Cost Ratio is 1 or greater, that project is viable, less than 1 means it is unviable (all other things being equal). Once this has been calculated for all competing feasible options you can then choose the option with the highest Benefit Cost Ratio from those that are classed as viable.

The option with the highest Benefit Cost Ratio will also add the most shareholder value as well.

7.Provides basis for sensitivity analysis

No doubt, when you build your assumptions some elements are more sensitive to change and produce a greater impact on the overall result than others. The process to test these elements is called Sensitivity Analysis. Since the assumptions are clearly laid out, it is usually quite easy to create a Sensitivity Table. This can add a lot of weight to your proposal.

8.Makes post completion review a breeze

Once the correct option has been chosen, funded and implemented and has been operating for about a year it is a good time to go back and assess the quality of your original assumptions. You can check on the cost and benefits elements-compare assumed prices with actual. and see how close they were.

What lessons can be learned here? Mostly costs are underestimated and benefits overestimated. Were there any mistakes made?

This analysis can help you ensure that any mistakes made are not transferred to the next project.

9.Proven framework–makes selling easier

If you need to ‘sell’ your project to various stakeholders, be they employees, shareholders, the press, unions, politicians or the Board of Directors, the fact that you have used the proven, tested process will make the selling easier.

These are just a few of the ways Cost Benefit Analysis can help you make better decisions.

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How can index analysis be used to reinforce the insight gained from a trend analysis of financial ratios?

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Review of what we’ve learned. Introduction to the standard deviation.

We Have a Problem!
There was no doubt that improvements were needed at Brown Fintube. No systematic method of planning or scheduling was in place and jobs were accepted without  regard to capacity or loading. Consequently, we were not able to accurately predict shipment dates for contracts and never knew when a job was going to be late until it  was late. Our on-time delivery performance to meet original promise dates was dismal (in the low 40% range). Designs and drawings were too often late getting to the shop  because we were unable to provide Mechanical Engineering and Drafting with real need dates. There was confusion on the shop floor about how to prioritize jobs. In order to  compensate for problems and still attempt to meet ship dates, overtime and intense expediting was necessary. Each month began from scratch. By the end of the month,  the floor was clean and there was no new work in progress.

Because we couldn’t accurately anticipate or account for variation in the process, we were unable to correctly predict revenue or forecast late shipment of jobs for any  current month. We were able to meet customer needs, but only through last minute, heroic efforts by the organization. We realized that, like so many long-time  manufacturers, our order fulfillment process was out of sync. In order to bring our system under control, planning and execution needed improvement. The operations group  proposed implementation of a formal scheduling system using drum-buffer-rope (DBR), a Theory of Constraints (ToC) solution.

We were aware of the Theory of Constraints and thought it held promise, but realized there much was much to do before we could harness it successfully. We decided to  cultivate a clear understanding of the Theory of Constraints among Brown Fintube personnel and develop an effective methodology for applying it.

We were still uncertain on how to apply the Theory of Constraints to our business because most texts on the subject addressed machine shops and our business consists  of fabrication and welding with some assembly. The difference is not trivial; capacity at most machine shops is based on machine availability and our capacity is based on  labor skill availability. We researched whether or not Theory of Constraints – based scheduling software could help our business by discussing it with others who had  implemented it. Each of them confirmed our original thinking – they advised us not to implement the software without first establishing a thorough organizational  understanding of the Theory of Constraints. They also strongly advised us to use DBR manually before moving to the software phase.

We hired a respected theory of constraints consultant and together, we devised a plan for implementation of Drum Buffer Rope scheduling in our fabrication shop.  Our  implementation was not intended to be just a production solution; it was intended to be a complete turnaround for all of Brown Fintube. The goals of the implementation  were to improve on-time delivery to a sustainable level of performance greater than 95%, improve our ability to accurately predict monthly revenue amounts, and provide a  method to predict man-hour loading and capacity requirements.

The Implementation
We set the implementation in motion immediately, focusing the first group of changes where the greatest impact could be achieved. The idea behind the implementation  was to gain control of operations in increments of time. First, a few days were controlled, then a week, then a month. Finally, an implementation of a medium-range sales  and operations planning process that would manage the next several months after that, was established.

We then proceeded to train our employees in Theory of Constraints concepts. Every  shop floor employee was given an introduction, as were engineers, project managers, and key support people. Once training was complete, our shop supervisors were  excited and dedicated to making the implementation a success.

The most significant step towards bringing production under control came with the introduction of a full time scheduler. The scheduler has responsibility for generating the  production schedule, handling day-to-day reconciliation of demand to capacity, promising deliveries and overseeing the components (released and unreleased  manufacturing orders) of schedule execution. Although controversial at the time, by giving responsibility and accountability to a single person, premature release of  materials into the shop was prevented, halting misallocation of capacity and preventing late arrival of components to the constraint. We selected a drum (constraint)  resource and created a workable, daily schedule. This step was significant because the decision making processes for the entire company would now center on this  resource. No capacity, sales, or order delivery decisions would be made, from this point forward, without considering their impact on this resource. To formalize the  decision, procedures and policies were written and people were trained how to apply them. One of the tools created was the “lead time report.” This report from the  scheduler gave Sales a tool to accurately promise customer deliveries.

We then separated normal process variation from unnecessary variation (that had been introduced by lack of plant synchronization). Unwanted fluctuations were  compensated for through the addition of an effective planning and execution management process that included time buffers.

Daily “buffer management” meetings were initiated to synchronize the different departments; paying sharp attention to the constraint and to what orders were shipping – two  of the most important factors in operations. This process ensured that the constraint resource always had at least a one-day queue of parts from which to work, thereby  eliminating month end spikes in shipments and leveling our shipping rates. It also served to smooth out the flow of work in the plant by reducing spikes in capacity load.
On-time delivery performance started improving immediately. Within 90 days, we improved on-time delivery performance from 40% to more than 90%, and since February  2002, we have consistently performed on time at or above 95%. We felt we were better organized as a result of systematically planning business activity.

Our first two goals were fully accomplished and proved to be an unqualified success. Our accuracy in predicting monthly revenue is now very high. Our accuracy in the  area of “available to promise” is close to 100%. Revenue has increased while the number of direct labor employees has declined (through attrition) and it has been  unnecessary to replace them. Over 18 months, our average annual revenue per shop employee increased by $72,000.

Benefits realized inside Brown Fintube include a more responsive shop and shorter lead times. The process analysis, policy and procedure development, and execution  management means that all steps taken now work together to culminate in process improvement. For example, we are now able to determine which orders to pursue  based, not on which will cost the least per unit to make, but on which will yield the greatest profit per minute.

Results
Rather than fighting fires, we are now able to focus on anticipating and preventing tomorrow’s problems as well as planning future growth. Due to our vastly improved  reliability in predicting delivery times, we have also been able to increase the amount of premium-priced business for which we are able to provide “rush” turnaround.

Dramatic results achieved from the time of initial planning through implementation of  our Theory of Constraints scheduling initiative include:
•    Sales growth of 35% ($1.7mm per month to $2.3mm)
•    Inventory turns have increased from two to 10
•    Productivity improvement of $72,000 per employee
•    20% reduction in overtime
•    Consistent 95% or better on-time delivery

We are convinced that our reliability on ship dates gives us a definite competitive edge. As customers become more and more accustomed to our vastly improved service,  we easily win business over competition that is still merely promising.

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