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Write a report on Feasibility of implementation of helium recovery.

History of Helium

The discoveries that have been made in the past have contributed to the devilment of the various sector of the economy. Some of these discoveries are yet to be completed.

Helium is just but a chemical element whose symbol is He. It has atomic number of 2. This a colourless gas with no tastes, non-toxic, on- reactive, mono atomic and the first gas in the periodic table. Helium has the lowest boiling point as compared to other elements. It is the gas with the largest quantity after hydrogen in the universe taking about 24%. The very discovery of Helium was made on August 18, 1868. (Feuz, 2012, p. 789)

The discovery was in the form of a yellow line whose wavelength was 587.49 nanometres. French astronomer, Jules Janssen detected this line during a total eclipse while in the Guntur town of India. The assumption made on this line was that it was of Sodium element. Three months later, Norman Lockyer, an English astronomer also identified a yellow line in the spectrum which he namedD3 since it fell between D2 and D1 Fraunhofer line of the sodium element. His conclusion was that this line was as result of an element in the sun which was unknown to the Earth.

 The two therefore decided to name the element with a Greek word called Helios which is for the sun. The analysis of a sublimated material from Mount Vesuvius by an Italian physicist called Luigi Palmieri became the basis of the first discovery of Helium on the Earth.

In the year 1895 March, Helium was isolated on Earth by Sir William Ramsay. This Scottish chemist treated cleveite with 10% of rare elements that were mixed with mineral acids. The individual was actually looking for the Argon but after separating nitrogen and oxygen, a bright yellow line that matched the D3 appeared. This line matched the D3 of the spectrum of the sun.

The same sample had been identified as Helium by Lockyer and William. Helium was completely separated from the cleveite by the two chemists Per Teodor Cleve and Abraham Langlet from Sweden who collected samples of the gas and determined its atomic weight. William Fancis Hillebrand an American geochemist also isolated Helium when he noticed unusual spectral line during a sample test on the mineral uranite. (Fawcett, 2013, p. 121)He however, congratulated Ramsay who had made similar discovery. Ernest Rutherford and Thomas Royds, in the year 1907, studied the nuclei of the Helium and found that it contained alpha particles.

Discovery of Helium

 A year later the Dutch physicist Haike Kamerlingh Onnes did the first experiment on the attempts to liquify the gas to a temperature below one kelvin. His attempts to solidify the gas were not successful since the gas does not solidify at the atmospheric pressure. A student of Onnes, Willem Hendrik was able to solidify the gas and this was achieved through addition of external pressure. In the year 1913, a publication was released by Niels Bohr on the atomic structure. This publication made reconsideration on the Pickering Fowler series as the key evidence the model of the atom he had discovered. (Fawcett, 2013, p. 543)

 According to Pickering, the observation lines were as a result of hydrogen with half-integer transition levels. In the year 1912, a guy called Alfred Fowler managed to obtain the same lines using a mixture of hydrogen and helium and this was in support to the Pickering conclusion on the origin of the gas. Bohr model however does not recognise the quantum mechanics and therefore marked the spectral lines to charged helium, He+. Fowler later confirmed that Bohr was right. Other discoveries related to Helium were made like that of Pyotr Leonidovic Kapitsa in which helium-4 was found to have no viscosity at temperature near absolute zero. This is commonly referred to as superfluidity.

Any Helium separation process should provide the following

A recovery efficiency that is above 98%

Independent programmable packages for the control system

The compressors that do not use oil piston seals to avoid possible contamination of the gas.

Standard vessels for the storage of gas that is certified.

Continuous on-line monitoring of the gas traces levels to check on the concentration.

An automatic system for starting the process.

The design features should include reliability. (Farmer, 2013, p. 785) The cover of the crank should be reinforced with a breather valve that serves to prevent entry of dust particles or any other material from outside. The spring loaded seals that compensates for the horizontal rod movement. The cushion devices such as valves should be built in such a way that it provides long life and silent and smooth operation.

The cylinders should not be lubricated to allow for the maintenance

To facilitate Helium recovery, the gas is first separated from the fluid mixture. The general steps are as illustrated. Table

In most cases, the composition of the natural gas varies depending on where the gas is obtained. The impurities are removed according to the standard of the company. The following procedure will illustrate

Isolation of Helium on Earth

The pre-treatment which involves the removal of impurities such as heavy metals, Removal of hydrocarbons and liquefaction. Removal of nitrogen, the upgrading of Helium, Purification process and finally Liquefaction of Helium.

The pre-treatment process helps in the removal of hydrocarbons before the mixture is allowed into the refrigeration chamber or unit. (Farmer, 2013, p. 436) Since the gas has a very has a very low boiling point, it will be concentrated in the overheads. This is achieved through a cryogenic distillation process. Such technologies usually work at a temperature below -65 degrees. This process only accomplishes 90% of the entire process.

The tracer gas in the bulk is introduced into the vacuum surge tank. The tracer gas is passed through a series of water cooled heat exchangers with high efficiencies. This takes place during compression stages C1 and C2. (Erickson, 2013, p. 89)Finally, the compressor output to the last tank [3] completes the cycling process.

The demand of helium has grown so that there is need to recover Helium. The producing industries should exploit the end users to recover and recycle the resource. The products for recovering give the dealers a chance to do production at a cheaper cost. The Helium recovery should be taken seriously to completely meet the demand and solve the scarcity problems.

Figure 1: Recovery steps diagram sourced from: (Coallier, 2017, p. 453)

The radioactive element such as Uranium and thorium while undergoing radioactive decay produces a lot of helium thus serving as the primary source of this gas. These minerals are believed to have been trapped underground millions of years ago in the old rocks. When air is liquified and its component separated, the helium can be obtained. The problem however is that the gas produced here is very little since the percentage composition of helium in the air is extremely low. The cost of production using this particular method is very high. The method therefore is never preferred for the production. (Cox, 2015, p. 256)

During natural gas treatment and processing, helium may be produced as a side or secondary product.

The demand for helium is generally a derived demand/. This means that most users never consumed the gas directly as helium but rather as a raw material or an input to the manufacture or production of other goods. In order to predict the demand of this gas, the demand of these products must be determined first. There is a market consolidation among the potential suppliers since the market has multiple stages.

Other Discoveries Related to Helium

Figure 2: Price of helium and demand source from: (Cox, 2015, p. 342)

There are very many different designs on the helium recovery. Despite this difference, the principle of operation remains the same. NMR helium recovery system has been singled from the many. The helium outlet of each magnet is always connected on the body and tilted at an angle. (Coallier, 2017, p. 266)

The higher side of the flow is connected using a stainless-steel metal. Such metals are usually used in the vacuum system where they provide a leakage proof with very low back pressure in the recovery. (Coallier, 2017, p. 372) The connection is made in such a way that it withstands the reduced temperatures of the gases leaving from the exhaust. The system must also accommodate the low vibration which is a key characteristic of the floating NMR magnet.

The lower side that is connected to the boil off meter allows for the monitoring for the leaks that should be maintained at zero. The blockage of the pipe is a common problem with this system. There is a ball valve that is found at the point of high connection. This valve is always closed but becomes open during flowing process.

When the valve opens, helium is allowed to flow down on the lower side. To reduce the excess weight and stress on the helium pipes, the valve must be on the wall .The helium passes through an adjustable pressure valve after it has boiled off . (Blokdyk, 2017, p. 543)At this point the pressure should be as low as possible. This pressure should be kept slightly above the atmospheric pressure.

The pressure differences which exist between the two regulators control the flow. The constant pressure can be achieved if the back -pressure regulator is adjusted close to the atmospheric pressure. In higher field system which are usually having vendor manostat, the monostat replaces the back-pressure regulator

The magnets each has a manifold made of copper. This manifold is connected to the header that connects to the recovery system. The system is highly finned as shown below to heat the helium to room temperature (50MINUTES.COM, 2015, p. 756).

This helps to prevent possible damages to the lower components. The existing flow to the metres is used to monitor the helium exhaust. In order to observe the flow effectively, the float can be marked with a black marker. The manifolds and header are connected to the vacuum pumps for not less than a week before installation. To detect the presence of any leakage, portable leak detectors are used.

Helium Recovery and Production

Helium is used in the semiconductor manufacturing and also required in the manufacture of fibre optics. Such applications usually require high thermal conductivity which is very important.Thi9s process is applied in the Czochralski method which involves using a cooled helium in superconducting magnets that are already stabilized mechanically regulate the melt during the pulling process. (Fawcett, 2013, p. 326) This process cannot happen without helium.

The helium gas is used in the chemical welding. The inert property is potentially exploited here .In the arc welding that involves the use of the metals such as stainless steels, aluminium and other metals with  high value and demand on the reliability .In this practice, helium is basically used to shield the gas. The plasma arc welding is always used in the fabrication of products made from specialty material that need helium too. This prevents the atmospheric particles from contaminating the t molten metal that is u (Flynn, 2015, p. 523)ndergoing welding, thus making the weld or the arc very strong and stable. Helium gas is used in the industries that carry out lifting due to the low density of the gas. Since helium has very low boiling points, it has applications in the following areas.

Purging: The bodies such as defence and even space administration may require to purge liquid hydrogen and liquid oxygen fuel tanks especially when they are at low temperatures. Oxygen gas would have been preferred for the similar task but since it is more reactive with the oxygen it may not be good for the task. Nitrogen is therefore not required because it will interfere with or contaminate the liquid oxygen. It is important to note that in the liquid environment, gases will always freeze a part from helium and hydrogen. This may lead to the blockage of the engine pipes of the rocket hence they cease to function.

Superconductor: The current materials and applied technologies have shown that only helium can be used as a vital refrigerant in the superconducting magnets. These magnets are used in the magnetic resonance imaging. (Klammer, 2018, p. 78) The MRI uses very strong magnetic field just to align or arrange the hydrogen particles in the body before setting them to a radio frequency. After the detection on the properties of the aligned particles, a tomographic process is used to analyses the densities. The only available machine that can carry out this task is made from liquid helium cooled.

The NMR Helium Recovery System

Scientific research: The investigations and researches that are done at temperatures above 4.2kelvin, only helium gas can be used as a refrigerant. This element is used to cool the superconducting equipment for particle detectors, accelerators etc. It is also used in the laboratory for research because it possesses very unique superfluid properties usually at a temperature below2.17kelvins besides having very high thermal conductivity. Leak detection: Helium has very low viscosity and means higher diffusion rate. (Lawrence, 2017, p. 231) This property enables it to be used as a leak detector. This is a very crucial property for those companies that rely on vacuum for their efficiency in the production e.g. in the electronics.

The potential alternatives to helium include the following; In the cryogenics, applications that require very low temperatures require the use of helium gas. However in the absence of this this element, cooling of substances has been achieved in MRI scanner magnet that requires super conductors. (Matanovic, 2013, p. 295) Most companies are today using liquid nitrogen to cool their systems besides a water chilling system to cool MRIs.

In the shielding of the gas welding, helium is predominantly used to prevent the contamination of the molten metal and to stabilize the arc weld. Some companies today use Argon instead since they are all inert. However, this is only done to the specific metals that require arc welding as opposed to the other methods.

The most weather balloons were used to be filled with helium gas. This application exploited the light property of this gas Fortunately hydrogen that is readily available can today be used for the same task and this has reduced the over reliance on the helium gas. This application does not take into consideration the flammable property of hydrogen gas. This is however a disadvantage.

The two gases helium and argon are the most commonly used gases in the purge. This is due to the fact that the two gases are inert in nature .It is however surprising to note that Nitrogen performs the same function perfectly. This because helium is scarce in the market as opposed to the nitrogen gas which is not only abundant but also cheap. The scarcity of helium is likely to lead to the exploration of other alternatives for those kinds of applications.

In the controlled atmospheres; helium is commonly used to prevent any form of reaction in the secluded area. Researches done have shown that nitrogen can be used to preserve many foodstuff .It is therefore preferred due to its availability and cheapness. (Matanovic, 2013)

In the deep sea diving, helium is mixed with oxygen to protect the divers from contracting or developing Nitrogen narcosis symptoms .A mixture of Hydrogen and Oxygen is today used by deep sea divers since the price of the helium has been on the increase.

In the gas chromatography, hydrogen gas has been in the lead against helium. The advantages of hydrogen includes lower cost, it is readily available through electrolysis of water. Hydrogen gas also has a very quick sampling speed. This is the main reason why many chromatography laboratories slowly but steadily changing from having helium as their raw material to hydrogen.

In the manufacture of semi-conductor and fibre optics production, helium might be playing a major role. Helium is used as an inert gas to flush vessels used in the processing plant. The gas also helps in the heat transfer in the rapid gas cooling applications which usually make such engines preferred. Such applications exploit the high thermal conductivity as a property of the gas. In some companies, hydrogen is used as an alternative option. Argon can also be used because it has inherently high temperature endurance. (Namanda, 2017, p. 265)

It refers to the identification of problems that may leads to the collapse of the project started and checking forward the achievement. Planning it the most useful object needed for the success of a business so, one should make proper and detailed information when planning for the project, in financial data, security matter, checking market gap and target.

Importance of risk analysis

  • Help in project planning when there is a need of problem anticipation and neutralization possibilities
  • It helps in decision making that is one need to decide on which step to make to continue with the project or not
  • It required when one need to improve safety and in management of the risk
  • It ensure that problems that may lead to failure of the project such as technology failure, calamities and even theft are protected
  • One cover the problems like the introduction of competitor in the market

Identification of the threats

The step is compost by checking the possible risk that may hinder business success. These include things to do with employees’ performance diseases, deaths and injuries. Operational problems example loss of customer suppliers and even distributors. Some are technology failure, political instability, natural calamities and financial problem. Therefore one should adhere with these threats for the project to succeed. (Needles, 2010)

This deals with frequencies occurrence of the risk identified and how possible of their outcome. it is calculated by multiplying the probability of the event by the cost of the event.

It comprises with different mechanism like identification, analysing, evaluation and determine hazards,   identification is where the things that may lead to failure are identified, evaluated the check away determining appropriate way of eliminating them.  One should keenly look if the workplace is conducive and identify thing that can Couse harm.

Risk assessment is very important since it checked safety, health of employees and planning management

  • It helps in creating awareness of risk and hazards to be encountered
  • It help in knowing the who is most expose to the risk example  whether employee , employer or even a visitor
  • Used in determination of whether there is a specific control for a specific risk or one control program can be used for different hazards.
  • Injuries and illness and be prevented if an appropriate planning done in the planning stage.
  • It makes it possible to arrange the hazard in the priorities.
  • Through assessment, the law and regulation requirements are followed

Assessment aims to minimize an occurrence of a risk by evaluating the risk and providing the control measure. Therefore risk assessment should be done before introduction of a new project or when a change is made within an existing project. The scope of the risk being assessed must be known in terms of the time for example if the hazard is for lifetime of the product or just for a season. (Niles, 2012, p. 334) The tools used for the assessment should determine especially in checking whether the assessment requires a train individual or a group of individuals

A person conducting the assessment should be competent person who have the knowledge in study even the team, information sources, supervisor and the co- worker should be the individual of high integrity.

By following the procedure of the assessment and risk analysis, it therefore clear that the risk can be identified, this done as we record the present possibility of risk in the workplace.  The familiar working area can also help in making conclusion. After the assessing, it is also very important to learn the past and present encounter when inculcating the experiences of others and protective measures should be put in place to provide an appropriate protection. Therefore these steps should be considered  

  • A clear knowledge of the risk must be in consideration
  • Ensure that the information  source used in risk identification is gathered
  • Identification of tools and techniques to be used
  • Documentation of the risk

Ensure the effectiveness of risk identification. After these procedure, ensure that the all hazard are found, it better if we checked

  • Inspect the working  conditions.
  • Accident exposure
  • Site of work
  • Safety of the machineries
  • The type of work to be done
  • The risk of the visitor or the society
  • The risk to the different of people must be put into consideration for example young, untrained workers, old and disables.

Example

A driver is exposing to accidents, fatigue especially when driving alone thus increasing work hours which may ends to collision.

This is the process of identifying the seriousness of the risk so as to be controlled before other. Ranking is done   considering the priority to the employee’s exposure and the incidence of injuries and diseases. Example a major fracture, poisoning, fatal accidents can be rank high followed by sprain asthma, and injuries as the medium while dizziness short-term pains and irritation as the low ones. (Nwogugu, 2017, p. 184) High means that they are likely to happen   annually or more while medium may happen after five years and low rarely happens.

When the steps in the assessment, analysis and identification of the risk are well followed, the project goals must achieve successfully the risk analysis in helium recovery.

This study help in identification of all types of risk that can affect personnel, equipment and environment  as a result of failure of from cryogenic that can lead to accidents in the cryogenic system of Large Hadron Collider in the steps of the machine operation  and checking to their elimination through a design. (Pahl, 2009, p. 523)Then recommend on the prevention and corrective measure to be put in place.

There are three steps presented on a paper work

Step one:  identification

Consist of presentation of the machine to be used, called later node, and failure related to cryogenics and in its operations. The data collected from different sources to be read, discussed and experiences is put at CERN.

Step two: The combination phase

The stage of collection of potential failure in every node in the mode of the collider operation.

Step three: Analysis (Phillips J. J., 2012, p. 312)

Performed in two steps , the first step only require yes or no answer to retain credible failure only the descriptive analysis is performed to investigate the causes and consequence of the credible failure. The event is numbered depending on their gravity in that if gravity one failure does not affect that of two and three;

Illustration diagram. source from: (Farmer, 2013, p. 433)

LHC cryogen system node

Here the cryogenic system of LHC is treated while the separate helium enclosures are composed this process is referred to the later on node. Every node is entitled by the amount and thermodynamic parameters of the enclosed helium. The classification of the LHC Cryogenic node according to their location

Nodes found in tunnels, that related to letter R are LHC cryomagnets, cryogenic distribution line QRL. (Revie, 2015, p. 563)

Nodes found in cavern, they are related to later U, they include cold compressor boxes QURC.

The shaft nodes, related as later  including the cryogenic interconnecting lines QPLA

Nodes at the surface they are connected by later S e.g. helium compressor stations, QSCA, QSCB and QSCC.

The LHC Philosophy declared a certain feature designed for resting

When there is high capacity, cold recovery header D which works at minimal pressure of 1.3 bars and at temperature of 20K having a volume of 60 m3. After the loss of insulation vacuum or magnet resistive transition, the helium expelled from a cold mass is flowed into header D. On the other the header also has got the mechanism of accommodating the helium released from the cryogenic distribution line QRL after the vacuum insulation degradation.  However due to low pressure, the header is protected by a safety venting directly to craven is to header B. a warm recovery line (figure 3) were the helium from theft is accommodated after cooling S current mode  

  • The liquid Nitrogen is used in pre helium  cooling  at the  ground surface during cooing therefor is not present in the tunnels
  • Due to the missing helium force by the pump in the cooling lead to quasi-state behavior of liquid of header rapture.  

The future differs as one chose from the option for the cryogenic system of other large super conduction acceleration which results on making LHC cryogenic system safer and with limited risk and failure.

 The cryogenic – related mode is defined as an accidental event that involves helium mass that is between helium closure, insulation and environment which end in any construction element or malfunctioning. As a result of van extended magnet resistive transition or electrical arc is also a failure mode that Leeds to an unexpected realizing se   of energy to the cold mass helium thus assuming that the LHC system, only failure mode can happen depending on time.

  The scheme of LHC cryogenic system nodes generically has been shown based on the scheme with a definition of the following failures including    the one for LHC cryomagnets though few of them e.g. for the medium- pressure helium storage tanks the possible failure is helium flowing to the environment. The cryogenic failure mode (Phillips J. M., 2013)

  1. Air flow to insulation vacuum
  2. Helium flowing to insulation vacuum
  3. Air flowing to sub-atmospheric helium.
  4. Air flowing to the environment.
  5. Air flowing to beam vacuum.
  6. Helium flowing to beam vacuum.
  7. Pressurized helium flow to sub-atmospheric helium
  8. Energy release to the mass helium due to a sector quench
  9. Energy releases to cold  helium mass due to electrical arc
  10. Oil flowing to environment due to helium compressor only

The failures that relate to LHC can be classified in separate gravity e.g. gravity 1, 2 and 3

 Gravity one: Here the failure is not inclusively in helium relief from the machine and not environment or personnel risk

Gravity two: Comprised the blowing of helium out of the machine to the atmosphere.

Gravity three: The helium is blown out of the machine to a confine area e.g. to the tunnel, cavern shaft and to the surface of the building.

Gravity three is further divided into two  that is 3a and 3b, where t3a deals with the access  of the tunnels is forbidden while in 3b the assessment to the tunnel is allowed  though are controlled under specific condition

From AIWG (Access and Interlock Working Group) endorsed the LHC Technical committee  concluded that the access to LHC will be always be controlled

This is the rate of return that is expected to be earned on the investment. The Internal Rate of Return is a device that tries to the Net Present Value (NPV0 to zero. The internal rate of return is calculated when the cash flow of the project and the Net Present Value (NPV) is given and then is equivalent to zero while the initial cash during the start to be equivalent to present value for the future cash flows of a particular investment (cost paid =present value of future cash flows, thus net present value = 0)

The internal returns rate is the compared to the company’s capital cost. The company usually accept the project only the internal rate of return is greater than or equal to the cost of the capital. In many cases the quantitative and qualitative factors that are considered in the investment decision is that the lower the cost of capital the high rejection possibility.

Formula of internal rates of returns

Calculation of Internal Rate of Return

Calculated by using IRR or XIRR function in excel programs

 Calculated using financial calculators

 Using process of iterative where the different discount rates are analysed until Net Present Value is equivalent to zero

 Help companies in picking project since it help in increasing revenue and in cutting down the cost, therefore has a great impact when there is a need for investment and in developing new product to be successful.

 During capital budgeting, people need to know the return on investment and internal rate of return therefore, this method allows the comparison and the project ranks based on yield and the one with high internal rate of return is prefer. (Revie, 2015, p. 564)Though in helium, the internal rate of returns is perceived in different ways that is with the concern to helium, cost heat etc. as in the figure below checked the internal rate of returns with heat in consideration.

It refers to the decrease or decline in the value of money with time. This is caused by the following reasons

  • The Inflation which may terrible affect the economy
  • When the opportunity cost of any capital is delayed
  • Delayed receipts of cash with the associated risks

The above factors contribute differently on the decline of the value of money. A number of formulas are used in the determination of this parameter. The present value formula measures how the value of money declines with the time

. PV=FV/(1+r) where PV stands for the value of money in today, FV is for the value of money that will be received in the future while r simply refers to the discount rate. It is very true that if the sum of money is invested today, it will earn interest with time and increase in the value. The value that this money finally becomes is called the future value when the future value of money is calculated. (Romm, 2013, p. 97) The practice is known as compounding. The present value is the amount value that will be taken after compounding.

The future value of a sum of money depends on the interest rate to of the financial institution.

FV=PV*(1+r) r where FV refers to the value of the future sum and t is that periods

r= the periodic interest rate

PV= the present value

t=the number of periods up to when the money was received.

The period may be a year, days or weeks.

The formula for calculating the present Value sum is as shown below. It is usually the inverse of the future value. PV=FV/(1+r) t

Compounding frequencies refers to those frequencies that were used to determine the interest rates charged during a given year or period. This is one of the most factors that determine the future value and the current value of the sum of investment. (Slorach, 2015, p. 143) If the interest is compounded semi-annually, then the dealer or the investor will receive half of the annual rate times two in a year.

As the frequencies of the compounding increases, the interest earned during the given period also remains fixed or unchanged. The compound interest however increases. For example, an investor receives 1% every three months for a quarterly investment. It is therefore observable that as the compounding frequency increases, the future value of money also increases.

In the present value, very high compounding frequencies will definitely contribute to the decrease in the present value. This is explained in simple terms as the more compound earned that reduces amount that must be saved now to the worth future sum.

This is a period stream of equal sum payments. Although this term was specifically meant for the annual calculations only, it is treated as just equal payment. The annuities are of two types, i.e. ordinary annuity and annuity due.

In the ordinary annuity, the first payments are made in the future. The examples of the ordinary annuities include car loan payments, student loan payments, social security funds etc

In the annuities due, the first payments are usually made on the spot. Taking an example of a lease agreement or taking of a loan where the first payments is required on the spot. As a result of the timing of cash flows, the present value or the future value of an annuity will be affected by both the ordinary and annuity due.

The future value of the annuity rate will be given by FV due=FVAordinary*(1+r). This shows that the future value of this an annuity will be bigger than the value of an ordinary annuity. This is attributed to the fact that each of the cash flows of an annuity due is invested for an additional one year.

The present value of an annuity due is calculated using the formula of; PVA due=PVA ordinary*(! +r).This also indicates that the present value of an annuity due is much greater than the present value of an ordinary annuity. (Surhone, 2010, p. 111) The reason for this outcome is due to the fact that each of the cash flows of the annuity due is paid one year sooner. This means that the invested capital will earn less capital. In order to generate some good amount of money huge capitals must be invested.

An investment in which interest are paid forever but with no payment In the principal is commonly known as a perpetuity An individual with a stock that brings, a regular steam of payment is called a perpetuity since the same amount of money or cash flows are paid each year with the stock having an infinite lifetime.

The present value of a perpetuity that normally pays a n annual cash flows is given by the formula PV=C/r in dollars per period. The present value of a growing perpetuity is also given by PV=C/(r-g) where g refers to the annual growth rate of the perpetuity.

The interest convention rates address the loans rates and bank account assets. This achieved in two different ways that includes Annual percentage rate and effective percentage rate. In most of the financial statements the annual percentage rates reflects on the simple interest of an investment while effective interest rates handle both the simple and compound interests. The conversion from the APR t EAR allows for the comparison of the interest rates and this will also help in knowing the true value of a commodity or the cost of borrowing especially when the interest is compounded more than once in a year.

In the continuous compounding, the highest frequency is used. It is therefore taken as the limit of the compounding frequency. This compounding indicates that the rate is being compounded at every instant time which means that the interest is compounded infinite times. This compounding frequency is not a continuous therefore it is taken as the discrete. The compounding can be done monthly, yearly, daily etc.

The individuals whose lives and operations or activities are affected by the project or will affect the operation of the project are called stakeholders. (Transportation, 2013, p. 453) In order for the project to succeed and for smooth operation to be realised, these people must be engaged both partially and fully. The manager therefore is expected not to exercise full power to force things work but rather to be consultative. The stakeholders are effectively managed through the following ways

Effective communication

Prior to the engagement of the stakeholders, a lot of information about them should be gathered This was very key since you would be working with these people or relying on them in one way or the other. Poor communication is usually regarded as the root causes of project failure, misunderstanding, poorly coordinated teamwork together with the ineffective risk. Successful outcomes are realised upon making good communication. When this communication is ignored for no good reason then the project may suffer consequences such as withdrawal of support from the stakeholders, a lot of cost due to confusion delays in deliveries etc (Vesilind, 2013, p. 23)

Develop a proper relationship which will later increase trust. The trust makes people to work together easily. The confidence across the project environment is thus increased with elimination of uncertainties’ personal qualities such as respect for others and courage will matter a lot here. The benefits of this includes increased mutual trust, better problem-solving methods that are speedier, improved chances of retaining staff, personal development and maturity. When this is lacking then reduced motivation, greater unknown resistance to the project and loss of the company reputation.

The quality communication will ensure that the stakeholders do the right thing based on the given data and not assumptions. There will be improved efficiency since people reach the right place at the right time. Effective communication will also help to avoid much risks and protect the reputation of the company.

Proper and regular consultation; Sometimes a project may be unclear to the target stakeholders in terms of approach, scope and purpose. Regular consultations will ensure that the solutions are negotiated and accepted by the majority of the stakeholders.

Humane treatment and acceptance recognises the fact that stakeholder’s behaviour may not always be rational, consistent and predictable .After understanding the cause of the stakeholder behaviour; it is possible to asses if there is a better way to work together. By understanding the root causes of opposition for example, one can adequately address issues such as blocking of roads

A proper planning to the stakeholder approach is highly recommended. The investment in careful planning always makes the project to succeed. This can be achieved by developing the most appropriate methods to engage stakeholders face to face for the dialogue.

Taking the prior actions that are pre-emptive actions to ease later resistance to implementation. The sensitive behaviour by the team of the project may make it easier for the concerned stakeholders to respond accordingly. (Vesilind, 2013, p. 243)The team members should be advised to remain vigilance to spot any sign of disquiet besides having responsiveness and flexibility to act faster.

The stakeholders should have engaged actively in the establishment of risks,

 A formal meeting thus should be conducted with the aim of incorporating them in the risk assessment. This helps to build a rapport within the stakeholders and the communities and making them feel that are value and taken care of besides being listened to. It is important to note that when the stakeholders concerns are not listened to or misunderstanding assumed can lead to very big project risk. These concerns should be addressed using the project management language that the team are more familiar with especially to explain the practice that is often not clear.

There is need to compromise as one seeks to establish the most acceptable ground for dealing with the stakeholders. (Vesilind, 2013, p. 412) These people predictably have divergent views on the same project but a satisfactory solution that all parties accept should be sought. The company may be required to make some compromises .A project manager is viewed as a problem solver and failure to solve or compromise may weaken the stand. This can be achieved by developing the most appropriate methods to engage stakeholders face to face for the dialogue.

Taking the prior actions that are pre-emptive actions to ease later resistance to implementation.

The use of SWOT analysis in the management of the projects has made very many companies to succeed. S.W.O.T is just but an acronym that stands for strength, weaknesses, opportunities and threats.  Strengths and weaknesses are internal to the company since they involve things like location, patent and the company’s reputation. Opportunities and strengths are externally driven. They may include factors such as competitors, prices etc. Unlike the internal environment that can be changed over time, the external factors like competitor are always there to stay as long as the project will be kept running.

The weaknesses are internal factors that are considered negative to the prosperity of the business. These areas should be enhanced so as to remain competitive in the market. The questions such as what factors are within control that detract business should be asked. What improvement should be made?

Any project can use the SWOT analysis to assess the changing environment and t5he respond appropriately. For a project that is yet to be started. This analysis can be used as part of the planning tool. It will surely put the business on tract.

The analysis is rapidly conducted a square template. In each of the four stages, brainstorming is very important. (Weisend, 2016, p. 78) This can be done in groups after each person has completed with the template. In the template, the strengths are defined as the positives attributes that are both tangible and intangible and are just within the control of the decision maker. It may involve asking questions such as what internal resources do we have? The responses should be positive like knowledge, skills, reputation, background and even network.

Tangible assets of the company such as capital, credit and patent are more advantages. Are the strong research and manufacturing facilities? What other positive aspect adds value to the business that will make it more competitive. The opportunities are those external but very attractive factors that motivate an individual into starting a business. Is the perception of the business positive? Is the opportunity ongoing or just short-lived.

The threats refer to those factors which are beyond our control. They tend to keep the business at risk but if the entrepreneur addresses them properly then success a wait. The questions such as what are the potential competitors should be asked. What factors beyond control place the business at risk? Has a new technology been introduced? Any factor that usually changes the consumers behaviour?

Strengths and weaknesses are within the company since they involve things like location, patent and the company’s image. Opportunities and strengths are externally driven. They may include factors such as competitors, prices etc. Unlike the internal environment that can be changed over time, the external factors like competitor are constant that is they never change.

The weaknesses are internal factors that are considered negative to the prosperity of the business. These areas should be enhanced so as to remain competitive in the mar

The overall advantages of SWOT analysis therefore include

Prevention of possible threats, capitalisation on the opportunities, full exploitation of the strengths, helps one to understand business better and to develop goals and strategies for a achieving those goals. Just like any other business strategy tool, SWOT too has limitation which include; it does not provide alternative solution to the entrepreneur. Although many ideas can be generated, it does not help in choosing the best option. It can help in generation of many solutions but none of them may be useful. (Wheeler, 2015, p. 123)

It refers to a financial tool that quantifies the earning power of any investment. This tool serves to evaluate the profitability of the investor. It is normally expressed as a ratio of net income to the investment. A high value of ROI implies the investment is efficient.

ROI= (gains-costs)/costs

Functions of the ROI

It is used to measure the profitability of the investment.

It’s used to do the comparison on the profitability of all that investments of an investor and makes his decisions wisely.

The limitations of the ROI include the following:

  • It does not take into account holding periodic investment
  • It assumes the non-financial benefits of the investment
  • They are subject to manipulation to suit particular interests.

It refers to the difference that exists between the present value of cash inflows and the present values predictable for the outflows for certain duration of time. The technique is used normally in the capital budgeting to evaluate the profit competence of any projected project.

During this analysis there are two possible values that one can obtain .A positive value or a negative value. When the projected earnings exceed the expected value or cost then the positive net present value will be obtained. The investment with a positive NPV is profitable .Also an investment with the negative value is and indicator of loss realized. To solve the problems including merger the discounted cash flow methods are used.

The process of determining the NPV is never easy because there are other methods to measure the value of cash in the future .Due to the influence of the time value of money, money has more value in the present than in the future. The inflation factors in the country plays a major role in this phenomenon.

In simple terms the value of a dollar today will not be any comparable to the value of the dollar in ten years to come.  A car may cost twenty thousand dollars today but in the next ten days to come the same car will not be purchased at the same cost. (Victor Joffe, 2011, p. 235)

The net present value is very much crucial in the financial modelling due to the fact that the future cash flows depend on the discounted rates that were applied on them. The companies have different ways of calculating or determining the discount rate. The most common existing ones include using the expected return of the other investments whose levels of risk are almost the same. The cost associated with the money that has been used to finance other projects.

The Net Present Value Drawbacks and Alternatives

When gauging an investment benefits using NPV that relies on multiple assumptions and with several estimates, errors do occur. The estimated factors may include investment costs and projected returns. Sometimes projects may require unforeseen demand on money for it to kick off. Unfortunately, discount rates and cash inflow estimates do not inherently account for the risks associated with the project itself. Such factors may need to be adjusted to take care of the losses.

A payback method may be used as an alternative to the NPV. It is normally used to engage the time required to get back the money that was used for the investment. It is a very simple technique for the process as compared to NPV itself. However, this method does not factor in the value time of money. It follows that the payback periods that are calculated for longer investments have greater chances of being inaccurate.

It is the resultant amount of cash and other cash- equivalents being pumped into or out of the business. The cash flows help in the determination of the liquidity of the company the company’s ability to pump back some amount of money into business after paying debts. The cash flows are of different types

Cash flows from operating activities  

Cash flows from financing activities.

A schematic diagram on the cash flow is as shown below.

Cash flows from operating activities:

Consolidated net income

3,283

(Income) loss from discontinued operations, net of income taxes

Income from continuing operations

3,283

Adjustments to reconcile consolidated net income to net cash provided by operating activities:

Depreciation and amortization

2,319

Deferred income taxes

(159)

Other operating activities

239

Changes in certain assets and liabilities:

Receivables, net

782

Inventories

(1,475)

Accounts payable

(319)

Accrued liabilities

(919)

Accrued income taxes

695

Net cash provided by operating activities

4,446

Cash flows from investing activities:

Payments for property and equipment

(2,203)

Proceeds from the disposal of property and equipment

68

Other investing activities

22

Net cash used in investing activities

(2,113)

Cash flows from financing activities:

Net change in short-term borrowings

(741)

Proceeds from issuance of long-term debt

43

Payments of long-term debt

(915)

Dividends paid

(1,579)

Purchase of Company stock

(280)

Dividends paid to noncontrolling interest

(69)

Purchase of noncontrolling interest

(70)

Other financing activities

(84)

Net cash used in financing activities

(3,695)

Effect of exchange rates on cash and cash equivalents

(14)

Net increase (decrease) in cash and cash equivalents

(1,376)

Cash and cash equivalents at beginning of year

9,135

Cash and cash equivalents at end of period

7,759

The Helium gas has a number of benefits and its discovery has changed lives. It is however regrettable that the gas is being depleted. The available methods of recovering this gas should be advanced in order to increase on the supply and meet the demand. The setups used should allow for the safety and quality. To avoid over reliance on this particular elements, the alternative sources should continue to be exploited.

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