Effect of Solar Magnetic Field (SMF) on Solar Radio Flux

Effect of Solar Magnetic Field (SMF) on Solar Radio Flux Paper published in the proceedings of Conference on Recent Trends of Research in Physics (CRTRP 2012); Page no. 85-91, 2012, ISBN: 9788190436298 3.1. Introduction: The solar activity appears to be straightforwardly associated with the strong and complex solar magnetic field.The huge solar magnetic field is a result of the flow of plasma currents within the Sun, which impel charged particles to move about from one of the Sun’s poles to another. The mean magnetic field is the strength of the longitudinal component of the photospheric magnetic field averaged across nearly all the visible hemisphere of the Sun. The sun’s magnetic field has the remarkable property that it is not distributed uniformly, but concentrated in flux ropes which appear on the surface of sunspots, plages and network. Hale first found the evidence of strong magnetic field in the sunspot from the Zeeman splitting (Hale 1908). Sunspots are the seats of the strong magnetic field and the field strength of a large sunspot can be as high as 3000 Gauss. Due to the strong magnetic field inside the sunspot, the convection is inhabited and the region becomes relatively cooler and hence darker compared to its surrounding region. So sunspots can be treated as the best manifestation of the Sun’s magnetic field (Solanki 2003). Figure: 3.1.1. Solar magnetic field (Image credit- http://www.nasa.gov) The variations of sunspot number have well-established periods of about 11 years (Hathaway et al.2002). The period of magnetic activity cycle is twice as that of sunspot cycle, about 22 years on average (Hale et al. 1919). Most of the solar activity parameters vary consistently with the sunspot cycle. Among these parameter solar radio flux is one which has its own importance in Radio Astronomy as the precise information about its emission from its origin region provides the details about the temperature, constituents, density, ionization, magnetic fields and the physical nature of the various sources inside Solar structure (Kundu, 1965). Thus to diagnose the solar atmosphere and the magnetic energy release in solar corona, radio observations serve as a powerful tool. The radio flux has its origin from atmospheric layers high in the solar chromospheres and low in the solar corona, though the accurate level of origin is not yet fully known (Kane, 2003). Observations at different radio frequencies provide the information about the various depths and the physical structure on the solar atmosphere. Accurate daily radio fluxes at different frequencies are very useful for the study of solar physics of the different layers of solar atmosphere (Zieba, 2001). Many workers have performed correlation and spectral analysis of solar radio flux variations (El-Raey and Scherrer, 1973). Watari (1996) analyzed solar radio emission at several frequencies to investigate their irregularities, time variation and solar coronal activity at different heights. Kane et al. (2001), Vats et al. (1998) and Mouradian et al. (2002) used the solar radio fluxes at different frequencies to study the coronal rotation period at different heights and its differentiality as a function of the altitude. Meheta (2005) has studied the relationship of rotation period with different phases of solar cycle. It is already evident in the literature that various frequency bands in the range starting from 245 MHz to 15400 MHz originate from different layers of solar atmosphere starting from lower chromospheres to upper corona as illustrated in the Table 3.1. Thus study of radio flux at different frequencies within this range provides the information about different layers of solar atmosphere. Table 3.1. : Different radio frequencies and their origin in solar atmosphere The quiet Sun emission at different frequencies contains information about densities and temperatures in different layers of the solar atmosphere (Watari, 1996). It is one of the prime reasons of studying solar radio emission at different frequencies during the Solar Figure: 3.1.2. Monthly variation of sunspot number for the year 2009. (Image credit- http://www.greatdreams.com/solar/2009/space-weather-december-2009.htm) minimum period which provides an opportunity to the scientific community to study the physical behavior of Solar atmosphere. It also provides very useful information about the temperature and the shape of the solar corona (Kundu, 1965). Thus the study of solar radio emission during the minimum period serves as an important tool for the study of solar corona. The current minimum of cycle 23-24 has been treated as a peculiar minimum characterized by reduced polar field strength, extremely low level of solar activity and extending for longer duration (Gopalswamy et al, 2012). Various solar indices like F10.7 cm, EUV flux, solar wind etc. behaved unusually during this minimum. Even the ionosphere also showed an anomalous behavior (Eduardo et al, 2011). The boundary between the Earth’s upper atmosphere and space also moved to an extraordinary low altitude (www.sciencedaily.com/releases/2008/12/081215121601.html) during the period. This type of unusual behavior of this minimum has c reated the interest among the solar science community to make a rigorous study on this period. The microwave brightness temperature during this minimum was substantially diminished compared to the 22-23 minimum which is also consistent with the decrease in solar magnetic field strength (Gopalswamy et al, 2012). Basu (2010) found the evidence of difference of Sun’s internal structure during the current minimum from the minimum of previous cycle. During the minimum period, the 2800 MHz radio flux showed an anomalous behavior in its correlation with Sunspot number (Tapping, 2011). In the context of above peculiarities of current solar minimum, it is interesting to see the variation of correlation of solar radio flux at several frequencies with sunspot number during this period. In this chapter the preliminary results regarding the study on the relation of solar radio flux and solar magnetic field parameters have been presented. Here the frequency distributions of correlation coefficients of solar radio flux with sunspot number and solarmagnetic field have been investigated for solar minimum and maximum period. We have also make analysis of periodic variation of basal component of solar radio emissions. 3.2. Observation: Here we studied the behavior of solar radio flux for the extended solar minima of Solar cycle 23 (2009). Firstly, we calculated the correlation between the solar radio flux and Sunspot number which is the index for measuring the variability of these two solar activity parameters. We have found the correlation coefficient at eight frequencies (245, 410, 610, 1415, 2695, 4995, 8800, 15400 MHz) using data from Sagamore Hills radio Solar observatories. For the calculation of correlation coefficient, we excluded the points from dataset of those radio fluxes, which are having values greater by 40% of the average flux value of a day. It has been done for neglecting sudden variation in flux due to several transient activities. The correlation coefficients are plotted in figure. 3.2.1 3.2.2. Correlation coefficient between the sunspot and radio flux Many workers (Das and Nag, 1999, Das and Nag, 1996) have shown that the frequency distribution of correlation coefficients of the solar radio flux and Sunspot numbers follows a pattern. We have calculated the correlation coefficients for solar maximum (2001) and minimum (2009) of solar cycle and found that the frequency distribution of the correlation coefficients does not show the similar pattern as has been reported in the literature. During the maximum period the correlation coefficient is highest for 1415 MHz but in minimum it’s highest for 2695 MHz. In literature also it has been reported that the correlation coefficient attains its maximum value at Figure 3.2.1: Frequency distribution of correlation coefficients of solar radio flux and sunspot number 2695 MHz as it is very close to the 2800 MHz (Das and Nag, 1996). But during the solar maximum period the highest correlation has been found for 1415 MHz while at solar minimum period it is for 2695 MHz. Rather that this after 2695 MHz there is a decline in the correlation coefficient of higher frequencies for maximum period where as for minimum period the trend is Figure 3.2.2: Frequency distribution of correlation coefficients of solar radio flux and sunspot number not same as the 8800 MHz shows a correlation which is greater than for 4995 MHz. Rather than this the variation of correlation coefficient has also been checked for different solar minimum period. Das and Nag, 1996 has already reported the correlation coefficient of the radio flux and the sunspot number for the 1975, 1986, 1996 minima. We have compared these correlation coefficients with the obtained ones for 2009 solar minimum. From the plot it can be noted that during this period the value of the correlation coefficient is very low in comparison to the value of the previous three minima. 3.2.3. Correlation coefficient between the solar mean magnetic field and radio flux Like the radio flux and sunspot number, the correlation between the radio flux and solar mean magnetic field has also been checked for this minimum period. It has been found that the values of the correlation co-efficient are very low and the there is a pattern in the variation of the frequency distribution of the correlation coefficients. Figure 3.2.2: Frequency distribution of correlation coefficients of solar radio flux and solar mean magnetic field 3.3. Discussion: In this chapter, the relation between the solar magnetic field and the solar radio flux has been investigated. In the foregoing analysis the correlation coefficient of radio emission and sunspot number, has been found to be low with respect to the correlations of other cycles. Where as the correlation of solar mean magnetic field and radio flux is also very low. During this minima period, the frequency distribution of correlation coefficient of radio flux and sunspot number and the periodic behavior of solar radio flux is random whether it has a similar pattern for previous three minima (Das, 1998). The anomaly in correlation of radio flux with sunspot number might be due to the unusual behavior of the microwaves as it has been already reported for the correlation between 2800 MHz and sunspot number (Hudson, 2009). There was a change in activities between photospheric and chromospheric or coronal indices during the later part of cycle 23, through the extended minimum (Tapping, 2011) and the polar magnetic fields of Sun have an important role in shaping the Solar corona and heliosphere around the Solar minimum period when the polar dipole moment becomes leading component of large scale magnetic field of the Sun (Wang and Sheeley, 2002). During this minima period, Sun’s polar field was 40% less compared to the previous three minima (Wang et al, 2009). Consistently, the corona also retained some complexity during the lowest activity level (Toma et al, 2010a). During the current minimum, the Solar corona never reached at a simple dipolar configuration (De Toma et al, 2010b) rather the eclipse data showed higher order multi-polar structure (Judge 2010). Thus different magnetic configuration is supposed to give rise to a different morphology of Solar corona rather than from the previous three minima. Thus different magnetic configuration is supposed to give rise to a different morphology of Solar corona rather than from the previous three minima. The variation obtained in correlation coefficient’s pattern could also be due to this complex behavior of Solar corona and heliosphere. 3.4. Concluding remarks: The preliminary study presented in this chapter points that during the recent solar minimum, the correlation coefficient of radio emission and sunspot number has been low with respect to the correlation coefficients of previous solar minima. Rather than this the correlation of solar mean magnetic field and radio flux is also found to be very low during this minimum period. During this minima period, the frequency distribution of correlation coefficient of radio flux and sunspot number is random whether it has a similar pattern for previous three minima (Das and Nag 1998). The frequencies studied at the present work for analyzing the characteristics of Solar radio flux, provide information about the complex behavior of Solar corona and different shape of corona with respect to the previous minima during (Toma et al, 2010b). However we believe that detail investigation with more independent analysis using different parameters is required to critically analyze different Solar features especially during the current minima period to have more insight about the physical processes going on inside the Sun at different time scales. References: Hale, G. E. (1908), On the Probable Existence of a Magnetic Field in Sun-Spots, Astrophysical Journal, 28, 315. Solanki, S. K. and Krivova, N. A. (2003), Can solar variability explain global warming since 1970? Journal of Geophysical Research: Space Physics, 108, A5. Hathaway, D. H., Wilson, R. M., Reichmann, E. J. (2002), Group Sunspot Numbers: Sunspot Cycle Characteristics, Solar Physics, 211, 1, 357. Hale, G. E., Ellerman, F., Nicholson, S. B., Joy, A. H. 1919, ApJ,49, 153 Kundu, M. R. (1965), Solar Radio Astronomy. Interscience Publishers, New York. Kane, R. P., Vats, H. O., Sawant, H. S. (2001), Short term periodicities in the time series of solar radio emissions at different solar altitude, Solar Physics., 201, 181. Zieba. S., Maslowski. J., Michalec. A., Kulak. A. (2001), Periodicities in data observed during the minimum and the rising phase of solar cycle 23; years 1996 1999. Astronomy Astrophysics, 377, 297. El- raey. Mohamed, Scherrer. Phillip (1973), Correlation and spectral analysis of daily solar radio flux, Solar Physics, 30, 149. Watari, S. (1996), Separation of periodic, chaotic and random components in solar activity, Solar Physics, 168, 413. Kane, R. P. (2004), Long term and medium term variations of solar radio emissions at different frequencies, Solar Physics 219, 357. Vats, H. O., Deshpande, M. R., Shah, C. R., Mehta, M. (1998), Rotational modulation of microwave solar flux, Solar Physics, 181, 351. Mouradian, Z., Bocchia, R., Botton, C. (2002), Solar activity cycle and rotation of the corona, Astronomy Astrophysics, 394, 1103 Mehta, M. (2005), Solar coronal rotation and phase of solar activity cycle , Bulletin of Astronomical Society of India, 33, 323. Gopalswamy, N., Yashiro, S., Mà ¤kelà ¤, P., Michalek, G., Shibasaki, K., Hathaway, D. H. (2012), Behavior of Solar Cycles 23 and 24 Revealed by Microwave Observations, Astrophysical Journal, 750, 2, L42. Eduardo, A. A, Redmon, R, Fedrizzi, M, Viereck, R, Fuller-Rowell, Tim J. (2011) Some Characteristics of the Ionospheric Behavior During the Solar Cycle 23 – 24 Minimum, Solar Phys, 274, 439. Basu, S. (2010), Differences Between the Current Solar Minimum and Earlier Minima, SOHO-23: Understanding a Peculiar Solar Minimum, Astronomical Society of the Pacific Conference Series, 428, 37. Tapping, K. F., Valdà ©s, J. J. (2011), Did the Sun Change Its Behaviour During the Decline of Cycle 23 and Into Cycle 24? Solar Physics, 272, 337. Das. T. K., Nag. T. K. (1997), Periodicity in the basal component od radio emission during maximum and minimum solar activity, Solar Physics, 179, 431. Das. T. K., and Nag. T. K. (1999), Frequency dependence of the periodicity of the intensity of the non-magnetic component of solar radio emission, Monthly Notices of Royal Astronomical Society, 303, 221. Hudson. Hugh S., Svalgaard. L., Shibasaki. K., Tapping. K., Microwaves in the recent solar minimum 2009, Hinode-3: 3rd Hinode Science Meeting. Wang. Y.M., Robbrecht. E., Sheeley jr. N. R. (2009), On the weakening of the polar magnetic fields during solar cycle 23, The Astrophysical Journal , 707, 1372. G. de Toma, Gibson, S.E., Emery, B.A., and Arge, C.N. (2010a), The Minimum between Cycle 23 and 24: Is Sunspot Number the Whole Story? SOHO23 Proceedings Understanding a Peculiar Solar Minimum, 217. De Toma G., Gibson. S., Emery. B., Kozyra. J. (2010b), Solar Cycle 23: An Unusual Solar Minimum? AIP Conference Proceedings, 1216, 667. Judge, P. G., Burkepile, J., Toma, G. D. (2010), Historical eclipses and the recent solar minimum corona, SOHO23 Proceedings Understanding a Peculiar Solar Minimum, Astronomical Society of the Pacific Conference Series, Astronomical Society of the Pacific, 428, 171.

American football Essay

Actuality There are so many scenarios in life that are made out to be completely different than they actually are because of media. Movies and shows make everything seem like something is one way and then in actuality it’s nothing like it. Throughout movies from scene to scene things are dramatized, over exaggerated, and made out to be better or worse than the situation or things really are. As a child I always watched movies and was deceived by them without even realizing it. I always enjoyed football movies most because I could relate to most of the things and could compare things in the movie to my actual life. They have always drawn my attention and I usually was misled by the way they made the sport in general seem. I wanted to play football at a young age but was always mistaken on the way the game actually was. It was made out to be way harder and worse than actuality. Friday Night Lights and Remember the Titans are two movies I always referred to. Throughout the years of playing football from elementary school to being a college athlete now these movies are the ones that stood out to me. In Friday Night Lights and Remember the Titans the teams have many similarities: The atmosphere isn’t just an  ordinary family, its boys that love each other and play like no one is different. They act like they have grown up together on the field and off and have a bond that can’t be separated even when it’s a tough game or things are falling apart. The teams have a passion for the game and get emotionally invested in it. Practices always came off to be miserable and extremely tough in movies. The drills they run through and exaggerate make football seem really intense. The coaches are very into every second of the practices with little down time and a lot of things to be covered. The  practices are long and drawn out so there is no room to screw up or mess around. The coaches show the passion for the game by the way they get into the practice and are tough on each player. Although they are tough, they build very personal relationships and bonds with each of their players. The coaches in movies seem to be a father figure and a great example to all the players. The relationships show in the games and when they are playing as they lead each other to have selfmotivation and push not only one another but themselves as well. My real life experiences with football have  been very opposite to the way movies portray these instances to be. I had always thought practices and the sport would be painstaking because of the movies and in reality it was completely wrong. I went into high schools nervous and worried that the first practice would be intimidating and eerie as I would wait for the bell at the end of each day and dread the fact that now it was time for football. What I mean by that is I would sit in my desk and repeatedly think of getting killed by the bigger kids. I would continue to look at the clock and every minute felt like 30, I was just scared and  nervous. I soon began to realize and understand that it was just the way the movies make things seem. Practice was not actually full of the coaches yelling and making us do drills that were unbearable. It was all made out to be something it was not. In reality the team isn’t bonded and nearly as close as the movies make them out to be. Some people get along and some don’t, football is not the only reason for everyone to get along. Maybe it was where I went to school but I just couldn’t compare much to the movies. Drills in the movie would last hours and throughout my life of playing football my drills would be short. The drills wouldn’t take your breath away and you wouldn’t be at a loss of energy. In the movies you have coaches in your ear yelling at you, grabbing your facemask to get your attention, and every time they got close to your face their spit would go all over you. Throughout my life coaches were not physical, they wouldn’t grab you, pull you, or throw you around. Practice would consist of cone drills, where you had to set up cones in different areas and run full speed. Another drill we did was seven versus seven, which consist of 7 offensive  guys and 7 defensive guys with no line men. There would be four receivers sometimes five depending on the formations, a quarterback, and a running back also with two occasionally. The coach would call a play and you would have to try and move the ball down field only by passing the ball. Another drill we would do as a team consisted of all eleven players on both sides of the ball in a game-like situation. Everything in the movie seemed to consist of screaming, drills that would look like it could almost kill you, and coaches just all over you every time you made a mistake. It seemed like you just couldn’t catch a break. They really are great, inspirational movies. I even sometimes wished my school was the way movies were. Most people can relate if they play football and have seen either two movies. If you are a high school freshman or student athlete they can really make you nervous and scared to go and play. Maybe it was my school, but most people I have talked to can relate and have the same opinion. That is why I always thought playing football was going to be miserable and harsh but I have now come to the realization in my own life that it is nothing like I had ever expected.

Medication Errors Essay

Approximately, 1.5 million people are injured in the United States due to medication related errors. Errors involving prescription medications kill up to 7,000 Americans per year, according to the Institute of Medicine, and that the financial costs of drug-related morbidity and mortality may run nearly $77 billion a year. FDA also reviews about 1,400 reports of medication errors per month. Before administering a medication, it is the responsibility of the nurse to ensure that the right patient is receiving the right medication, for the right reason/s, the right dosage and route, at the right time. Whoever administers the medication is ultimately responsible for any error that may occur. Therefore it is the nurse’s duty to report a medication error is accordance with facility protocol. The nurse is supposed to notify the physician and monitor the patient for any adverse reactions related to the error. An incident report is also done and is used by the hospital for reeducation t o avoid future occurrences. Failure to report or take appropriate action when a medication error occurs may lead to loss of employment, action by the state board of nurses, civil or criminal changes. It is the nurse’s responsibility to document appropriately, in a timely manner, and failure to do so is also considered a medication error. Students` Legal Role and Responsibility: Student nurses have the responsibility to acquire theoretical and clinical skills necessary to deliver the best of care to the public. It is a student’s responsibility to communicate with the assigned staff nurse constantly and their clinical instructors as well. Most errors occur with medications that a give during the non standard hours, including early morning. Students and staff nurses should use the same MAR and bring the patient’s MAR to the bedside and document drug administration immediately after the patient has taken the medications. Hence clear communication between student and staff nurse, as well as the instructor is of utmost importance in decreasing the risk of making medication omission errors. Anxiety makes a student prone to medication errors as well. Breathing  exercises have proven effective in relieving anxiety. Medication errors lead may lead to dismissal from a nursing program. Depending on the severity and frequency of medication errors by stud ents, the school may lose its privilege to practice in some facilities. Therefore it is important that student avoid making any medication errors. Medication errors and years of experience Administration errors reflect knowledge deficits, with errors declining in the first few years of clinical experience (C. G. Bailey, et al.). Each year of experience, up to 6 years, reduced the risk of error by 10.9% and serious error by 18.5% (J. Westbrook et al. 2013) These findings suggests that inexperienced nurses constantly require training and supervision with a focus on correct medication administration. Knowledge gained from this study I learnt that the nurse are the doctor’s eyes and ears; and they rely on them to identify errors, changes of condition, abnormal lab values etceteras so that they may prescribe the right medication appropriately. It is important to always have your reference material available such as, drug reference book, patho-physiology reference book etceteras; because medication administration goes beyond just following the doctor’s written order and giving the patient the medication. If a nurse does not know why the medication is being given, they are not be able to identify an error before administering, or know when to hold the medication and notifying a physician. Good clinical practice begins while a nurse is in school; therefore it is crucial to always comply with facility protocol. Hence knowledge deficit compromises the patient’s safety. Reference C. G. Bailey, B.S. Engel, J.N. Luescher, M.L.Taylor: (date unknown) Medication Errors In Relation To Education & Medication Errors In Relation To Years of Nursing J., Treiber L. When the 5 rights go wrong: medication errors from the nursing perspective. Journal of Nursing Care Qual 2010;25:240–7 Experience: retrieved July 31 2013 from http://www.lagrange.edu/resources/pdf/citations/nursing/Medication%20Errors.pdf J. I. Westbrook, A. Woods, Rob MI, et al. (2010) Association of

Investment Risks and Discounted Cash Flow Applications - Free Essay Example

Sample details Pages: 10 Words: 2996 Downloads: 6 Date added: 2017/06/26 Category Management Essay Type Analytical essay Did you like this example? Investment Risks and Discounted Cash Flow Applications You are the company accountant with a medium sized, privately owned company. The company has surplus funds which it does not believe it will be able to invest in company operations for at least five years. The majority shareholders are also the directors of the company and they do not wish the surplus finds to be distributed as dividends. Don’t waste time! Our writers will create an original "Investment Risks and Discounted Cash Flow Applications" essay for you Create order A board meeting has, therefore, been called to discuss the proposal that the funds be invested in a portfolio of medium to long term securities. Three of the directors have recently attended a short course at the local university on Investment and the Management of Risk. They make the following comments at the meeting, based on their interpretations of what they have learned on the course: If we hold a portfolio of stocks we need only consider the systematic risk of the securities As a cautious investor we must always consider total risk We should not buy anything if the expected return is less than the market as a whole and certainly not if it is below the return on the risk free asset. Question 1(i): Explain to the members of the board the meaning of systematic, unsystematic and total risk and advise them about how all three types of risk can be measured. Reasons for Dissecting Risk Investing in securities is an inherently risky proposition (unless one invests in the risk free asset). Prudent investors are risk-averse (Damodaran 2002, pp. 70), and as such they need methods to quantify the risk associated with potential investments, in order to make informed investment decisions corresponding with their risk tolerance and objectives for return. Thus, the concept of risk needs to be reduced into separate elements which can be calculated. Total, Systematic, and Unsystematic Risk The total risk involved in holding any security has two distinct components: systematic risk and unsystematic risk. Systematic risk refers to the risk of holding securities in general, and is also known as market risk (Ross, Westerfield, Jaffe 2005 pp.275). This is the risk associated with macroeconomic variables beyond the control of any one company, and this risk measure serves as a floor for the amount of risk in a portfolio of stocks that can be eliminated by diversification (McAlister, Srinivasan, Kim 2007, pp. 39). When an investors portfolio is properl y diversified, this is the level of risk that such an investor should concern themselves with (Howard 2006, pp. 29). Unsystematic risk refers to the level of risk associated with a particular security, which can fluctuate greatly depending on the underlying value of the assets which the security represents (Howard 2006, pp. 30). For instance, while the economy may be rather steady at any given time (and a diversified portfolio would reflect such stability in its measures of systematic risk), an individual company may be undergoing dramatic changes which cause the company valuation to fluctuate wildly. Unsystematic risk is the portion of total risk that an investor in a diversified portfolio seeks to minimize. To illustrate the difference between systematic and unsystematic risk, one helpful analogy is the schism in physics between the smooth macro-level curvature of space-time at cosmic scales predicted by General Relativity, and the chaotic and unpredictable micro-level fluct uations of space-time at infinitesimally small scales predicted by Quantum Physics. At the scale of space-time discussed by Einsteins General Relativity equations, the effects of small-scale fluctuations are ultimately balanced out, and the picture of space-time is one of a smoothly curving space-time accentuated bent according to the gravitational effects of large masses. At the scale of space-time addressed in Quantum Physics, however, space-time fluctuates in such an unpredictable and chaotic manner that predictions become difficult, if not impossible (Feynman 1985, pp. 5). This corresponds to the macro-level systematic risk of the market, in which the volatility of individual securities is balanced out, leaving only the risk of the market as a whole, compared to the violent variances of individual companies at the micro-level which is measured by unsystematic risk. Total risk is a combination of systematic and unsystematic risk. Since unsystematic risk decreases asymptoticall y as stocks are added to a portfolio (meaning that the level of risk approaches, but never quite equals, the level of systematic risk), investors with properly diversified portfolios are most concerned with systematic risk as a measure of their total risk (Howard 2006, pp. 29). Investors with less diversified holdings should add the market level of systematic risk to the level of unsystematic risk associated with the securities held to compute total risk. Computation of Total, Systematic, and Unsystematic Risk Systematic risk, or non-diversifiable market risk, can be calculated as the average covariance of the securities in the portfolio (in this case, the portfolio should be considered to be a basket of stocks representing the entire market) (Ross, Westerfield, Jaffe 2005, pp. 273). Total risk is the average variance of the security in the portfolio, and by definition (total risk = systematic risk + unsystematic risk), the unsystematic risk of any security in the portfolio i s the average variance of the individual security minus the average covariance of the portfolio (Ross, Westerfield, Jaffe 2005, pp. 275). Question 1(ii): Discuss the directors comments If we hold a portfolio of stocks we need only consider the systematic risk of the securities This comment by the directors holds true, if the portfolio is sufficiently and adequately diversified. As mentioned above, a properly diversified portfolio creates a scenario in which the unsystematic risk asymptotically approaches 0, leaving only the systematic or market risk in the calculation of total risk. However, this assumes that the stocks selected in the portfolio are sufficiently diverse (Damodaran 2002, pp. 735). For an example, a diversified portfolio that includes a broad cross-section of securities from many industries can be considered more properly diversified than a portfolio which gives extra weight or emphasis to specific industries. Otherwise, there is an industry-specific leve l of risk that remains in the unsystematic risk of the entire portfolio. As a more concrete example, consider a portfolio that consists of a group of energy stocks and a group of petrochemical companies. No matter how many stocks are added to this portfolio from the group, the risk associated with petroleum price shocks has not been removed via diversification (while it is true that petroleum price shocks would affect the market at large, they would disproportionately affect industries in which petroleum is the critical input). The stocks in the portfolio must be sufficiently diverse for the effects of diversification to be realized as a reduction in unsystematic risk. However, if the stocks in the portfolio are assumed to be sufficiently diverse to account for a truly diversified portfolio, the statement made by the directors certainly coincides with financial theory, and should be applauded a sound understanding of the concept of diversification and its relation to investment a nd risk management. As a cautious investor we must always consider total risk This statement certainly rings true for the investment decisions of the directors, and demonstrates an understanding of both the impacts of diversification and the demarcation between the different types of risk involved in the total risk of an investment (Howard 2006, pp. 29). To support this statement by the directors, three scenarios will be used to illustrate the importance of a focus on total risk. In the first scenario, a hypothetical investor has no information regarding any of the components of total risk. The hypothetical investor has little knowledge of the inherent risk factors of the current market (no understanding of current levels of systematic risk), and has randomly selected a single security (perhaps by using the dart toss stock selection scheme). This investor may not understand that the market as a whole is in an upswing or decline, and has no information to understand how any random stock in the market at large should perform, on average. Thus, the investor has no information on systematic risk. This investor also selected the security at random, so the investor has no information regarding the proclivity of the particular security to fluctuate in value. Here, the investor has no way to deduce total risk, since the investor cannot arrive at a conclusion regarding either the systematic risk or the unsystematic risk. Any profits made by the investor in this scenario can only be regarded as the fortuitous results of chance. In the second scenario, a hypothetical investor has performed a thorough analysis on a particular company, and thus has a solid understanding of the companys earnings potential and true valuation relative to its market capitalization. However, the investor has not performed an analysis on the economy as a whole, and as such has no information as to whether macroeconomic conditions support or invalidate a decision to purchase the parti cular security in question. So, while the investor feels confident that they understand the unsystematic risk associated with the security, they have no information regarding the systematic risk of the market as a whole, and thus the investment decision based on their research may be ruined by a change in overall market conditions. Finally, in the third scenario, the final hypothetical investor has performed an analysis of macroeconomic conditions to concoct an investment decision. This investor, however, has performed no analysis of the particular securities they plan to purchase (even to see if they form a properly diversified portfolio). Thus, even though this investor potentially understands the systemic risk portion of their investment, they have no way of determining if they have eliminated the unsystematic risk in their holdings. They may very well be correct regarding the markets overall risk level, but if they do not eliminate the unsystematic risk associated with indivi dual securities, their efforts will also be in vain as they are still subject to potential volatility and additional risk based on fluctuations in the securities held. We should not buy anything if the expected return is less than the market as a whole and certainly not if it is below the return on the risk free asset. The first portion of this statement is incorrect, unless the board has decided that the return on the market as a whole is equivalent to their required rate of return. The level of expected return on the investment should be a function of the risk tolerance of the investors. If the risk of the market as a whole (systematic risk) is higher than the risk tolerance of the investors, the investors should seek to invest in the risk free asset, or at least include the risk free asset in the portfolio to achieve the level of total risk that best suits the risk tolerance of the investors (Ross, Westerfield, Jaffe 2005, pp. 300). The directors have here made a very e asy mistake: equating the expected return on the market as a whole with the minimum acceptable return, without considering that even the systematic risk may be more risk than they are willing to tolerate. For instance, a troubling political climate or unexpected macroeconomic events may create levels of price fluctuations in the market as a whole which amount to risks that the investors are not willing to take. At such a point, the investors should seek to lessen their exposure by investing some portion of their holdings in the risk free security (to park their funds until the systematic risk of the market more closely mirrors their own risk tolerance) (Damodaran 2002, pp. 155). The second statement is correct. Since the return on the risk free asset is, by definition, devoid of either systematic or unsystematic risk, this is the minimum return that the investors should demand for their resources (Damodaran 2002, pp. 204). Any additional expected return should be balanced by the systematic risk associated with placing funds in risky securities. Investors in properly diversified portfolios should not expect any returns above market average, unless they are willing to assume some level of unsystematic risk as well. Question 2 (i): Why is it important to discount future cash flows? The Relevance of Discounted Cash Flows Valuation Models The notion that future cash flows should be discounted back to todays value by a factor equal to the opportunity cost of capital is central to the concept of the Time Value of Money. By discounting future cash flows by the opportunity cost of capital, we recognize the very real impact of financial decision-making (Ross, Westerfield, Jaffe 2005, pp. 195). Cash flows in the future are worth less because if they were available in the present, they could be earning a return equal to the opportunity cost of capital (which is always greater than zero based on the existence of the risk free asset). A dollar held today is worth more than a dollar held in the future, because todays dollar could (at the very least) be invested in the risk free asset and be worth more in the future. Whereas if we have to defer our receipt of cash until the future, we should expect compensation relative to the opportunity cost of not receiving the money up front. This is the basis of interest payments, the time value of money, and ultimately this concept is the crux of all financial theory (Damodaran 2002, pp. 11). To forego discounting future cash flows is to assume that there is no time value associated with cash, and that there are no investments with positive returns (Ross, Westerfield, Jaffe 2005, pp. 901). If future cash flows are not discounted, it becomes easy to lose sight of the potential returns that were missed based on the allocation of cash for a project. This will also skew the decision-making process and distort the perceived profitability of a project. The net present value (NPV) model allows inv estors to determine if a project makes financial sense based on their expected rates of return or opportunity cost of capital (Damodaran 2002, pp. 13). If the cash flows were not discounted, a project may look profitable in the initial feasibility study for the project, even though the project returns less over time than is expected by the investors, and the money would be better invested in other projects with a higher or positive net present value. Thus, discounting future cash flows allows quantitative models to presume that capital has other potential uses, and that a project should at least meet certain requirements for return over time before it is considered. As an example, consider a project which costs  £100, and is expected to generate  £150 in year 1. A similar project costs  £100 but will generate  £150 in year 2. Without discounting the deferral of cash flows in the project, they both appear to generate  £50, and both look equally p rofitable. In truth, however, the first project is more profitable, since the real profit over the time period in question is equal to the  £50 plus any profits that could be generated over the next year at the companys required rate of return. Thus, it is vital that future cash flows are discounted to make accurate decisions through financial analysis, or the opportunity cost of capital will be omitted from the final decision. Question 2(ii): Susie Lee owns the Lotus Blossom Bar and Restaurant. She is considering the following investment to upgrade the existing facilities. The cash flows for the investment are estimated as follows: End of Year Cash Flow ( £) 0 -(10,000) 1 10,000 2 20,000 3 40,000 4 50,000 5 30,000 Assuming the opportunity cost of capital is 12 percent, calculate the investments net present value. Based on your calculations advise Susie if she should undertake the investment project? Net Present Value of Upgrading the Lotus Blossom Bar and Restaurant Net present value is calculated as the sum of future cash flows discounted by the opportunity cost of capital (here, 12%) (Damodaran 2002, pp. 12). In this example, a  £10,000 investment yields five years of positive cash flows ( £10k year 1,  £20k in year 2,  £40k for year 3,  £50k for year 4, and a final cash flow of  £30k in year 5). All of these cash flows must be discounted to today (year 0), and if the sum of the discounted cash flows is greater than the  £10k cost of the project, the project will have a positive net present value and will make a sound investment for the Lotus Blossom Bar and Restaurant. The following table illustrates the present value calculati ons as performed on the cash flows, and summarizes by adding all of the projects cash flows to arrive at the projects net present value. Cash Flows Discount Formula Result Initial Investment (Year 0) - £10,000 =-10000 - £10,000.00 Year 1  £10,000 =(10000)/(1+.12)^1  £8,928.57 Year 2  £20,000 =(20000)/(1+.12)^2  £15,943.88 Year 3  £40,000 =(40000)/(1+.12)^3  £28,471.21 Year 4  £50,000 =(50000)/(1+.12)^4  £31,775.90 Year 5  £30,000 =(30000)/(1+.12)^5  £17,022.81 Total  £140,000.00 Net Present Value: Sum of DCF  £92,142.37 Even after considering Susie Lees opportunity cost of capital by discounting her expected future cash flows from the project, the net present value of the upgrade is overwhelmingly positive, and she is strongly advised to undertake the investment project (Boyes 2004, pp. 235). This project generates revenues well beyond her required rate of return. Generating  £150,000 in 5 years from a  £10,000 up-front investment is a very solid investment at a 12% required rate of return. In fact, the investment is incredibly profitable using the Internal Rate of Return (IRR) methodology, which yields the rate of return at which the project yields a NPV of 0 (Damodaran 2002, pp. 866). Solving for a zero value for net present value yields the following result: Cash Flows Discount Formula Result Initial Investment (Year 0) - £10,000 =-10000 - £10,000.00 Year 1  £10,000 =(10000)/(1+1.651814)^1  £3,771.00 Year 2  £20,000 =(20000)/(1+1.651814)^1  £2,844.09 Year 3  £40,000 =(40000)/(1+1.651814)^1  £2,145.02 Year 4  £50,000 =(50000)/(1+1.651814)^1  £1,011.11 Year 5  £30,000 =(30000)/(1+1.651814)^1  £228.77 Total  £140,000.00 Net Present Value: Sum of DCF - £0.00 In other words, until Susie Lee requires a 265.18% rate of return on her capital, this upgrade represents an extremely solid investment (Collis, Montgomery 1998, pp. 88). Works Cited: Boyes, W. The New Managerial Economics. Houghton Mifflin Company. Boston, Massachusetts. 2004. Collis, D. and Montgomery, C. Corporate Strategy: A Resource-Based Approach. Irwin/McGraw Hill. Boston, Massachusetts. 1998. Damodaran, A. Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Second Edition. John Wiley Sons, Inc. New York. 2002. Feynman, R. QED: The Strange Theory of Light and Matter. Princeton University Press. New Jersey. 1985. Howard, M. à ¢Ã¢â€š ¬Ã…“Accounting for Unsystematic Riskà ¢Ã¢â€š ¬Ã‚ . Financial Management. Sep. 2006. McAlister, L., Srinivasan, R., Kim, M. à ¢Ã¢â€š ¬Ã…“Advertising, Research and Development, and Systematic Risk of the Firmà ¢Ã¢â€š ¬Ã‚ . Journal of Marketing. January 2007. Ross, S., Westerfield, R. , and Jaffe, J. Corporate Finance. Seventh Edition. McGraw-Hill Companies. New York. 2005.