# Legal 500 Assignment 4

George Green LLP stands out in the market for its ability to handle mid- to large-cap cross-border M&A, and the team was active again in this regard, with private equity specialist Guy Green acting for Bakk AL Holdings in its acquisition of 51% of the shares in Bakkavor Group from Icelandic Institutions. In another significant cross-border deal, senior partner Paul Bennett, who heads the practice, acted for the shareholders of Dot Net IT in the sale of the company to Epicor. Bennett is also well versed in handling distressed transactions, and acted for Ash & Lacy Building Systems in its acquisition of Accordial Group’s business and assets from the administrator. While the team mainly operates from the firm’s Cradley Heath office, it also has presence in Wolverhampton, where Philip Round is noted for his expertise in the financial services sector; Round advised the shareholders of Network Direct on the £4m sale of the company to Harwood Wealth Management. The practice’s commercial offering was developed by the hire of James Bird, who joined from **Wright Hassall LLP**.

**Harrison Clark Rickerbys**’s substantial team is well known for its expertise in sectors such as healthcare, defence and security, and private equity, and the team is also well versed in handling M&A for listed companies. Notable clients include Gemini Group, Belgravium Technologies and London Graphic Supplies. The practice has particular depth in the firm’s Worcester office, where managing partner Rod Thomas, who is a ‘*class act*’, Alison Scott, and healthcare specialist Charlotte Thornton-Smith are based. Arpinder Dhillon is the name to note in Ross on Wye. Inger Anson, who is also located in Worcester, made partner.

Higgs & Sons continued to be highly active across a range of sectors and noted an uptick in cross-border work. In the telecoms space, Richard Griffiths acted for the management team of Wavenet regarding their private equity-backed buyout of the company, and department head Nick Taylor advised Encription on its sale to BlackBerry. Griffiths was also busy in the construction sector and advised the Stanford family on the sale of their shares in the management buyout of Stanford Industrial Concrete Flooring. Another key player is John Heaton, whose transactional work encompasses the retail, automobile and energy sectors; in one highlight, Heaton advised AF Blakemore & Son on the acquisition of the business and certain of the convenience stores owned and operated by MLCG and ML Convenience. In February 2017, Peter Manford joined from an in-house role to strengthen the practice’s commercial offering, and the practice was also boosted by the return of Adrian Cutler from a consultancy role.

Practice head Robert Lee and Steven Halkett ‘*provide strong leadership*’ at **Wright Hassall LLP**, where the team is commended for its ‘*strong skill set and reputation across the South Midlands*’. Areas of sector expertise range from healthcare and not-for-profit to advanced manufacturing, and the team has also developed a specialism in distressed retail. Highlights in 2016 included Halkett advising the shareholders of Flixmedia on its cross-border sale to a European joint venture between Advantage Solutions and Smollan Group, and Monica Macheng acting for Zip Textiles in its £18m sale to Johnson Service Group. In another significant cross-border transaction, Halkett represented High Performance Doors in its sale to Record UK. Lindsay Ellis is in charge of the commercial team, which acts for a portfolio of leading IT outsourcing providers; in one example of work, Christine Jackson assisted Q Associates with both private and public sector supply contracts across sectors such as defence, emergency services and higher education.

Ansons continued to feature strongly in deals within the pharmacy area, where the team has a reputation for being ‘*diligent and proactive in its approach, on behalf of both buyers and sellers*’. Former pharmacist Neil Jones, who along with Hilary D’Cruz heads the team, has a ‘*strong understanding of the client’s position and is able to take both a pragmatic and commercial view*’. The team also focuses on other healthcare-related businesses, including care homes, dentists, domiciliary care and children’s day nurseries. In other highlights, D’Cruz – who is a ‘*first-class lawyer*’ - advised on various multimillion-pound commercial contracts in the renewable energy sector. The fast-growing team expanded further with the hire of senior associate Adam Kudryl, who joined from Howes Percival LLP.

FBC Manby Bowdler LLP reported a strong increase in transactional work in 2016, and the team was busy on a number of multimillion-pound deals for its target audience of SMEs in the manufacturing sector. Another area of focus is the health sector, where newly promoted partner David Preece undertakes a range of corporate and commercial mandates for veterinary and dental practices. Practice head James Sage and Kam Johal are leading figures in the firm’s Wolverhampton office, and in Shrewsbury Stuart Rea is ‘*technically good and comes across well with clients*’. Rea’s caseload extends to the agricultural sector, where he has experience advising on significant cross-border acquisitions.

Hawkins Hatton Corporate Lawyers Limited is a ‘*niche corporate practice*’ whose fixed-fee approach makes it ‘*very competitive on price*’. The team is best known for handling transactions on behalf of substantial SME clients and entrepreneurs, and it has a broad-ranging client base that takes in steel stockholders, manufacturers and healthcare organisations. Work examples in 2016 included acting for the shareholders of Blundell Productions on the sale of the company to Hilco Capital, and advising Foragri on the cross- border sale of the company to a listed PLC based in Turkey. The team also advised on a number of corporate reorganisations for clients such as Ercho and Gilbert (Holdings). Practice head Colin Rodrigues is a ‘*practical and commercially minded lawyer*’ who ‘*understands the wider aspects of deals*’.

Beswicks Legal has a ‘*wealth of experience in providing legal advice to owner-managers of businesses on sale*’ and the team was active in a number of company share sales: Peter Ellis, who ‘*comes up with innovative solutions to legal issues and defuses potentially contentious situations*’, represented the shareholders of Motiva Group in the sale of the company to SG Fleet, and also acted for the shareholders of MCL Group Industries in the disposal of the entire issued share capital to the Cubis Group. The practice is led by managing partner Nick Phillips, who has particular expertise in advising sports organisations on commercial issues. Phillips also handles transactional work and assisted the owners of Burma Bacon Supplies with the sale of the business to a private company. Another name to note is solicitor Tom Sutcliffe, who is ‘*very knowledgeable and always contactable*’.

**Knights Professional Services Limited** handles a full range of corporate advice, including share and asset sales and purchases, private equity, MBOs/MBIs, and company restructuring. Key players include Jonathan Tyson, who specialises in the healthcare sector, with a particular focus on the sale of dental surgeries, pharmacies and children’s nurseries; and Lisa Bridgwood, whose commercial expertise takes in advising retail industry brands on the implementation of e-commerce and multi-channel initiatives, as well as negotiating franchising and agency agreements. The team is able to draw on the experience of CEO David Beech.

Under the leadership of Gráinne Walters, Lanyon Bowdler provides ‘*first-class support*’ to clients such as Assured Group Holdings, Jupiter Marketing and Dodd Group Midlands. As well as handling corporate M&A, buyouts, reorganisations and joint ventures, Walters has strong experience in the education sector, and is advising Severn Bridges Multi-Academy Trust on the formation of a multi-academy trust for three schools in Shropshire. At associate level, names to note include the ‘*experienced and practical*’ Edward Burrell and Timothy Roberts, who respectively focus on the agricultural and renewable energy sectors. In one example of work, Roberts advised Woodland Heritage on the acquisition of Whitney Sawmills. Commercial specialist Ruth James left for an in-house role.

Lodders Solicitors LLP’s ‘*very customer-focused team goes out of its way to get deals over the line*’. The practice is probably best known for its expertise in the healthcare sector, where it acts for clients such as Healthcare Management Solutions; in 2016, the team handled a number of high-value care home business sales. In other highlights, the well-regarded Kim Klahn acted for New Co on the purchase of shares from two individual shareholders, and the same lawyer also advised on the cross-border sale of a business to a private Belgian company. Head of practice Victor Matts is ‘*flexible and unflappable*’, and Mark Lewis, who leads on charities and not-for-profit matters, is a ‘*strong manager of his team*’.

mfg Solicitors LLP continued to see a good flow of cross-border work, with Kidderminster-based Stephen Wyer advising Isomerase Therapeutics on a £5.5m investment by Neurovive Pharmaceutical, and Worcester-based James Hayes assisting a foreign investor with a joint venture in the healthcare space. Wyer is also noted for his expertise in the education sector, where he assisted South Worcestershire College with its statutory merger with Warwickshire Group of Colleges. In other highlights, Hayes represented Skymark Packaging International in a multi-tranche share buyback from an insolvent company, and energy specialist Miles Dearden - also based in Kidderminster - advised Ecotricity Group on its first white label supply agreement for electricity and gas with Glide Utilities.

Shakespeare Martineau LLP’s team has expertise in a wide range of sectors and is particularly recommended for its work in the health sector, where it continued to handle a high volume of sales and corporate reorganisations relating to pharmacies and GP and dental surgeries. Andrew Smith leads the team and was active on a number of matters for key client Whitworths Holdings, including advising on the £36m acquisition of Carr’s Flour Mills from Carr’s Group, as well as the acquisition of the cake and heat treated flour business of Jas Bowman & Sons. Smith was also busy active in the distressed space, where he assisted Lee Longland & Co with its purchase of four retail stores and related assets from the administrators of the Furniture Barn.

**Thomas Horton LLP**’s ‘*very responsive and highly knowledgeable*’ team is led by

Jeff Taylor, who advises on a full range of commercial contracts, partnership agreements, corporate acquisitions and disposals, and start-up matters. Examples of the team’s varied caseload include acting for Global Pacific in a joint venture with Morrisons Supermarkets, and advising a medium-sized financial services software company on its proposed sale. In another piece of work, Taylor advised the Lord of Grafton and family in redrafting their partnership agreement concerning the Grafton Manor Hotel and conference facility. The practice also operates in niche areas, such as forestry.

Thursfields Solicitors has a ‘*fantastic reputation for delivering commercial, honest and technically relevant advice*’ to clients such as SFC Group and Level Peaks Holdings. The team is led by Gareth Burge, who is ‘*very commercially astute and doesn’t hesitate to grasp and solve difficult issues promptly and efficiently*’. Another name to note is consultant Stuart Price, who has particular expertise in assisting investors and start-up businesses with seed investment schemes in the film and technology arenas. The practice saw strong growth at the senior associate level in 2016 with the hires of commercial contracts specialist Jane Rudge, who joined from Higgs & Sons, and Tim Edwards, who joined from **The Wilkes Partnership**. Edwards specialises in the motor racing and media sectors and ‘*adopts a pragmatic, level-headed and commercial approach*’ to transactional work.

The well-regarded Sean Byrne leads the practice at **Band Hatton Button LLP**, which handles a good balance of corporate and commercial mandates. Recent highlights include acting on the £1.2m sale of a chemical cleaning company, and advising in relation to the £2.5m acquisition of a timber supply company. On the commercial contracts side, the team handled a range of supply agreements, including assisting with a long-term supply agreement relating to the supply of garden equipment. Other names to note include Haydn Jones and senior associate Marta Fisher, who has particular expertise in acting for healthcare professionals.

At Brethertons LLP, solicitor Katherine Cereghino specialises in the health, retail and property management sectors and draws on her previous experience as a commercial property lawyer. In 2016, she provided advice on a number of high-value business share sales to publicly quoted companies, including acting for the shareholders of Pentagon HS in the £14m sale of the company, and representing the shareholders of Malmesbury Medical Enterprises in the £10m sale of the business. Cereghino also handled various sales by way of asset purchase agreements, including assisting Carwood Motor Units with the purchase of the assets of Diesel Injection (UK). Colin Witherall has retired from practice.

Managing partner Samantha Wright heads the team at Brindley Twist Tafft & James, which works with a range of businesses, from long-established companies to start-up enterprises, as well as not-for-profit organisations. Wright is particularly active in sectors such as equipment sales and manufacturing and, in 2016, handled the £2m sale of a materials processing company, as well as the £4m purchase of 49% of a family-owned manufacturing company. Other names to note are consultant John Ruddick, who focuses on the not-for-profit sector, and John Chadaway, whose commercial expertise takes in a variety of commercial contracts, including distribution agreements.

Enoch Evans LLP’s ‘*well-informed, capable and conscientious*’ team is led by healthcare specialist Sukie Shemar, who ‘*handles matters promptly and efficiently*’. Shemar has particular experience dealing with the sale and purchase of pharmacies and continued to be highly active in this space for key client Medi-Zen Healthcare Services. Other names to note are senior solicitor James McFarlane, who was busy on a number of share purchases and reorganisations, and solicitor Amy Hylton, who ‘*provides valuable guidance*’ on commercial contracts. The team is able to draw on the experience of managing partner David Evans, who is ‘*very easy to get along with*’.

**Hatchers Solicitors LLP** ‘*always provides very timely responses, especially when dealing with sensitive issues such as purchasing shares from outgoing shareholders*’. The practice saw an increase in instructions from charities and not-for-profit organisations, where work included advising on the creation of Fields Multi-Academy Trust and the conversion of two primary schools to academy status. Other areas of focus are the manufacturing, farming and agricultural sectors, and the team assisted with the management buyout of a designer and installer of renewable power and heat systems serving the poultry and wider agricultural sector. Key contacts are practice head Ann Fisher, who wins praise for her ‘*really good manner and communication skills*’, and consultant David Saunders.

Martin Kaye had a strong year in 2016, with instructions buoyant in areas such as shareholder agreements and corporate restructuring. The practice also noted an uptick in instructions from newly incorporated businesses, particularly in the IT sector. Recent highlights include advising on the £4m share sale of a commercial engineering recruitment company to a leading PLC, and assisting with the restructure of a substantial Irish developer. In another multimillion-pound deal, the team assisted a mortgage broker with the £6m share sale of the company to a major national business. Key contacts are associate Eliot Hibbert, who heads the practice, and solicitor Barry Doherty.

At **Pickerings Solicitors LLP**, practice head Craig Davies handled a number of acquisitions for local accountants, and also advised a specialist vehicle company on a €14m joint venture partnership agreement with a manufacturing partner based in France. The team was also busy in the education space, with Davies acting for the vendor on the purchase of shares and property in a children’s day nursery, and solicitor Keri Pointon, who wins praise for her ‘*clear, in-depth knowledge*’, representing a pre-school on its liquidation and transfer of assets to an academy school. Pointon’s experience extends to sectors such as manufacturing, IT and agricultural, and in another example of work, she acted for a recruitment company in the purchase of shares in a company, accompanied by the assignment of intellectual property rights.

STA371G Homework Assignment 4 (40 Points. Due 5:00 pm on Friday, 02/27/2015. Group homework.) Please write down the NAME and EID of each group member. Each group consists of up to three members. Problem 1 A company sets different prices for a particular stereo system in eight different regions of the country. The table below shows the numbers of units sold (in 1000s of units) and the corresponding prices (in hundreds of dollars). Sales Price 420 5.5 380 6.0 350 6.5 400 6.0 440 5.0 380 6.5 450 4.5 420 5.0 (a) Let X denote Price and Y denote Sales. Using Excel or R: calculate the sample means of X and Y , sample standard deviations of X and Y , sample covariance between X and Y , and sample correlation between X and Y . ¯ = 5.625, Y¯ = 405 X sx = 0.744, sy = 33.806 Cov(X, Y ) = −23.571 rxy = −0.937 (b) In Excel or R, regress sales on price and obtain the estimates of the intercept b0 , slope b1 and coefficient of determination R2 . SUMMARY OUTPUT Regression Statistics Multiple R 0.937137027 R Square 0.878225806 Adjusted R Square 0.857930108 Standard Error 12.74227575 Observations 8 ANOVA df Regression Residual Total Intercept X Variable 1 1 6 7 SS 7025.806452 974.1935484 8000 MS 7025.806452 162.3655914 Coefficients Standard Error t Stat 644.516129 36.68873299 17.56714055 -42.58064516 6.473082556 -6.578109392 1 F Significance F 43.27152318 0.000592135 P-value 2.18343E-06 0.000592135 Lower 95% Upper 95% 554.7420336 734.2902244 -58.41970755 -26.74158277 (c) Using the results obtained in (a) to calculate the intercept b0 , slope b1 and the coefficient of determination R2 . Are the results the same as those obtained in (b)? s 33.806 0.744 b1 = rxy sxy = −0.937 × = −42.58 ¯ = 644.51 b0 = Y¯ − b1 X 2 = (−0.937)2 = 0.878 R2 = rxy 420 5.5 420 The results are the same as those in (b) 380 6 380 350 400 440 380 450 420 6.5 6 5 6.5 4.5 5 350 400 440 380 450 420 (d) Present a plot with the data and the regression line. 480 460 440 Sales 420 400 380 360 340 320 300 3.5 4 4.5 5 5.5 6 6.5 7 Price (e) Based on this analysis, briefly describe your understanding of the relationship between sales and prices. The sales tend to decrease as the price increases: the sales decreases by about 42.6 × 1000 units as the price per unit increases by 100 dollars. Problem 2 Suppose we are modeling house price as depending on house size. Price is measured in thousands of dollars and size is measured in thousands of square feet. Suppose our model is: P = 20 + 50 s + , ∼ N (0, 152 ). (a) Given you know that a house has size s = 1.6, give a 95% predictive interval for the price of the house. The point prediction is Pˆf = 20 + 50 × 1.6 = 100 The prediction interval is [100 ± 2 × 15] = [70; 130] 2 (b) Given you know that a house has size s = 2.2, give a 95% predictive interval for the price. The point prediction is Pˆf = 20 + 50 × 2.2 = 130 The prediction interval is [130 ± 2 × 15] = [100; 160] (c) In our model the slope is 50. What are the units of this number? 1,000$ / 1,000 Sq. Feet = $/Sq. Feet (d) What are the units of the intercept 20? 1,000$ (same as P ) (e) What are the units of the the error standard deviation 15? 1,000$ (same as P ) (f ) Suppose we change the units of price to dollars and size to square feet What would the values and units of the intercept, slope, and error standard deviation? Intercept: 20,000 $ Slope: 50 $/Sq. Feet error standard deviation: 15,000 $ (g) If we plug s = 1.6 into our model equation, P is a constant plus the normal random variables . Given s = 1.6, what is the distribution of P ? When s = 1.6 the mean of house prices is 20 + 50 × 1.6 = 100. The error standard deviation is the same, 15. Therefore P |s = 1.6 ∼ N (100, 152 ) Problem 3 Read the case “Waite First Securities” in the course packet. The data file is available on the course website. Consider the regression model T It = α + βSP 500t + t t ∼ N (0, σ 2 ) where T It represents the return on Texas Instruments in month t and SP 500t represents the return on the S&P 500 in month t. (a) What is the interpretation of β in terms of a measure of risk of the stock? β is a measure of the risk of the stock relative to the market. If the return on the market goes up (or down) by 1% then we expect the return on the stock to go up (or down), on average, by β%. (b) Plot T I against SP 500. What graphical evidence is there of a relationship between T I and SP 500? Does the relationship appear to be linear? Why or why not? Yes, by looking at the plot it appears that T I and SP 500 are linearly related... 3 increases (decreases) by 1%, then we expect the return on the stock to increase (decrease), on average, by E%. (b) Plot TI against S&P500. What graphical evidence is there of a relationship between TI and S&P500? Does the relationship appear to be linear? Why or why not? Scatter Plot: TI vs. S&P 500 y = 1.6192x - 0.0007 30% 20% TI 10% 0% -10% -20% -10% 0% 10% S&P 500 (c) Estimate E using the Regression command under Tools-Data Analysis in Excel. What is the interpretation of this estimate in terms of the risk of the stock? Why is Mr. Gagnon interested this estimate? There is evidence of in a relationship between TI and S&P500 because as the S&P500 increases, TI also tends to increase. SUMMARY OUTPUT The relationship appears to be linear because the data are scattered randomly about a Regression Statistics straight line.R Multiple 0.555135037 R Square Adjusted R Square Standard Error Observations 0.308174909 0.29624689 0.090755054 8 60 ANOVA df 1 58 59 SS 0.212799498 0.477715829 0.690515326 MS 0.212799498 0.00823648 Coefficients -0.000682785 1.61919734 Standard Error 0.012089016 0.318555642 t Stat -0.056479795 5.082934116 Regression Residual Total Intercept S&P 500 The estimate of E is 1.619. This implies TI is riskier than the market because a 1% change in the market return is associated, on average, with a 1.619% change in TI’s return. (c) Estimate β. What is the interpretation of this estimate in terms of the risk of the stock? Why is Mr. Gagnon interested in this estimate? Mr. Gagnon is interested in this estimate of E because he wants to know the risk of the stock. At aofpoint in his This career implies he is interested the stock thatthe is the least as a 1% The estimate β islate 1.619. that TinIbuying is riskier than market changerisky. in the market returns would result on a 1.619% change, on average, in TI’s return. Mr.(d)Gagnon is interested in theinrisk he isorinterest Is the estimate of E obtained partof (c)the the stock actual and valuehence of E? Why why not?in β... The estimate of E, which is 1.619, is not necessarily the actual value of E. However, we can be confident that 1.619 is close to the true but unobservable value of E. (We will quantify the idea of “closeness” as well as how likely the estimate is to be close to E later in the semester.) Now consider the regression models Hiltont = D + ES&P500t + Ht Ht iid N(0, V ) 2 4 where Hiltont represents the return on Hilton in month t, and (d) Is the estimate of β obtained in part (c) the actual value of β? Why or why not? No, it is an estimate and indeed our best guess about the “true” β. (e) Now consider the regression models Hiltont = α + βSP 500t + t t ∼ N (0, σ 2 ) where Hiltont represents the return on Hilton in month t, and Giantt = α + βSP 500t + t t ∼ N (0, σ 2 ) where Giantt represents the return on Giant in month t. How does the beta risk of the three companies compare? If Mr. Gagnon wants to lower the overall market risk of his portfolio should he buy Giant, Hilton or Texas Instruments? The market risk of Giant is estimated to be the smallest, with TI as the second riskier and Hilton as the stock with the highest market risk. Mr. Gagnon should buy Giant since he is interested in lowering the overall market risk of his portfolio. (see results below) 5 REGRESSION OUTPUT FOR PROBLEM #6 HILTON Scatter Plot: Hilton vs. S&P 500 y = 1.799x - 0.0059 30% 20% Hilton 10% 0% -10% -20% -10% 0% 10% S&P 500 SUMMARY OUTPUT Regression Statistics Multiple R 0.563390647 R Square 0.317409021 Adjusted R Square 0.305640211 Standard Error 0.09869166 Observations 60 ANOVA df Regression Residual Total Intercept S&P 500 SS 0.262692469 0.564922536 0.827615005 MS 0.262692469 0.009740044 Coefficients Standard Error -0.00592944 0.013146211 1.799029535 0.346413601 t Stat -0.451037971 5.193299362 1 58 59 11 6 GIANT Scatter Plot: Giant vs. S&P 500 y = 0.8954x - 0.0024 30% 20% Giant 10% 0% -10% -20% -10% 0% 10% S&P 500 SUMMARY OUTPUT Regression Statistics Multiple R 0.42681471 R Square 0.182170797 Adjusted R Square 0.168070293 Standard Error 0.070974288 Observations 60 ANOVA df SS 0.065079802 0.292166272 0.357246074 MS 0.065079802 0.00503735 Coefficients Standard Error -0.002417008 0.009454122 0.895442274 0.249123975 t Stat -0.255656515 3.594364104 Regression Residual Total Intercept S&P 500 1 58 59 12 7 Problem 4 Read the “Milk and Money” case in the course notebook. The data file is available on the course website. Important information: 1. The Federal government, through the Agricultural Marketing Service (AMS), sets the price that dairy farmers receive for different “classes” of milk (these classes are called Class I, Class II, etc.). The prices set by the AMS depend on, among other things, the wholesale price of milk and can vary significantly over a two or three year period. In this problem, we will be concerned only with Class III milk prices. 2. A farmer can purchase a put option that gives him the right but not the obligation to sell a futures contract on Class III milk at the “strike” price on or before the expiration date of the option. This puts a “floor” under the price that the farmer will receive for his Class III milk. He removes the downside risk but still has the upside potential. For example, suppose the strike price on a December 15 Class III milk put option is $12/cwt (cwt is a unit of measurement that is roughly 100 pounds of milk). If the AMS price on December 15 is below $12/cwt, the put option allows the farmer to sell his milk for $12/cwt. If the AMS price is greater than $12/cwt then he will sell his milk at the AMS price. The cost of the put option is the price a farmer must pay someone to take on the downside risk. For example, the cost of a $12/cwt December 15 put option purchased in June might be $0.45/cwt. The farmer must also pay trading costs for purchasing the option (e.g. brokers commission, etc.). For example, the trading cost on a $12/cwt December 15 option might be $0.05/cwt. Strike prices on put options for Class III milk are available every $0.25. For example, $11.50/cwt, $11.75/cwt, $12/cwt, $12.25/cwt, etc. 3. For historical and legal reasons, California dairy farmers participate in a California pricing system rather than the federal AMS pricing system. The price a California dairy farmer receives for his milk, called the “mailbox” price, is determined by a complex formula that depends on the value of various dairy products on the wholesale market. The California mailbox price varies a great deal over time just as the federal AMS price does. For example, between 2005 and 2007 the mailbox price varied between $10.16/cwt and $19.98/cwt with an average price in 2006 of $11.28/cwt. The dairy farmer in the case, Gerard, estimates his costs are $12/cwt so a price of $11.28/cwt creates a significant financial problem for him. 4. Gerard is interested in hedging his revenue six months in advance and guaranteeing a price of at least $12/cwt for his milk. For example, in June he wants to hedge his December 15 revenue. 5. Put options on the California mailbox price are not available. The federal Class III milk price is closely related, although not the same as, the California mailbox price 8 that Gerard will receive. For this reason, Gerard will use put options on the federal Class III milk price to hedge his revenue. 6. Gerard wants the probability to be at least 95% that his revenue will be $12/cwt or more no matter what the California mailbox price is. Parts (a) and (b) below provide an example of how to determine the value of a put option on Class III milk on its expiration date. The same idea is used in a slightly more complicated context in parts (c) – (j). The discussion of put options on pages 6-8 of the case, and in particular the example at the bottom of page 7 and top of page 8 will be helpful in answering parts (a) and (b). (a) Suppose Gerard buys a December 15 put option on Class III milk in June with a strike price of $12/cwt. If the Class III milk price on December 15 is $11.50/cwt, how much is the put option worth when it expires on this day? The put option is worth $0.50. The reason is that the option allows the holder to sell Class III milk for $12/cwt on December 15 while the price of Class III milk through the AMS government program is only $11.50/cwt. This means the option provides the holder with an additional $0.50/cwt in revenue that he would not receive if he sold his milk through the government program. Therefore, someone would be willing to pay up to $0.50 to purchase the option on the day it expires. (b) Suppose the price for the put option in part (a) is $0.30/cwt and that the trading costs for purchasing the option are $0.05/cwt. Combining the value of the option obtained in part (a) with the cost information, what is Gerard’s net gain on the option (i.e. what is the value of the put option minus the option cost and trading cost)? Gerard’s net gain is $0.15. This includes the $0.50 he makes on the put option minus the $0.30 premium paid for the option minus the $0.05 paid in trading costs. Therefore, his net gain is $0.50 - ($0.30 + $0.05) = $0.15. For parts (c)–(j), suppose Gerard in June decides to hedge his December 15 revenue by purchasing a put option on Class III milk with a strike price of $14.25/cwt and an expiration date of December 15. You should do the calculations for parts (c)–(h) assuming the costs of the option are zero. A way to incorporate the additional costs into the hedging process is discussed in parts (i) and (j). (c) Plot the Class III milk price against the California mailbox price and add the estimated regression line to the plot. To add the estimated regression line right click on any data point, click on Add Trendline, click on the box above Linear, click on the Options tab, check the box next to Display equation on chart and click OK. What is the equation of the estimated regression line? How much do you expect the Class III milk price to change on average for a $1/cwt change in the California mailbox price? 9 (c) Plot the Class III milk price against the California mailbox price and add the estimated regression line to the plot. To add the estimated regression line to a plot right click on any data point, click on Add Trendline, click on the box above Linear, click on the Options tab, check the box next to Display equation on chart and click OK. Class III vs. Mailbox y = 1.1822x - 1.5572 R2 = 0.9268 Class II $22 $18 $14 $10 $9.00 $13.50 $18.00 Mailbox Figure 1: The Class III milk price is expected to change $1.18/cwt for every $1/cwt change is the equation of price. the estimated regression line? inWhat the California mailbox ! 23#!#(*,7%*#&!$#+$#((,9)!5,)#!,(!Class III Price!B!>0/11CD!@!0/0EDD!Mailbox Price/! For the remainder of the problem use 0.60 as the value of σ (the standard deviation of the error term) and the estimated regression line as if it were the true regression line to answer the following questions. 15 (d) What is the probability that Gerard’s December 15 put option on Class III milk with a strike price of $14.25 is in the money (i.e. worth something) on December 15 if the California mailbox price on December 15 is $12.50/cwt? Note that for a December 15 put option on Class III milk with a strike price of $14.25/cwt to be in the money on December 15, the Class III milk price must be less than $14.25/cwt on December 15 (because the value of the put option on its expiration date is the difference between the strike price of $14.25 and the actual Class III milk price if the strike price is greater than the Class III milk price). This means the probability a put option with a strike price of $14.25/cwt is in the money on December 15 is the probability that the Class III milk price on December 15 is less than $14.25. Using the regression line and the distribution for the Class III milk price associated with a mailbox price of $12.50 (see the graph at the end of the answer to this problem), the distribution for the Class III milk price given that the mailbox price is $12.50/cwt is N (13.22, 0.602 ). Note that the mean is the point on the regression line when the mailbox price is 12.50, 10 i.e. −1.5572 + 1.1822 × (12.50) = 13.22. Therefore, P r(Option is in the money) = P r(Class III Price < 14.25) Class III Price − 13.22 14.25 − 13.22 = P r( < ) 0.60 0.60 = P r(Z < 1.72) = 95.7% (e) Suppose the California mailbox price on December 15 is $12.00/cwt. What is the probability that the value of the put option will be greater than $0.50? The value of the put option will be greater than $0.50 if the Class III milk price is less than $13.75/cwt (because the value of the put option on its expiration date is the difference between the strike price of $14.25 and the actual Class III milk price if the strike price is greater than the Class III milk price). Therefore, the probability that the value of the put option will be greater than $0.50 is the probability that the Class III milk price is less than $13.75/cwt. To compute this probability, note that the distribution for the Class III milk price if the mailbox price is $12.00/cwt is N (12.63, 0.602 ) see the graph at the end of the answer to this problem. Note that the mean is the point on the regression line when the mailbox price is 12.00, i.e. −1.5572+1.1822×(12.00) = 12.63. Therefore, P r(Option value is greater than 0.50) = P r(Class III Price < 13.75) Class III Price − 12.63 13.75 − 12.63 = P r( < ) 0.60 0.60 = P r(Z < 1.87) = 96.9% (f) Using your answer to part (e), what is the probability that Gerard’s net revenue (mailbox price plus payoff from the option) will exceed $12.50/cwt if the California mailbox price is $12.00/cwt? If the mailbox price is $12.00/cwt then the put option must be worth at least $0.50 for Gerard’s net revenue to be at least $12.50/cwt. The result in part (e) means there is a 96.9% chance Gerard’s net revenue will be at least $12.50/cwt if the mailbox price is $12.00/cwt. The reason is that he will receive the mailbox price of $12.00/cwt plus the revenue from selling the put option, and there is a 96.9% chance that the value of the put option will be at least $0.50. (g) Now suppose the mailbox price on December 15 is $11.50/cwt. What is the probability that the value of the put option will be greater than $1? Using your answer to this question, what is the probability that Gerard’s net revenue (mailbox price plus payoff from the option) will exceed $12.50/cwt? 11 If the mailbox price is $11.50/cwt then the put option must be worth at least $1 for Gerard’s net revenue to be at least $12.50/cwt. The value of the put option will be greater than $1 if the Class III milk price is less than $13.25/cwt (because the value of the put option on its expiration date is the difference between the strike price of $14.25 and the actual Class III milk price if the strike price is greater than the Class III milk price). Therefore, the probability that the value of the put option will be greater than $1 is the probability that the Class III milk price is less than $13.25/cwt. To compute this probability, note that the distribution for the Class III price if the mailbox price is $11.50/cwt is N (12.04, 0.602 ) see the graph at the end of the answer to this problem. Note that the mean is the point on the regression line when the mailbox price is 11.50, i.e. −1.5572+1.1822×(11.50) = 12.04. Therefore, P r(Option value is greater than 1.00) = P r(Class III Price < 13.25) Class III Price − 12.04 13.25 − 12.04 = P r( < ) 0.60 0.60 = P r(Z < 2.02) = 97.8% This means there is a 97.8% chance Gerard’s net revenue will be at least $12.50/cwt if the mailbox price is $11.50/cwt. The reason is that he will receive the mailbox price of $11.50/cwt plus the revenue from selling the put option, and there is a 97.8% chance that the value of the put option will be at least $1.00. (h) Is the probability at least 95% that his net revenue (mailbox price plus payoff from the option) will equal or exceed $12.50/cwt for any mailbox price below $12.50/cwt? Why or why not? The probability will be at least 95% that his net revenue will equal or exceed $12.50/cwt for any mailbox price below $12.50/cwt. One way to solve the problem: Parts (e) and (f) showed that the probability is 96.9% that his net revenue will equal or exceed $12.50/cwt if the mailbox price is $12.00/cwt. Part (g) showed that the probability is 97.8% that his net revenue will equal or exceed $12.50/cwt if the mailbox price is $11.50/cwt. A similar calculation can be done for any mailbox price less than $12.50/cwt (e.g. $12.49/cwt, $12.48/cwt, etc.) to show the probability is at least 95% that his net revenue will equal or exceed $12.50/cwt for any mailbox price below $12.50/cwt. This is a labor intensive way to do it but it is one way to verify the statement. A graphical explanation for why this is happening is that the regression line (which gives the mean of the Class III price distribution for a given mailbox price) is decreasing at the rate of $1.18 for every $1.00 decrease in the mailbox price while the line that connects the Class III prices that guarantee Gerard at least $12.50/cwt in net revenue is decreasing at the rate of $1.00 for every $1.00 decrease in the mailbox 12 price. To see that the latter statement is true, draw in a line on the graph at the end of the answer to this question that connects the points: (12.50, 14.25), (12.00, 13.75) and (11.50, 13.25). Carefully viewing this line will show that the Class III prices that guarantee Gerard at least $12.50/cwt in net revenue are moving farther out into the tails of the Class III price distributions as the mailbox price decreases from $12.50/cwt. This means the probabilities that the Class III price is below the price that guarantees Gerard net revenue of at least $12.50/cwt will increase from the value of 0.957 computed for the mailbox price of $12.50/cwt. Therefore, the probability will be at least 95% that his net revenue will equal or exceed $12.50/cwt for any mailbox price below $12.50/cwt. Another way to solve the problem: Denote X as the mailbox price and Y as the Class III price. Since Y ∼ N (1.1822 × X − 1.5572, 0.62 ), supposing that X < 12.50, then the net revenue would be max{X, X + (14.25 − Y )}. Denote R = X + (14.25 − Y ), then R is a normal random variable distributed as R ∼ N (14.25 + 1.5572 + X − 1.1822X, 0.62 ) = N (15.8072 − 0.1822X, 0.62 ) The probability for the net revenue R to be equal or greater than $12.50/cwt would be R − (15.8072 − 0.1822X) 12.5 − (15.8072 − 0.1822X) P (R > 12.5) = P > 0.6 0.6 12.5 − (15.8072 − 0.1822X) =P Z> 0.6 0.1822X − 3.3072 =P Z> 0.6 = P (Z > 0.3036X − 5.512) Thus when X < 12.5, {P (R > 12.5) = P (Z > 0.3036X − 5.512)} > {P (Z > 0.3036 × 12.5 − 5.512) = 95.7%} (1) Therefore, the probability will be at least 95% (in fact, at least 95.7%) that his net revenue will equal or exceed $12.50/cwt for any mailbox price below $12.50/cwt. For parts (i) and (j), suppose the price in June for a December 15 put option on Class III milk with a strike price of $14.25/cwt is $0.45/cwt and the trading cost is $0.05/cwt. (i) Is the probability at least 95% that Gerard’s net revenue (mailbox price plus payoff from the option minus option cost and trading cost) will equal or exceed his production costs of $12.00/cwt no matter what the California mailbox price is? 13 From part (h), the probability is at least 95% that his revenue before the costs of the option are included will be $12.50/cwt or more no matter what the California mailbox price is. This means that after the premium and trading costs of $0.50/cwt are accounted for the probability is at least 95% that his net revenue will be $12.00/cwt or more no matter what the California mailbox price is. (j) Has Gerard effectively hedged his net revenue (mailbox price plus payoff from the option minus option cost and trading cost) if $12/cwt is the amount he needs to receive for his milk to cover his production costs? Gerard has effectively hedged his net revenue because there is at least a 95% chance his net revenue will be $12.00/cwt or more. There is a small chance (5% or less) that his net revenue will be less than $12/cwt but this is a risk he is willing to accept. Class III Price ! "&$#)! í"$))+# + "$",##Mailbox Price "*$+)! "*$#)! "*$##! "#$(*! V!'!%$(! "#$%&! V!'!%$(! V!'!%$(! %! … "#$%%! ""$)%! 14 21 "#$)%! Mailbox Price

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