Mengchao Essay

Arley Merchandise corpObjectives and SynopsisT distributivelying course of studyThis teaching plan organizes the class as followsValuation of the Arley goodwhy include the ten-year tear down alternative?Ameri merchant ship- vs. European-style role?Similarities to a transmu prorogue subordinated unsecured bondThe choice made and the aftermathValuation of the Arley RightConsider starting line the case where the right is exercisable into $8 of cash. The whole proposed for sale in the Arley pay then can be characterized as the sale of a destiny of frequent rake plus a two-year European piece excerpt with a strike charge of $8 or, alternatively, through put- look to comparison, as the sale of a two-year zero-coupon note with face cling to $8 plus a two-year European call pickaxe on common old-hat with an exercise scathe of $8. Thus, the take account of the whole can be broken down in two ways grocery tax of the unit= Market determine of have a bun in the oven + market place value of put option= Market value of zero-coupon bond + market value of call optionApplying the Black-Scholes model with a two-year jeopardizeless calculate of 11% perannum, an initial stock determine of $6.50, and a unpredictability of 40% (as indicated in the assignment question), yields values of the put and call options of $1.44 and $1.45, respectively.1 introduce 4 shows historical unpredictability data for equal firms. The instructor can claim the students in a discussion of how to use this information in the digest. The accessory to this teaching note contains a discussion of these comparables and sensitivity analysis. However, Black-Scholes is not necessarily applicable because of thoughtlessness risk associated with this particular put option. That is, put option holders pull up stakes wish to exercise their right to receive cash at precisely the succession that Arleys stock is low, which is excessively when the firm will least be able to fund the $8 payment. Thus, the standard Black-Scholes formula, which assumes no default risk in the option, will all overestimate the value of the right. To top executivey value the put option requires a model of default risk in addition to the underlying equity risk.2Luckily, in this instance, the above put-call parity relation provides a simple and indirect way of valuing the right, since it separates stock price risk from default risk. There is little, if any, default risk associated with the call option, as holders will wish to exercise their right at a time when the firm1 The put and call values argon to the spiritedest degree equal since the strike price of $8 is very close to the commencement exercise stock price of $6.50 plusriskless provoke.2 See, for example, H. Johnson and R. Stultz (1987), The pricing of options with default risk, Journal of Finance, 42, 267-280.What remains is to value the zero-coupon note. This is a question purely of trust risk, the price of which can be approximated using usher 5, which contains yields on heterosexual debt of lowrated fruitrs comparable to Arley. The issues in the Exhibit atomic number 18 priced at spreads as high as 3.5% over Treasurys. Arleys subordinated debt would probably slabber a Ba or B rating, and would thus require a yield at the high end of the range. Assuming a flat term social organisation for the credit spread, the required spread on two-year Arley debt is most 3.5%, or a yield-to- maturity date of 14.5%. Discounting $8 at 14.5% per annum for two age gives a value for the two-year zero-coupon note of $6.10.Adding the value of the two-year note ($6.10) to the value of the call option ($1.45) yields an estimate of $7.55 for the value of the total package. The implied value of the put option is therefore $7.55 $6.50 = $1.05. The implied value of the put option is therefore $7.55 $6.50 = $1.05. This can be summarized asNote+Call$6.10+$1.45=Unit=Stock+Put=$7.55=$6.50+$1.05The variation of $0.39 between this value of the put option and the Black-Scholes value of the put option ($ 1.44) is the diminution in value ofthe option due to issuer default risk.The analysis so far has assumed that the put option is exercisable into cash. In general, and ceteris paribas, the issuers option to substitute debt for cash upon exercise of the option reduces the value of the right even further. However, this assumes the stock price of $6.50 is unaffected by the nature of this contract. For example, the tractableness to substitute debt for cash may importantly reduce the likelihood of monetary distress and enhance overall firm value.Here, the value of the right is believably to be significantly diminished by the flexibility to substitute debt since the debt is unbelievable to be worth as much as $8.00/ unit when issued. In late 1982 and early 1983, the lowest class of investment grade debt ( utter) sell at a yield of about 125% of the ten-year Treasury debt yield. Baa debt was ca lling at a yield which was solitary(prenominal) 116% of ten-year Treasury yields. As surmised earlier, Arleys subordinated debt would probably carry a Ba or B rating, and would thus require a yield substantially high than Baa-rated debt. In addition, the maximum issue surface of subordinated debt issued in exchange for Arley units would amount to only about $6 million (750,000 x $8.00). Trading would be extremely thin and the issue would be highly illiquid. It would trade at a still higher yield for this reason. In all, it appears that the Arley package was somewhat overvalued by the underwriters (assuming a value of $6.50 for the common stock). wherefore Include the Ten-Year Note option?The information asymmetry issue raised earlier in this note is grievous in understanding the significance of the inclusion of the ten-year notealternative. The force play of directions conviction regarding the deduction of future forecasts can be reflected in the form in which it chooses op tions for recognize the insure obligation. Managements stock possession position will in like manner play an important role in this choice.A management with little stock proprietorship will convey the strongest position of certainty if it restricted its options in honoring the guarantee to only cash. The weakest conviction will be conveyed 3if the options include the exchange of the right for additional common shares to bring the value of each Arley unit up to $8.00. This outcome would simply reallocate the equity value among Arleys shareholders without exposing the management to any default risk and potential want of employment. In companies where management owns little stock, as the options usable for meeting the guarantee expand along the spectrum of cash, senior debt, subordinated debt, preferred stock, and common stock, the strength of managements conviction about the future should decrease in the minds of investors.A management with significant stock ownership would conve y the strongestposition of certainty if shareholders could collect their value guarantee in either cash or market value of common stock at the option of the owner of the right. This arrangement would expose management to both default risk (and thinkable loss of jobs) as well as disastrous dilution of their accumulated wealthiness position if the stock price declined but the company was not in danger of default on the put. The underwriters bear suggested a prudent and interoperable position with regard to the form of the options the company will assimilate available for honoring the guarantee, but (given the fact that Arleys management owned over 50% of the companys stock) this is also one of the weakest positions possible in terms of the persuasive power of its information meaning to investors. Information content is obviously only one factor for Arley to consider in make its decision. The call for to preserve financial flexibility under adverse good deal is probably the mo st critical factor, and Arleys management would retain this flexibility, in the form of the option, to issue a subordinated debt to honor the guarantee.American- vs. European-Style Exercise?A endeavor question was whether holders of the security should be able to exercise their right at a specific point in time (European-style), or at any time until the expiration date (American-style). Arley favored a European-style exercise option. This made it possible to plan for and finance a mass redemption, quite than confronting one at an unexpected and inconvenient time.Similarities to a Convertible Subordinated debentureThe proposed Arley security can be viewed as a convertible subordinated debenture with somewhat unusual terms. The principal variations areThe conversion period expires in two years instead of spanning the life ofthe debenture (or until the debenture was called)In exchange for a two-year grace period on interest payments, Arley unit owners will receive what is intended t o be a market rate of interest on the security for the balance of its life. Normally, convertible subordinated debentures carry a below-market rate of interest (Exhibit 5)The life of the issue is twelve years rather than the more typical twenty to twenty-five years for a convertible subordinated debenture (Exhibit 5).Since the Arley issue is conceptually and economically corresponding to a convertible subordinated debenture, why didnt Arley simply issue a convertible subordinated debenture with termsequivalent to the proposed Arley units? There were two good reasons favoring the proposed Arley issueSince Arley had no publicly traded common stock, buyers of any Arley convertible subordinated debenture would have no traded equity security against which to price the debenture. A liquidity caper (only 6,000 debentures would be available for trading) would exacerbate the pricing difficulty.The retail optics of the Arley issue are better than the equivalent convertible subordinated deb enture. The proposed Arley unit can be marketed as an issue with a two-year money-back guarantee. The unit would almost certainly be sold to retail investors and might trade at a higher price than the equivalent convertible subordinated debenture.The Choice Made and the AftermathThe proposed Arley unit was sold in the form described in the case on November 14, 1984. Management had hoped that the units could be described as equity, but Arleys accountants had argued that the securities would have to be accounted for on a line entitled Common stock subject to repurchase under Rights, which fell between the debt and equity accounts on the Arley balance sheet. The operating performance of the company and the performance of its stock price following the passporting were both disappointing. network per share fell (versus the similar quarter in the prior year) for five successive quarters direct following the offering (Exhibit TN-1). Theprice of the Arley units fell after the offering, a nd did not encounter to $8.00/unit for fifteen months (Exhibit TN-2). The right traded well below the anticipated take aim of $1.50. Trading volume in the units and common shares combined sightlyd only about 50,000 per month, or about 1,500 per trading day. Volume in the rights averaged only 1,000 per trading day.In July, 1986, Arley management announced that they had agreed to accept a supplementd buyout offer at $10.00/share for all of the companys common stock from a group of middle-level managers at the company.In whitethorn, 1985, a similar offering was made by Gearhart Industries which raised $85 million at a premium of 23% above its then common stock price of $10.75/share. This offering featured five put dates at one-year intervals from one to six years following the offering date. The company also had the option to honor the put (at a price which escalated above the $13.25/unit issue price at the rate of 10%/ year) in common stock or preferred stock as well as subordina ted debt. The option to satisfy the guarantee with an equity security removed the need to characterize the security as anything other than equity for accounting purposes. Gearharts stock price collapsed after the offering. The right was designed to put a floor under the value of the Gearhart unit at the $13.25 offering price but this obviously was not the case as shown in Exhibit TN-3.The Arley and Gearhart cases are good examples of situations where the risk of default can enter significantly into the value of a put option. Here, it is when the put is to the company itself rather than to a third party of high credit quality.Exhibit TN-1Arley Merchandise Corporation Earnings Per Share by Calendar Quarter, 1983-1986198319841st Quarter.20second Quarter.33.20.254th Quarter.30*.281986.16.20.08.22.20opyo3rd Quarter1985* First Earnings Report following Initial Public Offering.November 1984Share + Right5 1/21/2January 19856 1/21/2February6 1/8N.A. frame in6 7/81/87April6 1/21/86 5/8 may6 3 /41/86 7/8June6 3/81/86 1/2July6 1/83/86 1/2August5 7/85/86 1/2September5 3/43/46 1/2October5 3/41 1/86 7/8tCopyoDecember67N.A.November67/86 7/8December5 7/83/46 5/8January 19865 7/81 1/47 1/8February6 7/8N.A.N.A.7 7/81/887 7/81/88MarchAprilNovember 19857 1/44 1/8December7 5/83 3/8January 19865 1/44 7/8February4 3/86March3 3/46April2 5/83 3/46 3/8May3 1/44 1/47 1/2Share + Right11 3/81110 1/810 3/89 3/4AppendixComparables and sensitivity analysisNormally, students encountering options are given either historical or implied excitability data. In this instance, as Arley does not yet have publicly traded stock, neither of these standard sources of data is available. However, the case does give data on a set of comparable firms no(prenominal) had traded options, so all of the data given is historical volatilities. The instructor can engage students on the issue of how to use this volatility data. The average volatility ranges from 18% to 39%, and averages 28% for the most recent volatil ity and 29% for the average volatility over the prior five years. nevertheless the assignment question asks the student to use a 40% volatility. Why would Arley probably have a higher volatility than the average category furnishing manufacturer more generally, what would drive volatility?Students may recognize that volatility should be related to fundamental business risk, which in turn would be related to the instability of supplyand demand, as well as variable quantity competition. More narrowly, one might expect that firms with higher fixed be might experience higher volatility as well as firms with greater debt, as operating or financial leverage would overstate movements in firm value for shocks in the underlying business. They might also expect that smaller firms might have greater volatility, in part due to lower scale economies. An especially diligent student might calculate the relationships between the volatilities in Exhibit 4 with firm size (market value of equity p lus firm value of debt), firm leverage (debt divided by market size), or profitability. Using average volatility as a measure, she would find the coefficients on these relationships to be directionally correct (higher volatilities on smaller firms, more levered firms and less profitable firms), but in an OLS framework, none are close to conventional significance levels.Given the uncertainty in volatilities, students might calculate the sensitivity of option values to respective(a) levels of volatility. The table below shows this sensitivity for various volatilities as well as for various maturities. Note this table uses the two-year risk free rate from Exhibit 7 (11.14%) which is quoted on a bond-equivalent yield basis, so the numbers will vary slightly from those in the text.VOLATILITY RANGE25%30%35%1.07 $ 1.20 $ 1.33$0.88 $ 1.06 $ 1.24$0.73 $ 0.93 $ 1.13 $0.61 $ 0.81 $ 1.02$0.51 $ 0.71 $ 0.92$25%0.39 $0.94$1.45$1.92$2.36$30%0.52$1.12$1.65$2.13$2.56$35%0.65$1.29$1.85$2.34$2.76$40% 0.78$1.47$2.05$2.54$2.97$45%1.59$1.59$1.52$1.43$1.33$50%1.72$1.76$1.71$1.63$1.53$45%0.91$1.65$2.24$2.75$3.18$50%1.041.822.432.953.3840%$1.46$1.41$1.33$1.23$1.12$DoNotCPUTS$1.4120%1 $ 0.952 $ 0.703 $ 0.534 $ 0.415 $ 0.32Time to maturityCALLS$1.4720%1 $ 0.272 $ 0.763 $ 1.254 $ 1.725 $ 2.17rPost