Mengchao Essay

Arley Merchandise CorporationObjectives and SynopsisTeaching PlanThis teaching cast organizes the class as followsValuation of the Arley rightWhy include the ten-year find alternative?Ameri stick out- vs. European-style exercise?Similarities to a convertible subordinated debentureThe choice made and the aftermathValuation of the Arley RightConsider first the teddy where the right is exercisable into $8 of change. The whole proposed for sale in the Arley financing then freighter be characterized as the sale of a sh are of familiar credit line plus a two-year European mould woof with a engage damage of $8 or, alternatively, through repose- betoken similarity, as the sale of a two-year zero-coupon note with face measure out $8 plus a two-year European c all(prenominal) selection on common filiation with an exercise charge of $8. Thus, the tax of the unit can be disquieted down in two waysMarket value of the unit= Market value of striving + market value of dedicate cream= Market value of zero-coupon bond + market value of call optionApplying the Black-Scholes model with a two-year riskless appraise of 11% perannum, an initial stock price 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 Exhibit 4 shows historical volatility entropy for comparable firms. The instructor can engage the students in a reciprocation of how to use this breeding in the abridgment. The Appendix to this teaching note contains a discussion of these comparables and sensitivity analysis. However, Black-Scholes is not necessarily applicable because of nonremittal risk associated with this particular put option. That is, put option holders will wish to exercise their right to receive funds at precisely the time that Arleys stock is low, which is alike 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 correctly value the put option requires a model of default risk in addition to the underlying legality 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. in that respect 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 are al almost equal since the strike price of $8 is very close to the beginning stock price of $6.50 plusriskless interest.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 credit risk, the price of which can be approximated using Exhibit 5, which contains yields on straight debt of lowrated u nloosers comparable to Arley. The issues in the Exhibit are priced at spreads as high as 3.5% over Treasurys. Arleys subordinated debt would probably carry a Ba or B rating, and would thus require a yield at the high end of the range. assume a flat term structure for the credit spread, the required spread on two-year Arley debt is rough 3.5%, or a yield-to-matureness of 14.5%. Discounting $8 at 14.5% per annum for two years 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 pile. 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 difference 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 temperament of this contract. For example, the tractability to substitute debt for cash may significantly reduce the likelihood of financial distress and call down overall firm value.Here, the value of the right is likely to be significantly diminished by the flexibility to substitute debt since the debt is unlikely to be worth as much as $8.00/ unit when issued. In modern 1982 and early 1983, the lowest class of investment grade debt (Baa) sell at a yield of closely 125% of the ten-year Treasury debt yield. Baa debt was trade at a yield which was single 116% of ten-year Treasury yields. As surmised earlier, Arleys subordinated debt would prob ably carry a Ba or B rating, and would thus require a yield substantially higher(prenominal) than Baa-rated debt. In addition, the maximum issue size of subordinated debt issued in exchange for Arley units would tot up 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).Why Include the Ten-Year Note Alternative?The information asymmetry issue raised earlier in this note is important in understanding the deduction of the inclusion of the ten-year notealternative. The strength of counsellings conviction regarding the certainty of future forecasts can be reflected in the form in which it chooses options for honoring the guarantee obligation. Managements stock ownership impersonate will also play an important role in this choice.A m anagement with little stock ownership 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 included the exchange of the right for additional common shares to found 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 loss of employment. In companies where management owns little stock, as the options for sale 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 convey the strongestposition of certainty if shareholders could collect their value guarantee in either cash or market value of common stock at the opti on of the owner of the right. This arrangement would wear management to both default risk (and possible loss of jobs) as well as inglorious dilution of their accumulated wealth position if the stock price declined but the association was not in insecurity of default on the put. The underwriters have suggested a prudent and practical position with regard to the form of the options the company will have 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 cable office of its information content to investors. Information content is apparently only one factor for Arley to consider in making its decision. The need to preserve financial flexibility under adverse circumstances is probably the most critical factor, and Arleys management would retain this flexibility, in the form of the option, to issue a subordinated debt to honor the guarant ee.American- vs. European-Style operation?A design 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 accompaniment (American-style). Arley favored a European-style exercise option. This made it possible to plan for and finance a mass redemption, or else 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 stoppage 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 to 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 cardinal to twenty-five years for a convertible subordinated debenture (Exhibit 5).Since the Arley issue is conceptually and economically similar to a convertible subordinated debenture, why didnt Arley simply issue a convertible subordinated debenture with terms similar 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 problem (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 debenture. 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 r etail investors and might trade at a higher price than the equivalent convertible subordinated debenture.The prime(prenominal) 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 oblation were both disappointing. honorarium per share fell (versus the similar quarter in the prior year) for five straight quarters immediately following the offering (Exhibit TN-1). Theprice of the Arley units fell after the offering, and did not recover to $8.00/unit for fifteen months (Exhibit TN-2). The right traded well below the anticipated level of $1.50. Trading volume in the units and common shares combined intermediated 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 leveraged buyout offer at $10.00/share for all of the companys common stock from a group of middle-level managers at the company.In May, 1985, a similar offering was made by Gearhart Industries which raised $85 million at a exchange 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 subordinated debt. The option to satisfy the guarantee with an equity security removed the need to characterize the security as anything oth er 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 terzetto party of high credit quality.Exhibit TN-1Arley Merchandise Corporation Earnings Per Share by calendar Quarter, 1983-1986198319841st Quarter.202nd 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. swear out6 7/81/87April6 1/21/86 5/8May6 3/41/86 7/8June6 3/81/86 1/2July6 1/83/86 1/2 rarified5 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 7/81/88 touchAprilNovember 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 volatility 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 none 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 volatility and 29% for the average volatility over the prior five years. Yet the assignment question asks the student to use a 40% volatility. Why would Arley probably have a higher volatility than the average home furnishing maker 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 protean competition. More narrowly, one might expect that firms with higher fixed costs might experience higher volatility as well as firms with greater debt, as operating or financial leverage would amplify movements in firm value for shocks in the underlying business. They might also expect that littler firms might have greater volatility, in part due to lower scale economies. An especially quick student might calculate the relationships between the volatilities in Exhibit 4 with firm size (market value of equity plus 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 relat ionships to be directionally correct (higher volatilities on smaller firms, more levered firms and less profi delay firms), but in an OLS framework, none are close to stately significance levels.Given the uncertainty in volatilities, students might calculate the sensitivity of option values to miscellaneous 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$1.41 20%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