Mengchao Essay

Arley Merchandise Corporation Objectives and Synopsis Teaching Plan This teaching plan organizes the class as follows: Valuation of the Arley â€Å"right† †¢ Why include the ten-year note alternative? †¢ American- vs. European-style exercise? †¢ Similarities to a convertible subordinated debenture †¢ The choice made and the aftermath †¢ Valuation of the Arley â€Å"Right† Consider first the case where the right is exercisable into $8 of cash. The unit proposed for sale in the Arley financing then can be characterized as the sale of a share of common stock plus a two-year European put option with a strike price of $8 or, alternatively, through put-call parity, as the sale of a two-year zero-coupon note with face value $8 plus a two-year European call option on common stock with an exercise price of $8. Thus, the value of the unit can be broken down in two ways: Market value of the unit = Market value of stock + market value of put option = Market value of zero-coupon bond + market value of call option Applying the Black-Scholes model with a two-year riskless rate of 11% per  annum, an initial stock price of $6.50, and a volatility 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 data for comparable firms. The instructor can engage the students in a discussion of how to use this information in the analysis. The Appendix to this teaching note contains a discussion of these comparables and sensitivity analysis. However, Black-Scholes is not necessarily applicable because of default risk associated with this particular put option. That is, put option holders will wish to exercise their right to receive cash at precisely the time that Arley’s stock is low, which is also 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 overestimate the value of the right. To correct ly value the put option requires a model of default risk in addition to the underlying equity risk.2 Luckily, 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 firm 1 The put and call values are almost equal since the strike price of $8 is very close to the beginning stock price of $6.50 plus  riskless interest. 2 See, for example, H. Johnson and R. Stultz (1987), â€Å"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 issuers comparable to Arley. The issues in the Exhibit are priced at spreads as high as 3.5% over Treasurys. Arley’s subordinated debt would probably carry a Ba or B rating, and would thus require a yield at the high end of the range. Assuming a flat term structure for the credit spread, the required spread on two-year Arley debt is about 3.5%, or a yield-to-maturity 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 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 as: Note + Call $6.10 + $1.45 = Unit = Stock + Put = $7.55 = $6.50 + $1.05 The 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 of the 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 issuer’s 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 flexibility to substitute debt for cash may significantly reduce the likelihood of financial distress and enhance 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 late 1982 and early 1983, the lowest class of investment grade debt (Baa) sold at a yield of about 125% of the ten-year Treasury debt yield. Baa debt was trading at a yield which was only 116% of ten-year Treasury yields. As surmised earlier, Arley’s subordinated debt would probably carry a Ba or B rating, and would thus require a yield substantially higher than Baa-rated debt. In addition, the maximum issue size 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). Why Include the Ten-Year Note Alternative? The information asymmetry issue raised earlier in this note is important in understanding the significance of the inclusion of the ten-year note  alternative. The strength of management’s conviction regarding the certainty of future forecasts can be reflected in the form in which it chooses options for honoring the guarantee obligation. Management’s stock ownership position will also play an important role in this choice. A management 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 3 if the options included 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 Arley’s shareholders without exposing the management to any default risk and potential loss of employment. In companies where management owns little stock, as the options available for meeting the guarantee expand along the spectrum of cash, senior debt, subordinated debt, preferred stock, and common stock, the strength of management’s conviction about the future should decrease in the minds of investors. A management with significant stock ownership would convey the strongest  position 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 possible loss of jobs) as well as disastrous dilution of their accumulated wealth position if the stock price declined but the company was not in danger 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 Arley’s management owned over 50% of the company’s stock) this is also one of the weakest positions possible in terms of the persuasive power of its information content to investors. Information content is obviously only one factor for Arley to consider in making its decision. The need to preserve financial flexi bility under adverse circumstances is probably the most critical factor, and Arley’s 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 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 date (American-style). Arley favored a European-style exercise option. This made it possible to plan for and finance a mass redemption, rather than confronting one at an unexpected and inconvenient time. Similarities to a Convertible Subordinated Debenture The proposed Arley security can be viewed as a convertible subordinated debenture with somewhat unusual terms. The principal variations are: The conversion period expires in two years instead of spanning the life of the 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 â€Å"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 similar to a convertible subordinated debenture, why didn’t Arley simply issue a convertible subordinated debenture with terms  equivalent to the proposed Arley units? There were two good reasons favoring the proposed Arley issue: Since 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 â€Å"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 retail investors and might trade at a higher price than the equivalent convertible subordinated debenture. The Choice Made and the Aftermath The 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 Arley’s accountants had argued that the securities would have to be accounted for on a line entitled â€Å"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 offering were both disappointing. Earnings per share fell (versus the similar quarter in the prior year) for five successive quarters immediately following the offering (Exhibit TN-1). The  price 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 averaged only about 50,000 per month, or about 1,500 per trading day. Vo lume 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 company’s 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 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 other than equity for accounting purposes. Gearhart’s 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-1 Arley Merchandise Corporation Earnings Per Share by Calendar Quarter, 1983-1986 1983 1984 1st Quarter .20 2nd Quarter .33 .20 .25 4th Quarter .30 *.28 1986 .16 .20 .08 .22 .20 op yo 3rd Quarter 1985 * First Earnings Report following Initial Public Offering. November 1984 Share + Right 5 1/2 1/2 January 1985 6 1/2 1/2 February 6 1/8 N.A. March 6 7/8 1/8 7 April 6 1/2 1/8 6 5/8 May 6 3/4 1/8 6 7/8 June 6 3/8 1/8 6 1/2 July 6 1/8 3/8 6 1/2 August 5 7/8 5/8 6 1/2 September 5 3/4 3/4 6 1/2 October 5 3/4 1 1/8 6 7/8 tC op yo December 6 7 N.A. November 6 7/8 6 7/8 December 5 7/8 3/4 6 5/8 January 1986 5 7/8 1 1/4 7 1/8 February 6 7/8 N.A. N.A. 7 7/8 1/8 8 7 7/8 1/8 8 March April November 1985 7 1/4 4 1/8 December 7 5/8 3 3/8 January 1986 5 1/4 4 7/8 February 4 3/8 6 March 3 3/4 6 April 2 5/8 3 3/4 6 3/8 May 3 1/4 4 1/4 7 1/2 Share + Right 11 3/8 11 10 1/8 10 3/8 9 3/4 Appendix Comparables and sensitivity analysis Normally, 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 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 supply  and demand, as well as variable 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 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 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 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 various 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 RANGE 25% 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% 1.04 1.82 2.43 2.95 3.38 40%  $ 1.46  $ 1.41  $ 1.33  $ 1.23  $ 1.12  $ Do No tC PUTS $1.41 20% 1 $ 0.95 2 $ 0.70 3 $ 0.53 4 $ 0.41 5 $ 0.32 ^Time to maturity CALLS $1.47 20% 1 $ 0.27 2 $ 0.76 3 $ 1.25 4 $ 1.72 5 $ 2.17 rP os t