AVON Percs
...e PERCS prior to maturity; 2. The dividends 380 million shares of common @ 0.30 per share plus 20 million PERCS shares @ 0.60 per share = $36 million in total dividends, divided by 100 million pseudo equity shares outstanding yields 0.36 per share quarterly dividend. PERCS Analysis - Page 4 on the common remain unchanged; 3. All dividends on the PERCS and the common are paid. Under these conditions, the cash flows accruing to the holder of the PERC, the holder of the common, and the holder of "pseudo common" (defined below) is shown on the following table. Quarter 0 1 2 3 4 5 6 7 8 9 10 11 12 Cash Flow to PERC Holder -30 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 0.60 + Redemption Value Cash Flow to Common Holder -30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 + Stock Value Cash Flow to "Pseudo Common" -30 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 + Pseudo Stock Value The PERCS holder receives a higher dividend than the common stock. The pseudo common stock is the common stock that would be outstanding if the company did not issue the PERCS security and paid an equivalent amount in total dividends.3 Define the price per share of pseudo common to be S* and the total value of the pseudo common to be S* times the number of shares that would have been outstanding: i.e., the total value of the pseudo equity, E* = 100 million times S*. PERCS Analysis - Page 5 Fundamental learning point. The value of the total equity (Common plus PERCS) at any point in time must equal the total value of the pseudo equity, i.e., NPPERCSt + NsSt = N*S*t This follows from the fact that the total cash outlay in the first three years is the same and the PERCS plus the common own the same equity of the company that the pseudo equity would own at the end of three years. Will the stock price at the end of three years be equal to the pseudo stock price? Only if the terminal stock price is less than or equal to the PERCS capped price. In this instance, the PERCS will be converted one-for-one and the share price will be the total share value divided by 100 million shares, which is the same as the psuedo share value. If the stock price exceeds the PERCS cap price, however, there will be fewer shares outstanding, the PERCS will own a smaller fraction of the equity, the common will own a larger fraction of the equity and ST > S*T. Example. Suppose the stock price ends up at $50. Each share will be converted into X/ST = 40/50 = .80 shares of stock. In total, there will be .80(20 million PERCS) = 16 million new shares of equity, for a total of 80 million + 16 million = 96 million. The total value of the equity is $50(96 million) = $4,800 million. Had the company remained all common stock with 100 million shares, the shares would be worth $4,800/100 = $48 per share. Figure 1 shows the returns to the PERCS holder and a pseudo share holder as a function of the terminal stock price. The returns are calculated as the annualized internal rate of return on the respective securities, assuming the cash flows on the table on page 4 and terminal payoffs as described above. If the stock price ends up below (above) $44, the PERCS holder earns a higher (lower) rate of return than he/she would have on a pseudo share. PERCS Analysis - Page 6 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 IRR 25 30 35 40 45 50 55 Terminal stock price PERCS vs. Common Stock Returns IRR's as function of terminal price Figure 1 The payoff on the pseudo shares, the common shares and the PERCS shares can be written as contingent claims on the value of pseudo shares as follows: Payoff at maturity Pseudo share PERCS share Common share if S*T < 40 S*T S*T S*T if S*T $ 40 S*T 40 S*T + (1/4)(S*T-40) A pseudo share is simply a share at date T. A PERCS share receives the equivalent of a pseudo share at maturity if the stock price ends up below the PERCS cap price of $40, but receives a payoff equal to $40 worth of stock if the pseudo share (and hence the common share) ends up worth more than $40. The PERCS Analysis - Page 7 tricky thing about the regular common stock is that its payoff is not like a simple common stock payoff: the common stock receives the payoff on one pseudo share plus the payoff on one long call option for every four shares of common stock (the one-to-four ratio being the number of PERCS per common share). The payoff at maturity on the PERCS shares is same as the payoff on a covered call write on one pseudo share: buying a pseudo share and selling a call option against the pseudo share. The cash flows prior to maturity show that the PERCS pays an excess dividend, XSDIV, relative to the pseudo share of PDIV - S*DIV, or .60 - .36 = .24. Therefore, assuming that the PERCS will only be redeemed at maturity, and assuming that all dividends will be paid on both the PERCS and the pseudo common (in fact, we will assume they are riskless), the PERCS valuation formula becomes: PERCSt = S*t + PV(XSDIV) - CALL(S*t,FS*,T-t,r,X,S*DIV) where PV(XSDIV) is the present value of the annuity of excess dividends defined above at the riskless rate, and CALL is the value of a constant-dividend yield adjusted Black-Scholes call value with the following parameters: S* t = Stock price = value of the pseudo shares X = Exercise price = PERCS cap price T = Time to maturity = time to maturity of PERCS r = risk free rate = risk free rate on bill maturing at the same time as the PERCS FS* =Volatility = standard deviation of the rate of return on the pseudo shares Dividend yield = dividend yield on the pseudo shares The next section applies the model to our example company. 2. Applying the PERCS model PERCS Analysis - Page 8 Our example company is offerring to exchange 20 million PERCS shares for 20 million common shares (one fifth of the outstanding stock). The current price of the common is $30 per share. It would seem that, if the PERCS are worth less than $30, the offer would not be fair to the shareholders who exchange their shares, and you would not expect to see many shares tender. Similarly, if the PERCS are worth more than $30, many shares would tender and the offer would not be fair to the non-tendering shareholders. But this logic assumes that the current share price would be the reigning share price if the firm did not offer the PERCS. It may be the case that information is transmitted to the market by the company's announcement of the PERCS issue. The dividend on the common is less than the PERCS; is the company issuing the PERCS in conjunction with a unexpected dividend decrease? If so, this could be considered bad news. If the common dividend is not being changed, then the PERCS issue represents a nominal increase in the total dividends being paid and this might be considered good news. The valuation of the PERCS and the question of its fairness is a function of S*, not the stock price before the offer. Therefore, the stock price to plug in the Black Scholes model is the value of a pseudo share, so an estimate of the impact of the signalling information (e.g., the change in total dividends) on S* should be taken into account. Because this is difficult to do, it is useful to examine the sensitivity of the call value to the assumed value of S*. Also, the volatility should be the volatility of the pseudo share and the dividend yield should the the dividend yield on the pseudo share. We consider these two parameters next. The volatility of a stock can be estimated using historical stock returns or by estimating the implied volatility of traded options on the stock. Historical volatilities are usually estimated using daily stock return data for recent 30-180 day period. For frequently-traded stocks, standard deviations based on daily PERCS Analysis - Page 9 returns data have good statistical properties. More recent data is preferred to more distant data to the extent that volatilities change over time. The assumption that is made in using historical volatility estimates to predict future volatiliyt is that the future volatility will be the same as the most recent volatility. The implied volatility of a traded option is the value of the volatility that, when plugged into the Black-Scholes model (with other parameters for S, X, r, T and dividends known), yields the market price of the option. As such, the implied volatility of a stock is a forward-looking definition of the volatility of the stock: it is the value of the volatility that the market believes will occur based on how they are pricing traded options. Using the implied volatility from a traded option assumes that the volatility for the maturity of the option you are trying to estimate will be the same as the volatility for the maturity of the traded option. The implied volatility also assumes that the model used to price the options is correct and that the market price of the stock and the market price of the option used are set in efficient markets at the same time. For most applications, some sensitivity to the vol...