Avon Products
...l be 0.7 of 18 million PERCS = 12.6 million new shares of equity. For a total of 53.7 million + 12.6 million = 66.3 million. The total value of the equity is $45 * 66.3 million = $2,983.5 million. Had the company remained all common stock with 71.7 million shares, the shares would be worth $2,983.5/71.7 = $41.61. a) ƒÞ The pay off structure of the PERCS in comparison to the others is the following Quarter Cash Flow to PERCS holder Cash Flow to Common Holder Cash Flow to ¡§Pseudo Common¡¨ 0 -24.125 -24.125 -24.125 1 0.5 0.25 0.3125 2 0.5 0.25 0.3125 3¡K¡K10 0.5 0.25 0.3125 11 0.5 0.25 0.3125 12 0.5 + Redemption Value 0.25 + Stock Value 0.3125 + Pseudo Stock Value b) ƒÞ The cash flows prior to maturity show that the PERCS pays an excess dividend (XSDIV) relative to the pseudo share of PERCSDIV-S*DIV, or $2.00 - $1.25 = $0.75 per or $0.3125 per quarter. This extra payment can be seen as the option premium, the company pays him for writing the option and giving up the upside potential. ƒÞ The PERCS share receives the equivalent of a pseudo share at maturity if the stock price (S) ends up below the PERCS cap price of $31.50, but receives a payoff equal to $31.50 worth of stock if the pseudo share (and hence the common share) ends up worth more than $31.50. ƒÞ WE CAN SHOW VIA GRAPH THE PAYOFF STRUCTURE OF PERCS VS: COMMON STOCK RETURNS o c) ƒÞ 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 assume they are risk less), the PERCS valuation formula becomes: PERCSt = S*t + PV(XSDIV) ¡V CALL Splitting up the PERCS-formula d) ƒÞ S*t: Sensitivity analysis for the value of the pseudo stock S*t Due to potential share price changes caused by signalling effects coming up with the announcement of the PERCS issue the valuation of the PERCS and the question of its fairness is a function of S* and not the stock price before the offer. Because it¡¦s too difficult to take such effects into account, it is useful to examine the sensitivity of the call value to the assumed value of S*. e) ƒÞ PV(XSDIV): The present value (at the riskless rate) of the extra dividend paid to PERCS relative to pseudo shares is 0.3125PVFA8.2%/4=2.05%,12 = $ 3.29 CALCULATION of PV IN SLIDE OR BACKUP? PVFA stands for ¡§Present Value Factor of an Annuity¡¨. The effective quarterly rate is approximated by dividing the annual rate by four. This is technically incorrect, but this is already an approximation because the dividend streams are not truly riskless. The value of these dividends is not that sensitive to these errors. f) ƒÞ Valuation of the CALL: Due to the fact that the PERCS structure is comparable to a ¡§Short Call¡¨ you use the Black Scholes Formula to evaluate the Option. ƒÞ The elements to plug in the Black Scholes formula are the following ƒÞ S*t = Stock price = value of the pseudo shares (scenario) ƒÞ X = Exercise Price = PERCS cap price of $31.50 ƒÞ T = Time to maturity = time to maturity of PERCS (3 years) ƒÞ r = risk free rate = risk free with same T than PERCS, (8.2%) ƒÞ £mS* = Volatility = standard deviation of the rate of return on the pseudo shares. Due to the fact that there is no market data to evaluate the volatility of the Pseudo Shares S*, we calculate the sensitivity of different volatility scenarios around the historical volatility of Avon Stock which is 31.3% per year over six months and 35.5% per year over the previous three months. Another indication is delivered by the implied volatility from the traded options from Exhibit 6. These implied volatilities are on average 33.5% (Vorlage!) ƒÞ Dividend yield = dividend yield on the pseudo shares We assume a steady dividend stream when pricing the option and calculate the dividend yield with $1.25/S*. Therefore the dividend yield will depend on the value of S* you use. ...