G,pter 32: Strudured Products 635 
Such discrepancies will be most notable when there is not a listed option that 
has terms near the terms of the PERCS's imbedded call. If there is such a listed 
option, then arbitrageurs should be able to use it and the common stock to bring the 
PERCS into line. However, if there is not any such listed option available, there may 
be opportunities for theoretical value traders. 
Models used for pricing call options, such as the Black-Scholes model, are dis­
cussed in Chapter 28 on mathematical applications. These models can be used to 
value the imbedded call in the PERCS as well. If the strategist determines the 
implied value of the imbedded call is out of line, he may be able to make a profitable 
trade. It is a fairly simple matter to determine the implied value of the imbedded call. 
The formula to be used is: 
Imbedded call implied value = Current stock price 
+ Present value of dividends - Current PERCS price 
The validity of this formula can be seen by referring again to Figure 32-7. The 
difference between the Final Value (that is, the profit of the covered write at expira­
tion) and the Issue Value or current value of the PERCS is the imbedded call price. 
That is, the difference between the curved line and the line at expiration is merely 
the present time value of the imbedded call. Since this formula is describing an out­
of-the-money situation, then the time value of the imbedded call is its entire price. 
It is also known that the Final Value line differs from the current stock price by the 
present value of all the additional dividends to be paid by the PERCS until maturity. 
Thus, the four variables are related by the simple formula given above. 
Example: XYZ has fallen to 32 after the PERCS was issued. The PERCS is current­
ly trading at 34 and, as in previous examples, the PERCS pays an additional $1.50 per 
year in dividends. If there are two years remaining until maturity of the PERCS, what 
is the value of the imbedded call option? 
First, calculate the present value of the additional dividends. One should calcu­
late the present value of each dividend. Since they are paid quarterly, there will be 
eight of them between now and maturity. 
Assume the short-term interest rate is 6%. Each additional quarterly dividend 
is $0.375 ($1.50 divided by 4). Thus, the present value of the dividend to be paid in 
three months is: 
pw = 0.375/(1 + .06)114 = $0.3696 
The present value of the dividend to be paid two years from now is: 
pw = 0.375/(1 + .06)2 = $0.338 
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