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Can you please explain about the variants of the Black scholes option pricing formulae. Specially the (Pa) and (Pe). Sometimes model answers are done with NPV of cashflow and investment value (in question MMC jun 2011). In question Furlion co (mar/jun 2016) NPV is given in current and after some time by saying ” project will justify the investment cost of $15m. But the NPV of expection is currently $0. Put model answer is done by taking investment value of $15m discounted for Pa and not discounted Pe.
How do we know what is Pa and what is Pe?Pa is the current value, and Pe is the exercise price.
In MMC the option is exercisable in 2 years time and is the option to spend £35M to then continue for 4 years.
So Pa is the PV of the flows after the exercise date, and Pe is the amount that would be paid to exercise.In Furlion, the logic is exactly the same. Since the current NPV is 0, the PV of the future flows after exercising must be equal to the PV of the amount paid to exercise (so as to end up with an NPV of 0). So this is Pa.
Pe is the amount paid to exercise.I got that Pe will be the exercise price. Which is $15m in Furlion but the Pa which spose to be the PV of the cashflow which is 0. But the model answer took $15m × 0.712= ……..
So my question is why does he take PV of exercise price rather taking Pa= 0?(NPV)
(In model answer Pa= $15m ×0712= $10.68)
Or we can take any of these?No – it is the NPV that is 0.
Since the outflow is 15M, then PV of the inflows must also be 15M.Pa is the PV of the inflows which is the PV of 15M.
Sir Im a little confused with calculating the value of Pa
initial invesment – present value of cash flows= NPV
so is 15 not equal to pv of cash flows? why are we discounting it again>?
Thanks
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