AGYO Exercise Price 20 cents, page-59

G'day machz.

Good question!

Here's some food for thought:

S = number of options to sell
C = number of options to convert
O = number of options held
P = price of options

So:

S x P = C x 0.20 [proceeds from options sale = cost to convert remaining options; 0.20 = 20c] (1)
O = S + C [number to sell plus remaining = total number held]
i.e. C = O - S (2)
Therefore [substitute (2) into (1)]
S x P = (O - S) x 0.2
S x P = 0.2O - 0.2S
(S x P) + 0.2S = 0.2O
S(P + 0.2) = 0.2O
Therefore:
S = 0.2O / (P + 0.2)

Test (with your example; O = 50000, P = 0.2):
S = 0.2(50000) / (0.2 + 0.2)
S = 10000 / 0.4
S = 25000

Test another; O = 100000, P = 0.1:
S = 0.2(100000) / (0.1 + 0.2)
S = 20000 / 0.3
S = 66667

Check:
Sell 66667 @ 10c = $6667 revenue
Remaining options: 33333
Covert 33333 options @ 20c each = $6667
[seems legit!]

S = 0.2O / (P + 0.2) !!

Where:
S = number of options to sell
O = number of options held
P = price of options


All that uni maths from so long ago seems to have paid off!

Cheers