I think the issue is the line:
$200,000 x 100cents/dollar= 20. 000,000cents
200 million is $200,000,000
Another (easier) way to do this is:
1) The current market cap is $71.35M,
2) if the Market cap is $200 M assuming no dilution, the share price must increase by a factor of 2.8
3) Current share price is 6.4c
4) Share prices at $200M is 17.9c (close to 20c)