“The best reason to start an organization is to make meaning; to create a product or service to make the world a better place.” 
-Guy Kawasaki, venture capitalist, CEO of Garage Technology Ventures
 
Understanding a Basic Venture Capital Formula to acquire stake in a company
The table below illustrates a simple example of how a Venture Capital/PE firm will value the firm, arrive at the current and future stock price, and deduce the % of shares to be acquired in order to meet the expectations of the investment.
It is based on expected rate or return (in this case 50%), number of years (5 yrs), investment amount ($3.5 mn), expected PE ratio of the firm in 5 years (based on comparables), expected cash flows of the firm  in 5 years.
 

Required IRR (%) — a	50.00%
Investment ($) — b	35,00,000
Term (Yrs.) — c	5
Year 5 revenue ($) — d	25,00,000
PE ratio (Year 5) — e	15
# of shares outstanding before investment — f	10,00,000
Terminal value of the firm ($) — (d * e) — g	3,75,00,000
Required future value of  investment ($) — Expected Future Value of Investment — h	2,65,78,125
Final ownership required= h/g=i	70.88%

# of shares to be acquired = f/(1-i)*i=j	24,33,476
New share price ($)=b/j=m	1.44
Post-money value of the firm @ t0 ($)=b/i=k	49,38,272
Pre-money value of the firm ($)=k-b	14,38,272
Share value at exit, for given discount rate=Expected Future Value of Current Share Price	10.92
Firm value at the end of each round = Post Money Valuation	49,38,272
RoI	659.38%

The above basic calculation is done assuming only one round of funding & no further dilution (i.e. no second/third round.. in which case the % of stake would obviously rise).
More on VCPE here