Your $100 at t=0 will be worth $55.2 thirty years hence.
Something that costs $100 today will cost 100*(1.02)^30 = $181 30 years later. So your original $100 can purchase only 100/181 worth of goods that it could purchase at t=0. So its value after 30 years is $100 * 100/181 = $55 in t=0 dollars. So it will have lost 45% of its value in 30 years.
You could use
B = ((a + a*r + r*s)*(1 + r)^n - a)/r
For example, the OP's calculation with s = 1000 and a = 100
year 3: B = s*1.1^3 + a*1.1^3 + a*1.1^2 + a*1.1 + a = 1795.10
Using the formula arrives at the same result
n = 3
r = 0.10
B = ((a + a*r + r*s)*(1 + r)^n - a)/r = 1795.10
The OP requires the sum of the compounding amounts, plus s ...
So, their book value is $648,323,000 (correct?).
If Netflix were to (hypothetically) go bankrupt immediately (considering that the numbers would be up to date and not from Dec. 31) and their assets sold & any liabilities paid, the shareholders would get only $11.711/share back.
Not necessarily. You are conflating book value with liquidation ...
What you're looking for is the intrinsinc value of a business, which would be, strictly from a money point of view, if you buy the stock right now, how much cash would you expect back in the future?
If you expect a company to run indefinitely, which we have no reason to expect Netflix won't given its current success, you can run a discounted cash flow (DCF) ...