The provided references do not pertain to the question at hand, which is about calculating the option value using the Black-Scholes formula. The calculation for a European call option with the given parameters would be as follows:

Let's denote: - S = Current stock price = $20 - X = Strike price = $21 - T = Time to expiration in years = 50/365 years (approximately 0.1369 years) - r = Risk-free interest rate = 5% = 0.05 - σ = Volatility = 50% = 0.50 - δ = Dividend yield = 0% (no dividends are paid)

The Black-Scholes formula for the call option value (C) is: C = S * N(d1) - X * e^(-r(T-t)) + Ke^(-r(T-t)) * N(d2)

Where: - d1 = (ln(S/X) + (r + 0.5σ^2T) / (σ * sqrt(T)) - d2 = d1 - σ * sqrt(T)

And N(d1) and N(d2) are the standard normal cumulative distribution function evaluated at d1 and d2, respectively.

To calculate the exact option value, one would need to calculate N(d1) and N(d2) using a standard normal distribution table or software. This calculation does not involve the provided references since it's a mathematical computation rather than an accounting principle.