Price a call in a two-state tree

Can you value a call without forecasting how often the stock will rise?

In a one-step arbitrage-free tree, use a pricing weight that makes the expected stock value grow at the risk-free rate.

q = (S × R − Sd) ÷ (Su − Sd); call = (q × up payoff + (1 − q) × down payoff) ÷ R

(105 − 80) ÷ (120 − 80) = 0.625. Payoffs are $20 and $0. Discount $12.50 by 1.05 for about $11.90.

Stock is $100, up is $120, down is $80, strike is $100 and R = 1.05. q is 0.625. Call value is $12.50 ÷ 1.05 ≈ $11.90.

(105 − 80) ÷ (120 − 80) = 0.625. Payoffs are $20 and $0. Discount $12.50 by 1.05 for about $11.90.

With the same tree and zero interest, what is the call value?