I am having some trouble wrapping my head around the binomial option valuation using no arbitrage approach… The formula for a call option is c = hS + PV(-hS^{- }+ c^{-}). I understand how the formula was arrived but have problem interpreting it. The book says this is long on stock and partly financed. If borrowing is considered positive cash flow then isn’t going long on a stock which is an investment be negative cash flow? In this case both are positive. What am I missing here?

The formula gives the cost (cash outflow) of a call option. So c is positive and _h_S is positive: both cash outflows.

Not necessarily. For example, if S_{0} = $20, S^{+} = $25, S^{−} = $18, and X = $22, then h = 0.4286, c^{−} = $0, and −_h_S^{−} + c^{−} = −$7.71, which is, of course, negative. And a negative outflow is, naturally, an inflow.

Skip the formula and use the tree instead. The tree is essentially the formula in various steps. The tree, using the risk neutral probability calculated thought the risk_free rate and the up/down magnitudes.

Another reason why I feel the tree is easier to use, if you land on a 2 year or 3 year binomial option calculations, the tree method is far simpler.

With that said, each time I run into one of these practice questions, I solve it both ways just to get some practice.