A New York firm is offering a new financial instrument called a happy call. It has a payoff function at time T equal to max(0.5ST , ST K), where ST is the price of a stock at time T and K is a fixed strike price. You always get something with a happy call. Suppose that the risk free interest is 10% per year and the volatility of the stock price is 20% per annum. The current stock price is $30 per share. Let K = $25. How to determine the present value of the happy call using the Black-Scholes formula.