Again consider the widget investment problem in Section 17.1. Verify that with $S=\$ 50, K=\$ 30, r=0.04879, \sigma=0,$ and $\delta=0.009569,$ the perpetual call price is $\$ 30.597$ and exercise optimally occurs when the present value of cash flows is $\$ 152.957 .$ What happens to the value of the project and the investment trigger when you change $S ?$ Why? What happens to the value of the project and the investment trigger when you increase volatility? Why?