What would an increase in discount rate do to an NPV?

Reduce PV of cash flow and therefore the NPV

capital structure.
Discount rate is the weighted average cost of capital or in other words opportunity cost of capital.
We use this discount rate to discount the future cash flow.
Now this discount rate is related to many factors such as beta (measurement of risk), risk free rate, market return and capital structure.
Further Explanation: Debt is a cheaper source of finance and on other hand equity is an expensive source of finance.
By introducing more debt the WACC can be lowered.
However high gearing can result the shareholder to ask for higher return.
So the best capital structure is the one which bring the WACC to the minimum.

Lower the NPV due to decrease in Net cash after discounting.

It would lower the NPV

Increase in discount rate increase the annuity factor thus decreased the present value of cash flows and NPV.