What does the discount rate (r) represent?

The discount rate represents the rate used to discount future sums to their present value. This is a fundamental concept in finance and valuation, as it allows investors and analysts to determine how much a future cash flow or series of cash flows is worth today.

When future cash flows are projected, they need to be evaluated in today's terms to understand their current value. The discount rate accounts for factors such as the time value of money, where money available today is worth more than the same amount in the future because of its potential earning capacity. By applying the discount rate, one can effectively assess the risk and opportunity cost of investing capital over time.

This concept is crucial in various financial analyses, including net present value (NPV) calculations, investment appraisals, and the valuation of financial instruments. Understanding the relationship between future cash flows and their present value aids in making informed financial decisions.