The relationship between present values and interest rates can be somewhat counterintuitive. When we consider the impact of positive interest rates on present values, the correct understanding is:
b) Assuming positive interest rates, the present value will decrease as the interest rate increases.
To explain this, we need to look at the concept of present value itself. Present value (PV) represents the current worth of a sum of money that you will receive in the future, discounted back to the present using a specific interest rate. This means that the higher the interest rate, the more we discount future cash flows to arrive at their present value.
Imagine you expect to receive $100 a year from now. If the interest rate is 5%, the present value of that $100 would be calculated as:
PV = Future Value / (1 + r)^n = $100 / (1 + 0.05)^1 = $95.24
However, if the interest rate rises to 10%, the present value of that same $100 would be:
PV = $100 / (1 + 0.10)^1 = $90.91
As we can see, with a higher interest rate, the present value of future money decreases. In summary, as interest rates increase, the present value of future cash flows decreases due to the increased discounting effect. This is an important concept in finance and investing, emphasizing how changes in interest rates can significantly impact the valuation of future cash flows.