Which statement describes the effect of changing the discount rate on present value?

• A. As the discount rate increases, present value decreases
• B. As the discount rate increases, present value increases
• C. Present value is independent of discount rate
• D. Present value becomes negative with a positive discount rate

Answer: (A)

Higher discount rates reduce the present value of future cash flows. This happens because the value of a future amount is divided by (1 + r)^t in the present-value formula, so as the discount rate r goes up, the divisor gets larger and the present value shrinks. For example, $100 received in one year is worth about $95.24 today at a 5% rate, but only about $90.91 today at a 10% rate. The discount rate reflects the opportunity cost or required return; a higher rate means waiting for money is less valuable because you could earn more elsewhere, so future dollars are worth less in today’s terms.

Therefore, as the discount rate increases, present value decreases. Present value is not independent of the discount rate, and a positive discount rate does not automatically make present value negative for a positive future amount.