Which statement about the relationship between IRR and the discount rate is true?

Which statement about the relationship between IRR and the discount rate is true?

• A. Higher discount rate always increases NPV.
• B. Lower discount rate always decreases NPV.
• C. NPV is unaffected by the discount rate when cash flows are positive.
• D. If IRR equals the discount rate, NPV equals zero.

Answer: (D)

IRR is the discount rate that makes NPV zero. That means the present value of all cash inflows equals the initial investment when you use the IRR as the discount rate. So, if you set the discount rate equal to the project’s IRR, the sum of discounted inflows minus the outlay is exactly zero, by definition. As for the other statements, a higher discount rate reduces the present value of future positive cash flows, so NPV does not typically increase with a higher rate. A lower discount rate generally increases NPV, not decreases. And NPV depends on the discount rate even when cash flows are positive—the rate changes how much future cash is worth today, so NPV changes with r. The defining property of IRR is precisely that NPV becomes zero at that rate.

IRR is the discount rate that makes NPV zero. That means the present value of all cash inflows equals the initial investment when you use the IRR as the discount rate. So, if you set the discount rate equal to the project’s IRR, the sum of discounted inflows minus the outlay is exactly zero, by definition.

As for the other statements, a higher discount rate reduces the present value of future positive cash flows, so NPV does not typically increase with a higher rate. A lower discount rate generally increases NPV, not decreases. And NPV depends on the discount rate even when cash flows are positive—the rate changes how much future cash is worth today, so NPV changes with r. The defining property of IRR is precisely that NPV becomes zero at that rate.