Which metric is more sensitive to changes in the discount rate: NPV or profitability index?

• A. NPV
• B. Profitability index
• C. Payback period
• D. Internal rate of return

Answer: (A)

The key idea is that discount rate sensitivity shows up directly in the value you calculate from future cash flows. NPV sums the present value of every future cash inflow minus the initial outlay, and each inflow is divided by (1 + r)^t. A small change in the discount rate changes every term in that sum, and the effect accumulates across all periods—especially for longer projects—so NPV can swing a lot with r.

Profitability index takes the same present value of future inflows but divides by the initial investment, effectively normalizing by the size of the project. That normalization dampens how much the metric changes when r changes, because the numerator (PV of inflows) shifts with r just like NPV does, but the denominator (the initial investment) stays fixed. So the absolute impact of a rate change on the profitability index is smaller than on NPV.

In short, changing the discount rate has a direct, compounded effect on NPV across all future cash flows, and the profitability index, being a per-unit-of-investment ratio, shares that effect but scaled down, making NPV more sensitive.