Why Small IRR Changes Can Produce Large NPV Differences
Article Quant Q&A · Author: LenaH
Summary
The document presents a question about calculating present values for a long cash-flow stream at two nearby internal rates of return. The author discounts each periodic cash flow by the corresponding power of one plus the rate, sums the results, and compares both the absolute and percentage differences. The main issue is whether the large NPV gap reflects a coding mistake or ordinary sensitivity to the discount rate.
The cash flows are large, numerous, and uneven over time, but the document provides no calculation output or answer. It therefore does not establish that the code is wrong or explain the observed difference. A useful check would be to verify the discount periods, independently evaluate NPV at each rate, and examine how the NPV curve changes around the two rates. The example is a finance calculation rather than a trading strategy, and its implications depend on the timing and scale of the cash flows.
Key ideas
- Present value discounts each cash flow according to its period and the chosen rate.
- A small rate change can have a substantial effect when cash flows are large or extend across many periods.
- The example compares two nearby rates but gives no computed present values or definitive diagnosis.
- Checking the discount exponents and independently evaluating NPV can help distinguish sensitivity from a coding error.
Tags
Full text
# Small difference in IRR, big difference in NPV?
# Small difference in IRR, big difference in NPV?
I calculated the following in Matlab 2019a, see code below. I was surprised about the big difference in present values (DiffPV, DiffPVpercentage) for only a small difference (DiffIRR, DiffIRRpercentage) in discount rates. Is there a coding error somewhere? Or is it maybe just the normal effect of discounting? How could I check for that? As it does not occur for other cashflow data I thought it was a coding/programming problem, but I am not sure how I can check.
```
clc
clear
close all
CF = 1.0e+12 * [-1.767330098188526...
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%% Test
IRR1 = 0.034366083131917;
IRR2 = 0.034364293602634;
DiffIRR = IRR1-IRR2
DiffIRRpercentage = (IRR1-IRR2)/IRR2
% PV1
for index = 1:length(CF)
CFdiscounted1(index) = CF(index)/((1+IRR1)^(index-1));
end
PV1 = sum(CFdiscounted1)
% PV2
for index = 1:length(CF)
CFdiscounted2(index) = CF(index)/((1+IRR2)^(index-1));
end
PV2 = sum(CFdiscounted2)
DiffPV = PV1-PV2
DiffPVpercentage = (PV1-PV2)/PV2
```Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.