I amcomputingtheIRRfor two time series of cash flows. For the
first 24 months, the cash flows are identical. After that, the longer
one continues with only large positive values for 18 more years.
Strangely, I am getting the sameIRRfor both cash flows. This does
not seem intuitively correct, since the NPV of the two cash flows is
quite different. Can anyone shed some light on this? Thanks.
Hello:
I am not sure you got an answer to your question, and it might be too
late to do you any good. But reason for your results are that process
of taking present values and computing rates of return is not linear.
If the discount rate is zero then the process does produce linear
results. If you add a $1 to a cash flow, even 500 period from now the
present value will go up by $1. But if the discount is positive the
value will go up by less than a $1. How much less depends on the
length of time and the discount rate.
Assume three projects. All projects in this example cost $500. Project
A returns $100 per period for 24 periods. Project B returns $100 per
period for 241 periods. Project C returns $100 per period forever.
Time / Cash flow
0 1-24 25-241 242-Forever
A ($500.00) $100.00 $0.00 $0.00
B ($500.00) $100.00 $100.00 $0.00
C ($500.00) $100.00 $100.00 $100.00
Rate per period 10.00% Incremental
A NPV $398.47
B NPV $490.77 $92.30
C NPV $500.00 $9.23
NPV@IRR IRR Incremental
A ($0.00) 19.73%
B ($0.00) 19.96% 0.22%
C $0.00 20.00% 0.04%
The NPV's are computed at 10% per period. Notice that extra cash flows
for Project B are worth $92.30 more today. That means all of the cash
flows from period 25 through 241 add only $92.40 to the value, while
the first 24 add $398.47 to value. Now look at Project C all the cash
flow beyond period 241 add only $9.23. If you used a zero discount
rate they would be infinitely valuable.
Now how much incremental value is added depends upon the discount
rate. The higher the discount rate the smaller the addition. You can
see that at a discount rate of about 20% the values of all three are
the same, zero. If you actually use 20% in the NPV calculation you
will see that the Project B is worth about $5 more and project C worth
about a $1 more than Project A.
So the results you got were to be expected. I doubt that they were
actually exactly the same. Format the result for a few more decimal
places and you will see that IRR for B and C are slightly higher than
A. If you use only 2 decimal places they will be the same.
The lesson is that future cash flow fall in value quickly as the time
period lengthens and the discount rate increases.
Pieter Vandenberg
