The PV of an Annuity of 10,000, N 10, R 9.79%, is exactly 62,004. (Close enough?)
But the NPV in this case is 5,101. The PV of an Annuity of 10,000, N 10, R 8% is 67,101.
And yes, you still have an IRR, even if NPV is negative. Check your definition of IRR again.
Reading notes from here
http://finance.thinkanddone.com/
Using this IRR calculator
http://finance.thinkanddone.com/tadIRR.e...
IRR = 9.79%
To perform the IRR calculations manually using this tool
http://finance.thinkanddone.com/online-i...
f(r) = -62000(1+r)^0 +10000(1+r)^-1 +10000(1+r)^-2 +10000(1+r)^-3 +10000(1+r)^-4 +10000(1+r)^-5 +10000(1+r)^-6 +10000(1+r)^-7 +10000(1+r)^-8 +10000(1+r)^-9 +10000(1+r)^-10
f'(r) = -10000(1+r)^-2 -20000(1+r)^-3 -30000(1+r)^-4 -40000(1+r)^-5 -50000(1+r)^-6 -60000(1+r)^-7 -70000(1+r)^-8 -80000(1+r)^-9 -90000(1+r)^-10 -100000(1+r)^-11
r0 = 0.1
f(r0) = -554.3289
f'(r0) = -263962.8111
r1 = 0.1 - -554.3289/-263962.8111 = 0.097899973330841
Error Bound = 0.097899973330841 - 0.1 = 0.0021 > 0.000001
r1 = 0.097899973330841
f(r1) = 3.9357
f'(r1) = -267722.2164
r2 = 0.097899973330841 - 3.9357/-267722.2164 = 0.097914674139569
Error Bound = 0.097914674139569 - 0.097899973330841 = 1.5E-5 > 0.000001
r2 = 0.097914674139569
f(r2) = 0.0002
f'(r2) = -267695.6664
r3 = 0.097914674139569 - 0.0002/-267695.6664 = 0.097914674868595
Error Bound = 0.097914674868595 - 0.097914674139569 = 0 < 0.000001
IRR = r3 = 0.097914674868595 or
IRR = 9.79%
To find the IRR in Excel using tadXL add-in found here
http://finance.thinkanddone.com/32_bit_t...
=tadIRR( { -62000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000, 10000 } )
IRR = 9.79%
Net investment 62,000
Useful life 10 years
Annual cash inflow 28,000
Annual cash outflow 18,000
Required rate of return 8%
I have an NPV of approx -129100
I can't find the IRR, NPV does not become 0 if I choose a 10% rate.
