IRR calculation

IRR - internal rate of return is the discount rate that brings down the net present value of an investment to zero. This turns out to be the break-even point at which the investment yield neither gains nor losses. To find this investment rate you would have to enter a series of cash flows and the guess rate ( a default guess rate of 10% is employed when finding the IRR). The reason you would require this guess is due to the lack of a IRR formula to find internal rate of return. This leads to hiring some complicated numerical methods that perform iterative calculations starting with a guess rate of 10%. When such repeated calculation converge then we have found one of the IRR values but it is not for certain that such as a value will be found. In such cases you would have to enter a different value for the guess rate so to enable the IRR calculator to redo such iterative calcualtions. The online IRR calculator will accept a series of cash flows and the guess rate of 10% and process such information using the IRR formula and return a detailed workout that was performed internally to calculate the IRR.

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#### Data ouput

f(r) = -100(1+r)^0 +50(1+r)^-1 +40(1+r)^-2 +30(1+r)^-3 +10(1+r)^-4
f'(r) = -50(1+r)^-2 -80(1+r)^-3 -90(1+r)^-4 -40(1+r)^-5

r0 = 0.1
f(r0) = 7.882
f'(r0) = -187.7356
r1 = 0.1 - 7.882/-187.7356 = 0.1419844551017
Error Bound = 0.1419844551017 - 0.1 = 0.041984 > 0.000001

r1 = 0.1419844551017
f(r1) = 0.4788
f'(r1) = -165.5692
r2 = 0.1419844551017 - 0.4788/-165.5692 = 0.14487617020274
Error Bound = 0.14487617020274 - 0.1419844551017 = 0.002892 > 0.000001

r2 = 0.14487617020274
f(r2) = 0.002
f'(r2) = -164.1783
r3 = 0.14487617020274 - 0.002/-164.1783 = 0.14488844256652
Error Bound = 0.14488844256652 - 0.14487617020274 = 1.2E-5 > 0.000001

r3 = 0.14488844256652
f(r3) = 0
f'(r3) = -164.1725
r4 = 0.14488844256652 - 0/-164.1725 = 0.14488844278586
Error Bound = 0.14488844278586 - 0.14488844256652 = 0 < 0.000001
IRR = r4 = 0.14488844278586 or 14.49%