On May 5, 12:42*am, "joeu2004" wrote:
"W" wrote:
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[1] AFAIK, IRR is only defined as the rate that causes the NPV to be zero..
Someone else in this forum claims that there are multiple definitions of
IRRs. *IMHO, he is misusing the term IRR per se. *The "other definitions"
are, in fact, different definitions of rate of return. *To paraphrase a
familiar syllogism: *"IRR is a rate of return, but not all rates of return
are an IRR".
Adding to my last reply, it wouldn't matter which of three underlying
IRR Equations we use, we will still come away with the same internal
rate of return
I will now show you IRR calculation for the cash flows of
-10000 3000 3000 3000 3000
using the three different IRR equations to find internal rate of
return with Newton Raphson method
Newton Raphson Method IRR Calculation with NPV equation = 0
http://finance.thinkanddone.com/find... _method.html
f(x) = -10000(1+i)^0 +3000(1+i)^-1 +3000(1+i)^-2 +3000(1+i)^-3
+3000(1+i)^-4
f'(x) = -3000(1+i)^-2 -6000(1+i)^-3 -9000(1+i)^-4 -12000(1+i)^-5
x0 = 0.1
f(x0) = -490.4037
f'(x0) = -20585.4046
x1 = 0.1 - -490.4037/-20585.4046 = 0.0761771182095
Error Bound = 0.0761771182095 - 0.1 = 0.023823 0.000001
x1 = 0.0761771182095
f(x1) = 21.5227
f'(x1) = -22427.1121
x2 = 0.0761771182095 - 21.5227/-22427.1121 = 0.0771367901805
Error Bound = 0.0771367901805 - 0.0761771182095 = 0.00096 0.000001
x2 = 0.0771367901805
f(x2) = 0.0376
f'(x2) = -22348.7961
x3 = 0.0771367901805 - 0.0376/-22348.7961 = 0.0771384729469
Error Bound = 0.0771384729469 - 0.0771367901805 = 2.0E-6 0.000001
x3 = 0.0771384729469
f(x3) = 0
f'(x3) = -22348.6591
x4 = 0.0771384729469 - 0/-22348.6591 = 0.0771384729521
Error Bound = 0.0771384729521 - 0.0771384729469 = 0 < 0.000001
IRR = x4 = 0.0771384729521 or 7.71%
Newton Raphson Method IRR Calculation with NFV equation = 0
http://finance.thinkanddone.com/find... _method.html
f(x) = -10000(1+i)^5 +3000(1+i)^4 +3000(1+i)^3 +3000(1+i)^2
+3000(1+i)^1
f'(x) = -50000(1+i)^4 +12000(1+i)^3 +9000(1+i)^2 +6000(1+i)^1
+3000(1+i)^0
x0 = 0.1
f(x0) = -789.8
f'(x0) = -36743
x1 = 0.1 - -789.8/-36743 = 0.0785047492039
Error Bound = 0.0785047492039 - 0.1 = 0.021495 0.000001
x1 = 0.0785047492039
f(x1) = -44.4448
f'(x1) = -32655.0869
x2 = 0.0785047492039 - -44.4448/-32655.0869 = 0.0771437131056
Error Bound = 0.0771437131056 - 0.0785047492039 = 0.001361 0.000001
x2 = 0.0771437131056
f(x2) = -0.1698
f'(x2) = -32405.7442
x3 = 0.0771437131056 - -0.1698/-32405.7442 = 0.0771384730295
Error Bound = 0.0771384730295 - 0.0771437131056 = 5.0E-6 0.000001
x3 = 0.0771384730295
f(x3) = -0
f'(x3) = -32404.7864
x4 = 0.0771384730295 - -0/-32404.7864 = 0.0771384729521
Error Bound = 0.0771384729521 - 0.0771384730295 = 0 < 0.000001
IRR = x4 = 0.0771384729521 or 7.71%
Newton Raphson Method IRR Calculation with profitability index
equation = 1
http://finance.thinkanddone.com/find...on_method.html
b(x) = +3000(1+i)^-1 +3000(1+i)^-2 +3000(1+i)^-3 +3000(1+i)^-4
c(x) = +10000(1+i)^0
b'(x) = -3000(1+i)^-2 -6000(1+i)^-3 -9000(1+i)^-4 -12000(1+i)^-5
c'(x) = 0(1+i)^-1
pi(x) = b(x)/|c(x)| - 1
pi'(x) = [c(x) b'(x) - b(x) * c'(x)] / c(x)2
x0 = 0.1
b(0.1) = 9509.59633905
c(0.1) = 10000
pi(0.1) = -0.0490403660952
b'(0.1) = -20585.4046234
c'(0.1) = 0
pi'(0.1) = -2.05854046234
x1 = 0.1 - -0.0490403660952/-2.05854046234 = 0.0761771182095
x1 = 0.0761771182095
b(0.0761771182095) = 10021.5226709
c(0.0761771182095) = 10000
pi(0.0761771182095) = 0.00215226708963
b'(0.0761771182095) = -22427.1121246
c'(0.0761771182095) = 0
pi'(0.0761771182095) = -2.24271121246
x2 = 0.0761771182095 - 0.00215226708963/-2.24271121246 =
0.0771367901805
x2 = 0.0771367901805
b(0.0771367901805) = 10000.0376078
c(0.0771367901805) = 10000
pi(0.0771367901805) = 3.76078036624E-6
b'(0.0771367901805) = -22348.7961359
c'(0.0771367901805) = 0
pi'(0.0771367901805) = -2.23487961359
x3 = 0.0771367901805 - 3.76078036624E-6/-2.23487961359 =
0.0771384729469
x3 = 0.0771384729469
b(0.0771384729469) = 10000.0000001
c(0.0771384729469) = 10000
pi(0.0771384729469) = 1.15274456647E-11
b'(0.0771384729469) = -22348.6591282
c'(0.0771384729469) = 0
pi'(0.0771384729469) = -2.23486591282
x4 = 0.0771384729469 - 1.15274456647E-11/-2.23486591282 =
0.0771384729521
x4 = 0.0771384729521
IRR = 7.71%
Annualized IRR = 7.71%