Back in 2010 I posted an explanation of how to compute net present values and internal rates of return in Mathematica. It worked but it was a little verbose. Considering that Mathematica can do things like optical character recognition with a single command, it seemed a shame that it couldn’t do these basic financial functions.

Wolfram has fixed this, and computing IRR and NPV in Mathematica is now much more civilized.

Using the same sample cash-flow as last time (but reformatting the date to list-format, as Mathematica’s Cashflow[] function demands for some reason),

testFlow = {{{2001, 1, 1}, -1}, {{2002, 1, 1}, .3}, {{2005, 1, 1}, .4}, {{2005, 1, 10}, .5}};

TimeValue[Cashflow[testFlow], .05, {2001, 1, 1}]

returns an NPV of .0256519, just as it should. And

FindRoot[TimeValue[Cashflow[testFlow], r, {2001, 1, 1}] == 0, {r, .05}]

gives us the IRR, in this case .0584316.

Mathematica clearly performs a compilation the first time my NPV is run, and while the native NPV and IRR computations are quicker than mine the first time one of them is run by about a factor of 50, the second time one of them is run (whether on the same data or not) my code is quicker than theirs by about 30%. Mine is also ecumenical about date formats, but in practice I find myself using their code anyway, as it is so concise.