TST: Move NPV-IRR congruence check to tests

The internal rate of return (irr) is defined as the rate of return
required for the net present values of a series of cashflows to be
zero. i.e the lowest rate of return required for a project to break
even.

This is currently checked by refering to the example output from
the ``irr`` and ``npv`` function documentation. This commit adds a
test to confirm the identity holds.

numpy/lib/financial.py

@@ -715,8 +715,6 @@ def irr(values):
     >>> round(np.irr([-5, 10.5, 1, -8, 1]), 5)
     0.0886
 
-    (Compare with the Example given for numpy.lib.financial.npv)
-
     """
     # `np.roots` call is why this function does not support Decimal type.
     #
@@ -785,11 +783,6 @@ def npv(rate, values):
 
     Examples
     --------
-    >>> np.npv(0.281,[-100, 39, 59, 55, 20])
-    -0.0084785916384548798 # may vary
-
-    (Compare with the Example given for numpy.lib.financial.irr)
-
     Consider a potential project with an initial investment of $40 000 and
     projected cashflows of $5 000, $8 000, $12 000 and $30 000 at the end of
     each period discounted at a rate of 8% per period. To find the project's

numpy/lib/tests/test_financial.py

@@ -9,6 +9,12 @@
 
 
 class TestFinancial(object):
+    def test_npv_irr_congruence(self):
+        # IRR is defined as the rate required for the present value of a
+        # a series of cashflows to be zero i.e. NPV(IRR(x), x) = 0
+        cashflows = np.array([-40000, 5000, 8000, 12000, 30000])
+        assert_allclose(np.npv(np.irr(cashflows), cashflows), 0, atol=1e-10, rtol=0)
+
     def test_rate(self):
         assert_almost_equal(
             np.rate(10, 0, -3500, 10000),