Is this price fair: present value and the break-even rate

presentValue[cash_, r_, years_] := Sum[cash/(1 + r)^t, {t, 1, years}]

npv = N[presentValue[1200, 0.05, 10] - 9000]

266.08191502177397

breakEvenRate = r /. FindRoot[presentValue[1200, r, 10] == 9000, {r, 0.05}]

0.05604463645158886

N[D[presentValue[1200, r, 10], r] /. r -> 0.05]

-44998.608919690494

Plot[presentValue[1200, r, 10] - 9000, {r, 0.01, 0.12}]

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