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

Workflow 5 steps, run in order in one session. Every step was executed against the engine and the output below is what it produced.

Step 1

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

No output - this step sets something up for the next one.

Step 2

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

Output

266.08191502177397

Step 3

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

Output

0.05604463645158886

Step 4

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

Output

-44998.608919690494

Step 5

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

Output

-Graphics-

Functions used