Dota 2 - Midas vs Tome (7.05 Item Analysis)

Tome of Knowledge gives 500 exp once per 10 minutes (50 exp / min)

but limited to one hero per team, at the cost of 150 gold per use.

10 minutes >> 500 exp (3.33 exp / gold)

20 minutes >> 635 exp (4.23 exp / gold)
30 minutes >> 770 exp (5.13 exp / gold)
40 minutes >> 905 exp (6.03 exp / gold)

Hand of Midas gives 1548 exp in 10 minutes (154.8 exp / min)

On average, using on large neutral creep or range creep or siege creep.

Requires a capital of 2050 gold (around 7 minutes of farming)

Midas break even at approx 16 minutes of constant use (cost around 23 minutes in total), below is the time after acquired Midas.

10 minutes mark (0.75 exp / gold)
15.5 minutes mark (1.17 exp / gold) break even
20 minutes mark (1.51 exp / gold)
44 minutes mark (3.33 exp / gold)

SUMMARY:

If your hero need exp, always spend gold on Tome of Knowledge.
If your hero need exp & gold in later game, Hand of Midas is a good investment.