From the left of the box containing the formulae:

Not all items adhere to these formulas. First and foremost, these few formulas aren't enough to truly gauge the exact differences between items. The price of a magic item may be modified based on its actual worth. The formulas only provide a starting point. The pricing of scrolls assumes that, whenever possible, a wizard or cleric created it. Potions and wands follow the formulas exactly. Staves follow the formulas closely, and other items require at least some judgment calls.

So... basically, things don't necessarily follow the formulae. I suspect that this is a just a case of limited utility; for example, an item capable of performing same-duration, same-level Protection From Energy with use activation is significantly more useful for the same nominal price by the formulae as a Lantern of Revealing in the vast majority of cases (energy-using foes being generally more common than invisible foes. ProtEnergy would also let you avoid friendly fire incidents, and doesn't have the downside of revealing your own invisible rogue like the lantern does).

Disclaimer: I will look only at what the rules (Pathfinder, mostly) say about pricing this item.
For an approach that takes the item's actual power into account, see KRyan's answer.

It's severely underpriced

The custom item creation rules for both D&D 3.5 and Pathfinder state that the item pricing tables are fallback solutions to be used when there is no precedent for pricing in the existing magic items. From the PFSRD, emphasis mine:

Many factors must be considered when determining the price of new magic items. The easiest way to come up with a price is to compare the new item to an item that is already priced, using that price as a guide. Otherwise, use the guidelines summarized on Table: Estimating Magic Item Gold Piece Values.

The correct way to price an item is by comparing its abilities to similar items (see Magic Item Gold Piece Values), and only if there are no similar items should you use the pricing formulas to determine an approximate price for the item. If you discover a loophole that allows an item to have an ability for a much lower price than is given for a comparable item, the GM should require using the price of the item, as that is the standard cost for such an effect. Most of these loopholes stem from trying to get unlimited uses per day of a spell effect from the "command word" or "use-activated or continuous" lines of Table: Estimating Magic Item Gold Piece Values.

The first paragraph is present also on the 3.5 SRD, but the second paragraph is PF only.

Looking at the item you posted, it is comparable to the following items (using PF now). Note that at will spells with a decent duration and no action cost are effectively continuous.

• Bracers of Armor +4 (16000 gp)
• Ring of Force Shield, but at +4, and without occupying a hand when in use.
  I'd price it at least at 32500 gp (500 gp overhead, then standard quadratic progresssion).
• An Intelligent Magic Item with
  • High stats (18500 gp, progression continued beyond table for Wis)
  • 4 skills, each with 5 ranks (10000 gp)
  • A 2nd level spell 3/day (7200 gp)
  • 120 ft. senses and darkvision and telepathy (2500 gp)
  • 2 more 1st level spells at will that can't be reproduced as easily as mage armor or shield. These are not covered by the rules.
    Using the price for 3/day (1200 gp) and using the estimation table backwards to turn 3/day into at will/continuous yields 2000 gp each. Increasing magic missile to CL 9 makes that one 18000 gp.

Shield and Armor Bonuses are different, and they would normally take up an item slot each, which means we multiply the lower cost by 1.5 according to the stacking rules for multiple different abilities. The intelligent item cost (42200 gp) is simply added on top.

The total price for this item would then be:

32500 + (1.5 * 16000) + 58200 = 114700 gp

Beyond mere gold prices: Personality and Ego

It is noteworthy that this intelligent item seems to have no alignment, which is not covered by Pathfinder rules. In any case, an intelligent item of this power has an Ego score of 24 (6 base price, 10 abilities, 4 skills, 1 telepathy, 3 spells).

Similarly, any item with an Ego score of 20 or higher always considers itself superior to any character, and a personality conflict results if the possessor does not always agree with the item.

which means it will never be

[a] simple hat holds a watchful spirit, dedicated to watching over and protecting its owner [which] will spontaneously cast its spells to aid him or her.

Overpowering the item's personality requires a DC 24 will save, lest the wearer of the item is dominated by it.