How many Sorcery Points should this cost? Lots. At least 5, since this metamagic is better than Careful Spell, Empowered Spell and Heightened Spell combined. I'm sure you can see where I'm going with this - it's too powerful to put a realistic cost on it.
Your new metamagic option does 3 things. The first is pretty simple - it multiples damage by 1.25, or 1.5 if it's an AoE spell. I'm going to look at Fireball (a pretty classic damage spell) as a standard example.
A Fireball does 8d6 damage, averaging 28 damage. An Empowered Fireball, assuming a Charisma of 20, does 8d6 with the option to reroll up to 5 dice, for an average of 31.75 damage. A Sharpened Fireball does 8d6 * 1.5 damage, for an average of 42 damage.
At this point, you might be thinking "But Fireball does 8d6 damage, where the entry in the Spell Damage table for a 3rd-level spell is only 6d6!" Unfortunately, the advice in the Spell Damage table bears little or no resemblance to the spells that were actually published.
Note that this is also the case for single-target spells. Disintegrate (which uses a saving throw, not an attack roll) deals 10d6 + 40 (average 75), Empowered Disintegrate deals 10d6 with up to 5 rerolls + 40 (average 78.75), and Sharpened Disintegrate deals (10d6 + 40) * 1.25 (average 93.75).
At any rate, hopefully you can see how Sharpened Spell is considerably more powerful than Empowered Spell.
Moving on, the second thing Sharpened Spell does is change the target making a saving throw into the caster making an attack roll. Ostensibly, this is a loss in damage, since most (though not all) spells that use saving throws deal half damage on a successful save. However, it is far easier to make an attack roll hit than it is to make an enemy fail their saving throw.
Firstly, it's a trivial matter to give yourself advantage on an attack roll; it's an extremely non-trivial matter to give an enemy disadvantage on a saving throw. For example, you have inspiration, True Strike, the Help action, the Hide action, The Wild Magic Sorcerer's Tides of Chaos, and heaps of other things to give yourself advantage on a roll. To give disadvantage, you have Heightened Spell, or Contagion. There's not many, and they require significantly more expensive resources than the advantage options.
Secondly, most powerful monsters (the kind that would be worth sharpening a spell for) have Legendary Resistance, which makes it impossible to make them fail their saving throws, since they can just say they didn't. You can make them burn through their uses of this feature, but if they're smart they'll only use it on your best spells.
Finally, attacks are (by design) easier to hit. Everyone uses attacks, and some characters use them exclusively, so monsters can't be impossible to hit without making some players feel useless. On the other hand, not everyone uses saving throws, and everyone can still function without them. It's difficult to prove this mathematically, but anyone can quickly observe that there are extremely few monsters with AC above 20.
A mid-level sorcerer (let's say level 8) with maxed Charisma only needs to roll 12 or higher to hit an AC of 20. With advantage, which you'd better believe they'll find a way to get on their Sharpened Fireball, that's a 69.75% chance to hit.
The same sorcerer casting a regular Fireball has a save DC of 16. Let's assume the monster isn't great at Dexterity saving throws (but not too bad at them, either) and give it a +3. It has a 60% chance of failing that saving throw, which is pretty good odds for the sorcerer, but not as good as the attack roll. On the other hand, if the monster gets advantage on the saving throw (which there are a lot of ways for it to do), it has a 36% chance of failing. Not so good. And, of course, this is assuming a monster with really good AC, which is more of a worst-case scenario than a usual one.
So that's why Sharpen Spell is also better than Heighten Spell. The third thing Sharpen does is change the spell from an AoE to a single-target. This looks like a drawback, and often will be, but in those situations the sorcerer just won't do it. For the sorcerer to be thinking about Sharpening a spell, they'll have a priority target in mind. This lets them use Fireball on the Big Bad without having to worry about hurting their allies. "But they could just use a single-target spell!" Well, they could. But they have a limited number of spells known, and there are in fact no 3rd-level single-target spells. Hence, this is also better (or at least as good as) Careful Spell, albeit only when you have a priority target.
With all that out of the way, this is a really cool idea. It gives us back the Spellwarp Sniper from 3.5, which was great. Focusing Fireballs into concentrated beams of destruction? Awesome.
I strongly recommend going ahead with this, but removing the damage bonuses. If your players choose to use this, they know they're turning an AoE spell into a single-target spell, and they know they're adding a chance of total failure. They'll use it when those aren't problems, so you don't need to boost it because of those drawbacks.
With that change in place, I'd recommend this metamagic option costing 3 sorcery points, the same as Heightened Spell. Wait, what? I said earlier that it was better than Heightened Spell! Well, it is, but it requires the player spending additional resources to make it that way. It's trivial to give yourself advantage on an attack roll, but it's not free. You have to spend an inspiration point, or use your previous turn to cast True Strike or to Hide, etc.
The 6d10 maximum damage is not relevant for an usual ranger, but is brought into play when casting the spell at higher levels than five, which can happen...
By being a Bard
The Bard has spell slots all way to ninth level, and the class feature magical secrets allows them to learn spells of any class. A Bard could cast the spell with a sixth-level slot or above, dealing 6d10 damage.
By multiclassing into a spellcaster
If a Ranger takes the spell early, they can multiclass into Wizard, Sorcerer, Bard, Cleric or Druid and eventually gain access to sixth-level and higher level slots and use them to cast the spell at higher-than-usual levels.
By casting Wish to duplicate the effects of Hail of Thorns
A high-level caster can use the spell Wish to duplicate the effects of any lower-level spell, including Hail of Thorns. In this case, it'd be cast as a ninth level spell as described here.
Best Answer
There is no direct advice in the books
So we have to derive it from other parts of D&D.
A combat is 3 rounds
Now this isn't actually true; combats are often longer. But the impact of damage-later is usually less than damage-earlier; by taking the average over 3 rounds of combat, you get a good approximation of how much a "feature" is worth.
To back this up, this is how the DMG advises you balance monster damage.
Action value scales with level
For a given action, a character can either use an at-will resource, or burn a non-at-will resource.
Spellcasters at-will resource is typically a cantrip; in some cases, it is a weapon attack. If you do a comparison of the two, they tend to (very roughly) scale with character level.
When you have an concentration spell that requires burning an action each round, the value the spell provides is the difference between the spell's action value and the at-will value you could have gotten without spending any spell slots.
Using Firebolt as our baseline, this is 1d10 damage per tier (miss for nothing); compared to normal spells, this is 4.5 levels 1-4 (1st - 2nd level spells), 9 levels 5-10 (3rd-5th level spells), 13.5 levels 11-16 (6th-8th level spells), and 18 levels 17+ (9th level spells).
This will underestimate the value of the action. Because by level 17, you have enough low level spells that the actual comparison is either using your action on your concentration spell, or casting a low level spell (of which you have plenty). But at least it doesn't discount it completely.
But first, let's ignore the multi-target and subtract that "baseline damage".
We then spread it over 3 rounds.
Multiple target damage is very similar to single target damage if you assume the spell hits 1.5 foes; or, rather, assume it hits 2 foes on average, and damage on the 2nd foe is worth half as much as damage on the primary target. (The ratio varies)
If you treat moonbeam this way (and you should), its equivalent single-target damage is 16.5. This is closer to a 3rd level spell.
Concentration is another resource that these spell use. We could simply give concentration spells a 1 level bump; a 3 round 3rd level spell should do 15 damage per round, and moonbeam is pretty close to that.
For spells that don't use your action to repeat their damage, we don't get the boost from the damage you forgo from your action.
We can neglect the cost of the bonus action per round to keep things simple (most spells should have that cost).
Let's double check.
Test with actual spells.
Mordenkainen’s Sword is considered an awful spell. It does 3d10 damage, 0 on a miss, and requires concentration and a single action to cast. So its damage budget over 3 rounds is 64.5 + 18 / 3 or 27.8 × 1.25 = 34.8 damage per round. Instead it does 16.5. So Mordenkainen's Sword evaluates as really bad.
Sunbeam is considered a good spell. It is 6th level, does 6d8 (27) and blinded to multiple targets, is concentration, requires an action per turn, and does half damage on a successful save.
As multiple target spell, that is 40.5 single-target equivalent damage. My table above says a concentration action-per-round spell 6th level spell should do 29.2 single-target equivalent damage. So sunbeam is above par.
Summon Fiend is a recent 6th level spell. It does 3 attacks of ~16 damage per attack, 0 on a miss. It requires an action when you cast it. As a 6th level concentration spell, it has a single target 3 round with 0 damage on a miss damage budget of 36.5; it actually deals 48. Which makes it an above par spell.
Storm Sphere is a 4th level concentration spell. It does an initial 2d6 AOE damage (0 on a miss), then you can use a bonus action to deal 4d6 each turn on one target (0 on a miss, advantage first turn). (Foes could choose to stand in the storm and boost these values; I assume they won't.)
A 4th level 0 on a miss single target damage budget is 67.5. Storm Sphere does 7 × 1.5 = 10.5 initial, plus 54 over 3 rounds, for a total of 64. Pretty close.
Spirit Guardians is a 3rd level concentration spell that requires 1 action to deal damage. It does 3d8 multi-target damage with a save for half. So its single-target-equivalent damage budget is 60.75. Its one-target damage budget is 44, which makes it an above-par spell.
Probably more work needs to be done, but the general idea of "actions have value", "slots have value", "measure damage over 3 rounds" and "concentration has value (and risk)" I used above should give you a good ballpark to start in. And when looking at existing spells, really good ones tend to be at the top end of the range, and poor ones well under it.
Where the Rubber meets the Road
Note that the budget I assigned to "value of an action" is going to be rather low for any game with a 5 minute adventuring day. The spellcaster isn't likely to ever use cantrips, so cantrips are not the cost of the action.
If you expect 3 rounds per fight that "matter" over 8 fights per day, that is 24 rounds. A 11th level wizard has 16 spell slots and arcane recovery for another 1 or 2 slots. They cannot cast a different leveled spell every round of combat; so they may want a concentration spell that more efficiently uses their action than a cantrip.
The same wizard with 1 fight with 6 rounds that "matter" will want to use every round that matters in casting a spell with a level; 1 6th, 2 5th and 3 4th level slots. The opportunity cost for the action using a concentration spell repeatedly is higher for this wizard.
As you are working on spells for your home game, you should take into account (a) you don't want to write a spell that nobody will use, and (b) if you have 5 minute adventuring days, you should have a higher opportunity cost for using an action to fuel a spell.