This is a simple optimisation problem. Ignore the sunk costs completely, what matters is how much you actually get for your money. If you can get it repaired and have it be as good as new, then anything up to £689.99 still means you come off better on the deal. If a repaired version will only last half as long as a new lens, then as long as you pay less than £345, you're OK.
You have two parameters - the cost to get a fully functioning lens, and the expected lifetime of said lens. Your options are:
1) Repair the existing lens. Cost = x, expected subsequent lifetime until breakage = y
2) Buy a new lens. Cost = £690, expected subsequent lifetime until failure = z.
Go for whichever is the smaller out of (x * y) or (£690 * z). If you like, you could add a third option:
3) Buy another second-hand lens. Cost = £400 (?), subsequent lifetime until failure = a. You can estimate a as being "a while", since that's how long the last one lasted.
no subject
You have two parameters - the cost to get a fully functioning lens, and the expected lifetime of said lens. Your options are:
1) Repair the existing lens. Cost = x, expected subsequent lifetime until breakage = y
2) Buy a new lens. Cost = £690, expected subsequent lifetime until failure = z.
Go for whichever is the smaller out of (x * y) or (£690 * z). If you like, you could add a third option:
3) Buy another second-hand lens. Cost = £400 (?), subsequent lifetime until failure = a. You can estimate a as being "a while", since that's how long the last one lasted.