Hi Nikesh,
I guess this way of proceeding might be suggested if the standard price you have in material master is coming from Costing, not from direct manual entry directly in the Std Price field or from MR21.
If it is so and you need to redo the costing to get the correct price, then first you should remove the old costing - unless you do it you might have problems while performing the new one (error saying something like: Cost estimate already exists for this material).
It also depends if you change the price in the same period or in different periods - CKR1 might be needed if it is the same one the price was originally added.
Best Regards,
Tomek