Why would a write down of inventory to NRV increase your COGS? Or really have any impact on your cost of sales? This is inventory on hand so I would think writing down the value of your inventory would reduce the cost of goods sold in the future?
You could just refer to the formula: COGS is Beginning Inventory + Purchases - Ending Inventory. If EI is lower (as it will be after a writedown), COGS becomes greater.
or alternately, you could view COGS intuitively as the cost of inventory “consumed” during the period. A writedown is (effectively) a loss in value in the inventory. So, it makes sense to allocate that loss against consumption of current period inventory.