A company is trying to determine whether or not they should move the processing of incoming payments from their own processing center to a lockbox. Annual collections are $165 M on 45,000 items and the estimate is that using a lockbox will decrease total collection float by three days. The company estimates that their costs to process payments themselves run about $1 per an item and that moving these collections to a lockbox would increase these costs to $2 an item, plus $12,000 in fixed costs. If the relevant cost of capital for the company is 5.5%, should they switch to the lockbox?

No. With the switch, the company is worse off by $27,589.

Yes. With the switch, the company is better off by $27,589.

No With the switch, the company is worse off by $17,589.

Yes. With the switch, the company is better off by $17,589.