Why would purchases of a new plant and equipment increase as the interest rate declines?
The law of demand says that the ability and willingness to buy a certain thing will increase (all other things being equal) when the cost of buying that thing decreases. When things are cheaper, people buy more of them. When interest rates go down, the effective price of buying new equipment or building a new plant go down as well. This means that more firms will want to do these things.
Purchasing new equipment or building new plants costs a great deal of money, typically more than a firm will want to pay in “cash.” Therefore, firms typically borrow money to pay for such actions. The interest rate is, in essence, the price of borrowing money. When the interest rate goes down, the price of borrowing money goes down. When the price of borrowing money goes down, it becomes cheaper for businesses to use borrowed money to buy new equipment and to build new plants.
Thus, decreasing interest rates make these sorts of investments by business more likely because they lower the costs of buying new equipment and building new plants.