Your firm has an opportunity to build a new factory today for $$2000,000.$ Eight months from today, the factory will generate a free cash flow of $$225,000.$ After this imitial cash flow, the factory will generate semianual cush tlows though five years and two months fom today. Calculate the rate at which the cash flows must grow for the net present value of the factory to equal zero if the cost of capital for the project is $7\mathrm{.}5\%$ APR with quarterly compounding.