$5.$ Woodbridge Accessories is considering the purchase of a land and the construction of a new factory. The land, to be bought immediately, has a cost of $$150,000$ and the building, to be developed by the end of the first year, would cost $$225,000.$ It is estimated that the firm's after$-$tax cash flow will be increased by $$80,000$ starting at the end of the second year, and that this incremental flow would increase at a constant rate of $20\%$ per year over the next $10$ years. What is the approximate payback period of this investment?

The CFs should be as follows:

Year $0$: $-150,000$ Year $1$: $-225,000$ Year $2$: $80,000$ Year $3$: $80,000*1\mathrm{.}2=96,000$ Year $4$: $96,000*1\mathrm{.}2=115,200...$ Year $12$: $495,338\mathrm{.}90$