Peter is the CEO of an agriculture products retailer. He is considering the purchase of a new software system to help with his new online retail venture. The software will cost $$650,000,$ and will be depreciated straight$-$line over five years $($to zero$).$ This is a new depreciation expense and does not offset any previous depreciation so you get the full benefit of the depreciation tax shield. Peter does not think the software will be viable after $4$ years and will have a market value of zero. But, since there is still some book value to the software, you can take a captial loss tax shield.

However, he thinks he will need to pay a programmer $$10,000$ at the end of year $4$ to get rid of the software at that time $-$ think of this as an additional salvage cost. The software will have several effects if it is installed. First, it will reduce incremental overhead expense by $$20,000$ per year due to savings in hardware needs. Second, it will reduce incremental labor expenses for custom programming by $$100,000$ per year. Lastly, due to its sophisticated inventory management system, it will allow Peter to permanently reduce inventory by $$200,000$ when he buys the software $--$ this will be effective immediately and there is no reversion expected at the end of the project $--$ so this is a one time reduction in working capital. The company has a target debt$/$equity ratio of $0\mathrm{.}3$ which they plan to maintain after adoption of the new software. Its current equity beta is $1\mathrm{.}1.$ Peter plans on paying for the project out of cash raised from a new bank loan with an $7\%$ interest rate $($its marginal pre$-$tax cost of debt$).$ Assume that the risk$-$free rate is $4\%,$ the market risk premium is $7\%,$ and all firms face a marginal tax rate of $30\%.$

$1.$ What are the free cash flows for the project for each year?

$2.$ What discount rate should the firm use for the project?

Explain in detail.

$3.$ Calculate the NPV$.$ Should Peter accept the project? Why or why not?