Amazon has a problem; It's too successful. It controls $44\%$ of the U$.$S$.$ e$-$commerce market, has well over $$200$ billion in annual sales, ships more than $1\mathrm{.}2$ billion packages a year, and has more than $100$ warehouses, $7,500$ truck trallers, and $40$ airplanes. However, its rapid growth has made quick and inexpensive delivery of packages crucial to its operations. In $2017,$ it spent nearly $$22$ billion on shipping globally or about $12\%$ of its overall revenue

To which market structure belong Amazon? Explain.

Amazon has relled on shipping using United Parcel Service $($UPS$),$ FedEx, and the U$.$S$.$ Postal Service $($USPS$).$ Amazon worries that these delivery services are relatively expensive and have trouble delivering on time, especially during heavy shipping near the December holidays. Consequently. Amazon says that it needs to develop its delivery services. One option Amazon is considering is Shipping With Amazon $($SWA$),$ a form of vertical integration. It requires a significant investment initially, with a payoff in the future. This investment cannot pay unless its present value is positive.

a$.$ Show formally using an equation involving interest rates to explain your answer.

b$.$ Use an Excel sheet to confirm your answer to question a$.$ in the excel sheel, use $1\%,2\%,3\%,4\%,5\%,6\%,7\%,8\%,9\%,$ and $10\%$ interest rates. $($Hint: follows Q&A $)$ pages $208-209$ in the textbook$).$