Problem $\backslash$#$3(35$ pts $).$ Dakota Innovation is considering a purchase of a patent with a cost of $\backslash (\backslash$$ $47,000\backslash )$ and an estimated revenue producing life for Dakota Innovation of $4$ years. Dakota Innovation has a required rate of return is $\backslash (8\backslash \%\backslash )$ and a cost of capital of $\backslash (7\backslash \%\backslash ).$ The patent is expected to generate the following amounts of annual income and cash flows: $3.$a $(\backslash (\backslash$mathbf$\{15\}\backslash$mathbf$\{$~ p t s$\}\backslash ))$ Calculate the NPV of the investment. You can use Excel or a present value table for calculation. $3.$b $(10$ pts $)$ What does the NPV calculation do$,$ i$.$e$.,$ what is the nature of the NPV amount? $3.$c $(\backslash (\backslash$mathbf$\{10\}\backslash$mathbf$\{$~ p t s$\}\backslash ))$ If the required rate of return increases, will the NPV increase or decrease?