FastTrack$$ Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the cost is $ $188,000$ per year. Once in$$ production, the bike is expected to make $ $263,200$ per year for $10$ years. Assume the cost of capital is $10\%.$

a$.$ Calculate the NPV of this investment$$ opportunity, assuming all cash flows occur at the end of each year. Should the company make the$$ investment?

b$.$ By how much must the cost of capital estimate deviate to change the$$ decision? $($Hint$$: Use Excel to calculate the$$ IRR.$)$

c$.$ What is the NPV of the investment if the cost of capital is $13\%?$

Note$$: Assume that all cash flows occur at the end of the appropriate year and that the inflows do not start until year $7.$