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Part $1$

FastTrack$$ Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the cost is $ $200$ comma $000$ per year. Once in$$ production, the bike is expected to make $ $300$ comma $000$ per year for $10$ years. The cash inflows begin at the end of year $7.$

Assume the cost of capital is $10\mathrm{.}0\%$ for parts$($a$),($b$),$ and$($c$)$ below.

a$.$ Calculate the NPV of this investment opportunity. Should the company make the$$ investment?

b$.$ Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

c$.$ With costs remaining at $ $200$ comma $000$ per$$ year, how long must development last to change the$$ decision?

Assume the cost of capital is $14\mathrm{.}0\%$ for parts$($d$),($e$),$ and$($f$)$ below.

d$.$ Calculate the NPV of this investment opportunity. Should the company make the$$ investment?

e$.$ How much must this cost of capital estimate deviate to change the$$ decision?

f$.$ With costs remaining at $ $200$ comma $000$ per$$ year, how long must development last to change the$$ decision?