You are deciding between two mutually exclusive investment opportunities. Both require the same initial investment of $ $10\mathrm{.}2$ million. Investment A will generate $ $2\mathrm{.}05$ million per year$($starting at the end of the first$$ year$)$ in perpetuity. Investment B will generate $ $1\mathrm{.}55$ million at the end of the first$$ year, and its revenues will grow at $2\mathrm{.}8\%$ per year for every year after that.

a$.$ Which investment has the higher$$ IRR?

b$.$ Which investment has the higher NPV when the cost of capital is $5\mathrm{.}5\%?$

c$.$ In this$$ case, for what values of the cost of capital does picking the higher IRR give the correct answer as to which investment is the best$$ opportunity?