You have two mutually$-$exclusive projects. The first project $($P$1)$ has an initial investment of $17\mathrm{.}2$ million Czech crowns $($CZK$),$ and the first year's positive cash flow of $25\mathrm{.}4$ million CZK$.$ The second year cash flow is a positive $5\mathrm{.}2$ million CZK$.$ The second project $($P$2)$ has an initial cash flow in year $0$ of a negative $20\mathrm{.}2$ million CZK$.$ The first year cash flow is a positive $36\mathrm{.}2$ million CZK$.$ The second year cash flow is a negative $3\mathrm{.}2$ million CZK$.$ MARR is $18\%.$

$($a$)$ The Annual Equivalent Worth of the first project $($P$1)$ is:

$$ CZK$.$

$($b$)$ The Annual Equivalent Worth of the second project $($P$2)$ is:

$$

$$ CZK$.$

$($c$)$ The cash flows for the incremental investment P$2-$P$1$ are:

$\backslash$table$[[-$ for year $0,,$CZK$,],[-$ for year $1,1,$CZK$,$ and$],[-$ for year $2,,$CZK$.]]$

$($d$)$ The Annual Equivalent Worth of the incremental investment P$2-$P$1$ is: $$ CZK$.$

$($e$)$ The break even interest rates for the incremental investment P$2-$P$1$ are as follows. The smaller of the two rates $i_1^{**}=\%$ and the larger of the two rates $i_2^{**}=\%.$ Please note that, if you are using the spreadsheet software built$-$in function to find these rates, you can apply a "guess" of $20\%$ for the first rate $(i_1^{**})$ and $100\%$ for the second rate $(i_2^{**}).$

$($f$)$ The Internal Rate of Return of the incremental investment P$2$P$1$ is: $\%.$ Please note that the "true" IRR is not one of the break$-$even interest rates and that only the case where $P{B}_1$ is positive needs to be developed, so there will be no need to solve a quadratic equation here. You can refer to Lecture $22$ material, including Video Example E$22.$