$2$ alternative pavement available for construction $9000m^2$ of local roads as follows:

$$concrete parement al

$-$total initial cost $=38$ million

$-$rehabilitation in the ${15}^{th}$ year $($the cost of rehab of $1m^2$ concrete pavement is $1500)$

$$asphalt pavement alt

$-$total initial cost $=35$ million

$-$first rehab in the ${10}^{th}$ year $($per $1m^2$ asphalt pavement:$800)$

$-$second rehab in the ${20}^{th}$ year $($per $1m^2$ asphalt pavement : $1200)$

$$ Analysis period $=30$ years.

Real discount rate $=5\%$

User cost a residual value are similar for both alternatives.

Determine:

a$.)$ Compare the alt. net present values $($NPV$)$ and indicate which one is better.

b$.)$ Conduct a sensitivity analysis to verify whether the conclusion in part I holds for other smaller discount rates and explain the results.