QUESTION $7$

$($a$)$ An existing road is $25km$ long and is carrying traffic at $1500$ vehicles per day, with annual maintenance costs of $$500$ per $km.$ It is proposed to re$-$align the road, thus shortening it to $20km.$ The cost of construction of the new road will be $$150000$ per $km,$ and the cost of the land to be acquired along the route is $$20000$ per $km.$ The average vehicle travels at $100k\frac{m}{h}$ at a cost of $$0\mathrm{.}1$ per $km$ and has one occupant whose value of time is estimated at $$3$ per hour.

The re$-$alignment is expected to lead to annual accident savings of $$50000.$ Assuming that the construction of the road will take one year and that the money for the construction is to be borrowed at $8$ percent interest per year, calculate the benefit$-$cost ratio $($B$/$C$)$ and the Net Present Value $($NPV$)$ of the project, assuming a project life of $20$ years and a traffic$-$growth rate of $5$ percent per year. Assume no diverted traffic. The re$-$aligned road will require a new surface dressing in year $10$ at a cost of $$1000000.$

$(20$ Marks$)$