$\begin{array}{cc}2021& 850\\ 2023& 900\\ 2024& 1000\end{array}$The Peacy Council is considering an upgrade to the road pavement system and has identified two possible methods: the Flexible Pavement Method and the Rigid Pavement

Method.

The construction commences in $2025.$ Below is the detailed cost breakdown for the Flexible Pavement Method and the Rigid Pavement Method:

Flexible pavement method takes one year to construction while Rigid pavement method, which takes about $2$ years to complete. The council has determined that both pavement methods provide substantial benefits in terms of vehicle time savings and fuel cost reductions. The specifics are as follows:

The council has identified that there is a fluctuating demand for vehicles per day. They are forecasting future demand based on historical vehicle data. The following table shows the number of vehicles per year. It is expected to increase the fuel price $15\%$ annually.

Please compare the financial viability of the project for $40$ years by calculating

$6\mathrm{.}1$ Benefit cost ratio

$6\mathrm{.}2$ Net Present Value $($NPV$)$

$6\mathrm{.}3$ Payback period

$6\mathrm{.}4$ IRR

$6\mathrm{.}5$ The capital cost may fluctuate by up to $5\%.$ Please analyse the effect of this variation on the Net Present Value $($NPV$\backslash$table$[[$Cost category,Flexible pavement,Rigid payment method$],[$Material cost$,$$$950,000,$$$80,000],[$Labour and equipment cost,$$80,000,$$$1,000,000],[$Maintenance & inspections,$$8,000$ annual,$$8,000$ every $2$ years$],[$Replacement$,$$$9,000$ Every $8$ years,$$10,000$ Every $12$ years$],[$Salvage value,$$4,000,$$$3,000]]$

Flexible pavement method takes one year to construction while Rigid pavement method, which takes about $2$ years to complete. The council has determined that both pavement methods provide substantial benefits in terms of vehicle time savings and fuel cost reductions. The specifics are as follows:

$\begin{array}{cc}\text{T}\text{i}\text{m}\text{e}\text{s}\text{a}\text{v}\text{i}\text{n}\text{g}\frac{s}{d}a\frac{y}{v}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}-\text{f}\text{l}\text{e}\text{x}\text{i}\text{b}\text{l}\text{e}\text{r}\text{o}\text{a}\text{d}& 30\text{m}\text{i}\text{n}\text{u}\text{t}\text{e}\text{s}\\ \text{T}\text{i}\text{m}\text{e}\text{s}\text{a}\text{v}\text{i}\text{n}\text{g}\frac{s}{d}a\frac{y}{v}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}-\text{r}\text{i}\text{g}\text{i}\text{d}\text{r}\text{o}\text{a}\text{d}& 40\text{m}\text{i}\text{n}\text{u}\text{t}\text{e}\text{s}\\ \text{V}\text{a}\text{l}\text{u}\text{e}of\text{s}\text{a}\text{v}\text{i}\text{n}\text{g}\text{s}\text{p}\text{e}\text{r}\text{m}\text{i}\text{n}\text{u}\text{t}\text{e}\text{s}& 2\frac{\text{\$}}{h}\text{o}\text{u}\text{r}\\ \text{A}\text{v}\text{e}\text{r}\text{a}\text{g}\text{e}\text{V}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}\text{f}\text{u}\text{e}\text{l}\text{c}\text{o}\text{n}\text{s}\text{u}\text{m}\text{p}\text{t}\text{i}\text{o}\text{n}& 0\mathrm{.}33\frac{V}{v}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}\\ \text{F}\text{u}\text{e}\text{l}\text{P}\text{r}\text{i}\text{c}\text{e}& 0\mathrm{.}189\frac{\text{\$}}{1}\\ \text{F}\text{u}\text{e}\text{l}\text{s}\text{a}\text{v}\text{i}\text{n}\text{g}\text{s}on\text{v}\text{e}\text{h}\text{i}\text{c}\text{l}\frac{e}{d}ay-\text{r}\text{i}\text{g}\text{i}\text{d}\text{p}\text{a}\text{y}\text{m}\text{e}\text{n}\text{t}& 0\mathrm{.}8\\ \text{F}\text{u}\text{e}\text{l}\text{s}\text{a}\text{v}\text{i}\text{n}\text{g}\text{s}on\text{v}\text{e}\text{h}\text{i}\text{c}\text{l}\frac{e}{d}ay-\text{f}\text{l}\text{e}\text{x}\text{i}\text{b}\text{l}\text{e}\text{p}\text{a}\text{y}\text{m}\text{e}\text{n}\text{t}& 0\mathrm{.}7\end{array}\backslash$table$[[$Cost category,Flexible pavement,Rigid payment method$],[$Material cost$,$$$950,000,$$$80,000],[$Labour and equipment cost,$$80,000,$$$1,000,000],[$Maintenance & inspections,$$8,000$ annual,$$8,000$ every $2$ years$],[$Replacement$,$$$9,000$ Every $8$ years,$$10,000$ Every $12$ years$],[$Salvage value,$$4,000,$$$3,000]]$

Flexible pavement method takes one year to construction while Rigid pavement method, which takes about $2$ years to complete. The council has determined that both pavement methods provide substantial benefits in terms of vehicle time savings and fuel cost reductions. The specifics are as follows:

$\begin{array}{cc}\text{T}\text{i}\text{m}\text{e}\text{s}\text{a}\text{v}\text{i}\text{n}\text{g}\frac{s}{d}a\frac{y}{v}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}-\text{f}\text{l}\text{e}\text{x}\text{i}\text{b}\text{l}\text{e}\text{r}\text{o}\text{a}\text{d}& 30\text{m}\text{i}\text{n}\text{u}\text{t}\text{e}\text{s}\\ \text{T}\text{i}\text{m}\text{e}\text{s}\text{a}\text{v}\text{i}\text{n}\text{g}\frac{s}{d}a\frac{y}{v}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}-\text{r}\text{i}\text{g}\text{i}\text{d}\text{r}\text{o}\text{a}\text{d}& 40\text{m}\text{i}\text{n}\text{u}\text{t}\text{e}\text{s}\\ \text{V}\text{a}\text{l}\text{u}\text{e}of\text{s}\text{a}\text{v}\text{i}\text{n}\text{g}\text{s}\text{p}\text{e}\text{r}\text{m}\text{i}\text{n}\text{u}\text{t}\text{e}\text{s}& 2\frac{\text{\$}}{h}\text{o}\text{u}\text{r}\\ \text{A}\text{v}\text{e}\text{r}\text{a}\text{g}\text{e}\text{V}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}\text{f}\text{u}\text{e}\text{l}\text{c}\text{o}\text{n}\text{s}\text{u}\text{m}\text{p}\text{t}\text{i}\text{o}\text{n}& 0\mathrm{.}33\frac{V}{v}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}\\ \text{F}\text{u}\text{e}\text{l}\text{P}\text{r}\text{i}\text{c}\text{e}& 0\mathrm{.}189\frac{\text{\$}}{1}\\ \text{F}\text{u}\text{e}\text{l}\text{s}\text{a}\text{v}\text{i}\text{n}\text{g}\text{s}on\text{v}\text{e}\text{h}\text{i}\text{c}\text{l}\frac{e}{d}ay-\text{r}\text{i}\text{g}\text{i}\text{d}\text{p}\text{a}\text{y}\text{m}\text{e}\text{n}\text{t}& 0\mathrm{.}8\\ \text{F}\text{u}\text{e}\text{l}\text{s}\text{a}\text{v}\text{i}\text{n}\text{g}\text{s}on\text{v}\text{e}\text{h}\text{i}\text{c}\text{l}\frac{e}{d}ay-\text{f}\text{l}\text{e}\text{x}\text{i}\text{b}\text{l}\text{e}\text{p}\text{a}\text{y}\text{m}\text{e}\text{n}\text{t}& 0\mathrm{.}7\end{array}$

The council has identified that there is a fluctuating demand for vehicles per day. They are forecasting future demand based on historical vehicle data. The following table shows the number of vehicles per year. It is expected to increase the fuel price $15\%$ annually.

$\begin{array}{cc}\text{Y}\text{e}\text{a}\text{r}& Noof\text{v}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}\text{p}\text{e}\text{r}\text{w}\text{e}\text{e}\text{k}\\ 2014& 500\\ 2015& 550\\ 2016& 600\\ 2017& 650\\ 2018& 700\\ 2019& 750\\ 2020& 800\end{array}$

The council has identified that there is a fluctuating demand for vehicles per day. They are forecasting future demand based on historical vehicle data. The following table shows the number of vehicles per year. It is expected to increase the fuel price $15\%$ annually.

$\begin{array}{cc}\text{Y}\text{e}\text{a}\text{r}& Noof\text{v}\text{e}\text{h}\text{i}\text{c}\text{l}\text{e}\text{p}\text{e}\text{r}\text{w}\text{e}\text{e}\text{k}\\ 2014& 500\\ 2015& 550\\ 2016& 600\\ 2017& 650\\ 2018& 700\\ 2019& 750\\ 2020& 800\end{array}\begin{array}{cc}2021& 850\\ 2023& 900\\ 2024& 1000\end{array}$