Consider a construction company that is susceptible to risk. There is an initial investment of $90000$ followed by a $4-$year projected cash flow as shown in the table below. There is a possible demand of $100000$ units of the products per annum till the end of the project. The discount rate is $12\%.$

$($a$)$ Calculate the NPV of this project

$($b$)$ Re$-$calculate the NPV for each of the following changes in parameters

$($i$)$ Sales price: $5\%$ increase and $10\%$ decrease.

$($ii$)$ Labour: $9\%$ increase and $15\%$ decrease.

$($iii$)$ Discount rate: $10\%$ increase and $10\%$ decrease.

$($iv$)$ Materials: $8\%$ increase and $12\%$ decrease.

$($c$)$ From the results in Question $5$b$,$ construct a sensitivity graph showing the changes in the NPV with respect to the four parameters.

$($d$)$ For the quantity demanded, when does a break$-$even happen and determine the percentage deviation before the break$-$even point. $($All other parameters are constant$).$