$xYZ$ is a Saudi company with an annual revenue of $18$ billion SAR and over $25,000$ employees. The company's mission is to help customers make people healthier, cleaner, and more secure$.$ The company helps its customers advance research in life sciences, solve complex analytical challenges, improve patient diagnostics, and increase laboratory productivity. Through the leading brands $-$Applied Biosystems, Invitrogen, and Unity Lab Services $-$ the company offers a combination of innovative technologies, purchasing options, and comprehensive support. In Saudi Arabia, the company has three locations. They are located in Riyadh, Jeddah, and Dammam, where the location in Riyadh is the largest with a factory, gamma radiation facility, and a number of regional and global functions. The following assignment deals with considerations regarding a new product. If the product in question is to be manufactured, it will be necessary to build a new production line, which will require the following investments:

Injection molding machine: $2$ million SAR

Molds: $2\mathrm{.}5$ million SAR

Vision system: $1\mathrm{.}5$ million SAR

Automation equipment: $4\mathrm{.}5$ million SAR

Interior furnishings, etc.: $1\mathrm{.}5$ million SAR

The expected receipts from sales of the product and the expected variable costs of manufacturing the product are shown in Table $1.$ NB: As the assignment concerns an investment problem, the theoretically correct terms are" receipts and payments". However, since many" payments" do not act as single payments at specific times, but as resource consumption over a period of time, i$.$e$.$ as a cost, such payments are usually referred to as costs, and this term is therefore also used in Table $1.$

Table $1$: Expected receipts and paymeats $($costs$).$

$\backslash$table$[[,,,],[,1,2,3,4,5],[$Receipts from sales $($million SAR$),3\mathrm{.}75,6\mathrm{.}6,15\mathrm{.}4,21\mathrm{.}9,27\mathrm{.}9],[$Costs for sterilization $($million SAR$),0\mathrm{.}05,0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}25,0\mathrm{.}3],[$Costs for materials $($million SAR$),1\mathrm{.}8,3\mathrm{.}1,5\mathrm{.}6,7\mathrm{.}4,8\mathrm{.}95],[$Payroil costs $($anilion SAR$),0\mathrm{.}15,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}5,0\mathrm{.}6],[$Additional costs $($maillion SAR$),0\mathrm{.}9,0\mathrm{.}3,0\mathrm{.}1,0\mathrm{.}05,0\mathrm{.}05]]$

Assune that the discount rate is set to $15\%$ per year.

Solve the following Questions:

Part I: Deterministic

Will it be profitable to make this investment?

What is the investment's inernal rate of retum? In the foregoing, the investment is estinated based on a life of $5$ years. However, after $5$ years, parts of the production line are expected to be used in the construction of new production lines, and therefore they will continue to have value:

Injection molding machine: $1$ million SAR

V$$sion system: $1$ million SAR

Automation equipment: $2$ million SAR

What is the net present value of the investment if considering the value that the three parts of the production line are expected to have after the $5$ years?

Will it be profitable to choose the alternative solution?

Part M: Sensitivity Analysis

$5.$ Sensitivity analysis is intended to tackle the impact of errors in estimating various values of the input parameters. The XYZ company has decided to conduct the sensitivity analysis with the aim of providing the higher management with information concerning the risk belavior on investment economic effectiveness due to possible uncertainty for some critical input cash flow parameters. The selected parameters for the analysis are:

a$.$ Discount rate

b$.$ Investment amount for Injection molding machine

c$.$ Costs for materials

d$.$ The cost Additional costs

Perform sensitivity analysis of Annual worth for $($Investment amount for Injection molding machine and discount rate$),$ over a range of $+-100\%$ of the selected input cash flow parameters and plot the one$-$at$-$a$-$time where $x-$ percent deviation from most likely value and $y=$ Annual worth $($SAR$)$

$6.$ Identify the most sensitive parameters and perform a multiparameter sensitivity analysis for this problem. Draw a diagram to illustrate your answer where $x=$ change in parameter I, and $y=$ change in parameter II$.($Hint: one graph for net future worth$).$