BACKGROUND

Analyze a project to manufacture a natural homeopathic substitute in syrup $($tiritoncixilina$)$ to alleviate almost all varieties of phonophobia, except for ampoules. Currently, a chemical compound is sold in liter units, and the aim is to compete by offering an alternative to those seeking natural medicine. The natural product will be sold in $0\mathrm{.}25-$liter containers.

Investments would be made during $2023$ to start operations in January $2024.$

Statistics show that the projected sales of tiritoncixilina in the country $($in liters$)$ can be explained by the function:

y $=1,672\mathrm{.}1$x $+129,996$

where x $=15$ for the year $2024.$

According to the results of a national survey of current consumers, it was concluded that $11\mathrm{.}2\%$ of them would be willing to purchase the product because it is $100\%$ natural. The selling price to pharmacies is $$16$ per bottle.

The variable cost of raw materials amounts to $$32$ per liter.

The packaging $($bottle and cardboard box$)$ has a unit cost of $$2\mathrm{.}9.$

The plant will be located on the outskirts of the city, and to install it$,$ a plot of land valued at $$60,000$ must be purchased. The construction will be masonry, requiring an investment of approximately $$320,000$ and depreciating over $40$ years.

The heavy manufacturing equipment will be purchased new, with a value of $$210,000$; lightweight tools cost $$15,000$; factory furniture costs $$7,000,$ and administrative and management furniture costs $$14,000.$ The years for depreciation, according to the fixed asset accounting useful life table, are $15,3,7,$ and $7$ years, respectively.

$$6,000$ will be invested in computer equipment, depreciable over six years.

Regardless of the accounting depreciation period, the actual useful life has been estimated at $12$ years for heavy manufacturing equipment, three for lightweight tools, eight for factory furniture, five for administrative and management furniture, and three for computer equipment.

The manufacturing process is carried out by four operators with a total monthly remuneration of $$550$ each. The remuneration of supervisory, administrative, service, surveillance, and maintenance personnel amounts to $$9,200$ monthly.

At the end of their actual useful life, factory and office furniture could be sold for $$500$ and $$3,200,$ respectively, and computer equipment for $$2,400.$

Lightweight tools will be retained by the company, as they will have no value in the secondary market.

Other expenses estimated for the project include office rent in a central area of the capital for $$1,200,$ insurance for $$250,$ energy for $$220,$ and other miscellaneous expenses for $$1,600$ monthly.

Working capital must finance a three$-$month lag period.

The tax rate is $25\%$ on profit, after deducting a $15\%$ employee participation.

To finance the investments, a loan of $$300,000$ at an annual interest rate of $11\%,$ payable in eight equal annual installments, is considered.

To calculate the cost of own capital, consider a risk$-$free rate of $4\mathrm{.}6\%,$ an average market return of $14\%,$ and a beta of $1\mathrm{.}12.$

To follow a conservative criterion, calculate the residual value by the accounting method.

$1.$ Build the cash flow R for the pure project and the investor.