Colatonic Ltd is a marketer of a range of non$-$alcoholic beverages. It commenced operations a few years ago with an authorized share capital of $500000$ ordinary shares and by $2023$ eighty percent $(80\%)$ of the shares had been issued. Its product mix includes soft drinks, juices, energy drinks and flavoured water. These products are marketed under various brands. The company has distribution outlets in all the provinces in South Africa, with the headquarters in Pretoria. It negotiated with its suppliers for all purchases to be made on credit terms of $90$ days and it was able to sell all its products to its customers on credit terms of $30$ days. Colatonic Ltd experienced a great dela of success in the recent years because of its excellent sales strategy and the clever use of social media. However the entry of cheap energy drinks and flavoured water into the South African beverage market from China and other countries led to a downturn in the financial performance in $2023.$ The company did, however, pay an interim dividend of R$670080$ to the shareholders during $2023.$ A final dividend was also declared at the end of $2023.$ The market price of each share of Colatonic Ltd was R$15$ on $31$ December $2023.$

This following are the financial statements for the past two years:

COLATONIC LTD

STATEMENT OF COMPREHENSIVE INCOME FOR THE YEAR ENDED $31$ DECEMBER:

$2023$

$2022$

R

R

Sales

$20000000$

$24000000$

Cost of sales

$(12000000)$

$(13000000)$

Gross profit

$8000000$

$11000000$

Selling, general and administrative expenses

$(5000000)$

$(6600000)$

Operating profit

$3000000$

$4400000$

Interest on investment

$?$

$?$

$3240000$

$4592000$

Interest expense

$?$

$?$

Profit before tax

$2940000$

$4352000$

Company tax

$(823200)$

$(1218560)$

Profit after tax

$2116800$

$3133440$

STATEMENT OF FINANCIAL POSITION AS AT $31$ DECEMBER:

$2023$

$2022$

R

R

Assets

Non$-$current assets

$3480000$

$2700000$

Investment $($maturity date $30$ June $2025)$

$2000000$

$1600000$

Inventories

$2200000$

$1800000$

Accounts receivable

$1400000$

$1100000$

Cash

$20000$

$16000$

$9100000$

$7216000$

Equity and liabilities

Equity

$5370000$

$4156000$

Long$-$term loan

$2000000$

$1600000$

Accounts payable

$1000000$

$800000$

Bank overdraft

$50000$

$40000$

Dividends payable

$600000$

$500000$

Company tax payable

$80000$

$120000$

$9100000$

$7216000$

The financial manager of Colatonic Ltd read about the plight of the local child welfare organisation which aimed to supplement its funds by making and selling cooking bags which can slow$-$cook meals or keep food warm for long periods. The financial manager approached the board of directors who agreed that the company should assist the organisation. After discussions with the president and treasurer of the welfare organisation the following budgeted information for $2024$ was gathered to assist with trying to improve the profitability and break$-$even quantity for the year:

The fixed and variable manufacturing costs are estimated to be R$240000$ per annum and R$42$ per unit respectively. The selling price of the cooking bags will be R$120$ each. The selling and distribution costs are expected to total R$15000$ per month plus $5\%$ of sales. The administration costs are estimated at R$31000$ per month plus R$6$ per unit sold. $15000$ cooking bags are expected to be sold.

In keeping with its plans for expansion, the company is appraising the production and sale of a new designer energy drink. This would involve the acquisition of a new machine with a purchase price of R$1600000$ which is expected to have a useful life of six years and a salvage value of R$200000.$ The installation cost of the machine is R$100000.5000$ units are expected to be sold annually. The net profit is expected to be R$30$ per

unit. The straight$-$line method of depreciation is used by Colatonic Ltd$.$ The company$$s cost of capital is $16\%.$ If approved, the implementation date would be $02$ January $2025.$QUESTION $3$

$(25$ MARKS$)$

REQUIRED

Study the information provided by the child welfare organisation and answer the following questions independently. The expanded contribution margin model must be used to answer questions $3\mathrm{.}1,3\mathrm{.}2$ and $3\mathrm{.}4.$

$3\mathrm{.}1$

Calculate the break$-$even quantity.

$(5$ marks$)$

$3\mathrm{.}2$

Calculate the sales volume required to achieve an operating profit of R$2112000.$

$(5$ marks$)$

$3\mathrm{.}3$

Calculate the selling price per unit $($expressed to the nearest cent$)$ that will enable to welfare organisation to achieve an operating profit of R$50$ per unit.

$(5$ marks$)$

$3\mathrm{.}4$

Suppose the selling price is decreased by R$20$ per unit with the expectation that this would increase the sales volume by $20\%.$ Is this a good idea? Motivate your answer with the relevant calculations.

$(5$ marks$)$

$3\mathrm{.}5$

Calculate the margin of safety $($in units$)$ if the selling price drops to R$110$ per unit with the expectation that the fixed costs can be reduced to R$711900.$