Tesa Limited has a relatively high level of current assets and this is evident in the amount of inventory it carries and the amount owed by trade debtors. A higher inventory level is maintained to absorb any sudden increases in product sales and any abnormal delays in procurement times. This achieves a higher level of customer satisfaction and leads to the smooth operations of the company. Higher levels of accounts receivables are due to the generous credit terms granted to debtors. This, in turn, attracts more customers leading to higher sales. The higher levels of inventory and accounts receivable have a direct impact on both liquidity and profitability. An analysis of the current situation reveals the following: The selling price of the only product that it sells is R$280$ per unit. The product is priced at cost plus $40\%.$ The holding cost is $10\%$ of the unit cost. The cost of placing an order for the product is R$18.$ The annual sales are $50000$ units, of which $80\%$ is on credit. The credit terms are $3/10$ net $60$ days but it takes approximately $73$ days to collect the debts from the credit customers. The discount applies to $40\%$ of the credit sales. Bad debts usually account for $6\%$ of the credit sales. The credit terms should be changed to $4\mathrm{.}5/10$ net $60$ days. This is expected to increase credit sales to $55000$ units, reduce the debtors collection period to $36\mathrm{.}50$ days, lower bad debts to $4\%$ of credit sales and increase the percentage of the credit sales to which the discount applies to $70\%.$qquestion $2$ Calculate the EOQ if discounts are not available. Question $3.$ If Proposal $1$ is implemented without considering Proposal $2,$ what purchase quantity would you recommend?

Motivate your answer with the relevant calculations.please use the attached example and solution to answer the question The supplier offers a discount scheme as follows:

Required

Determine the:

$($a$)$ EOQ if discounts are not available, and

$($b$)$ EOQ where discounts are available. Solution

$($a$)$

$\sqrt[\phantom{2}]{\frac{20CAS}{CC}}$

$\sqrt[\phantom{2}]{\frac{2R36160000}{R1\mathrm{.}08}}$

$=\sqrt[\phantom{2}]{R160000}$

$=3266$ units

$($b$)$ AT $5\%$ DISCOUNT

$($i$)$

Marginal holding cost $=\frac{E^{\text{'}}{H}^{\text{'}}}{2}-\frac{EH}{2}$

$=\frac{40011\mathrm{.}026}{2}-\frac{32661\mathrm{.}08}{2}$

$=R2052\mathrm{.}51-R1763\mathrm{.}64$

$=R288\mathrm{.}87orR289($ii$)$

Savings $in$ ordering costs $=\frac{O(D)}{E}-\frac{O(D)}{E^{\text{'}}}$

$=\frac{36(160000)}{3266}-\frac{36(160000)}{4001}$

$=R1763\mathrm{.}63-R1439\mathrm{.}64$

$=R323\mathrm{.}99orR324$

$(iii)$ Discount savings $=(160000R7\mathrm{.}20)5\%=,R57600$

$(iv)$ Net saving $=R57600+R324-R289=R57635$

AT $6\%$ DISCOUNT

$E^{\text{'}}($New order quantity$)=8001$

E $($EOQ$)=3266$

$H($Holding cost$),=($R$7\mathrm{.}2015\%$

$H^{\text{'}}($New Holding cost$)=(R7\mathrm{.}2015\%0\mathrm{.}94)=R1\mathrm{.}0152$

O $($Order cost$),=$ R$36$

D $($Demand$)=160000$

$($i$)$

Marginal holding cost $=\frac{E^{\text{'}}{H}^{\text{'}}}{2}-\frac{EH}{2}$

$=\frac{80011\mathrm{.}0152}{2}-\frac{32661\mathrm{.}08}{2}$

$=R4061\mathrm{.}31-R1763\mathrm{.}64$

$=R2297\mathrm{.}67orR2298$

$($ii$)$

Savings $in$ ordering costs $=\frac{O(D)}{E}-\frac{O(D)}{E^{\text{'}}}$

$=\frac{36(160000)}{3266}-\frac{36(160000)}{8001}$

$=R1763\mathrm{.}63-R719\mathrm{.}91$

$=R1043\mathrm{.}71orR1044($ii$)$

Savings $in$ ordering costs $=\frac{O(D)}{E}-\frac{O(D)}{E^{\text{'}}}$

$=\frac{36(160000)}{3266}-\frac{36(160000)}{8001}-21763\mathrm{.}63-R719\mathrm{.}91$

$=R1043\mathrm{.}71orR1044$

$($iii$)$ Discount savings $=(160000R7\mathrm{.}20)6\%=,$ R$69120$

$($iv$)$ Net saving $=$ R$69120+$ R$1044-$R$2298=R67866$