QUESTION $4$

$(20$ MARKS$)$

Using the information provided below and answer the following questions.

INFORMATION

Gold Coast Retails $($GCR$)$ is a prominent retail chain in Ghana, specialising in selling a broad range of consumer products, including groceries, household goods, clothing, and other daily essentials.

The following details pertain to the company's operations for the upcoming year:

Cash Management

Cash constitutes a significant component of the working capital requirements of GCR$\text{'}$s day$-$to$-$day operations. It is anticipated that the business will need R$15$ million, evenly over next year. The company intends to provide this cash requirement by periodically selling investments held. These investments currently earn an average return of $9\mathrm{.}5\%$ per annum and each transaction to sell investments incurs a fixed fee of R$135.$ In contrast, GCR earns an interest rate of $5\%$ per annum on its current account.

Inventory Management

In response to the findings from a recent market survey, GCR intends to introduce a new product, product K $,$ during the upcoming year. Total projected demand for product K next year is to be $625,000$ units, to be sourced from a Chinese supplier. The normal price of the product is R$300$ per unit. However, the supplier has proposed to supply product K at a $2\%$ discount provided GCR places three orders of product K each month uniformly throughout the year. Each order will incur a fixed cost of R$5,500,$ and the holding cost for each unit of product K will be $3\%$ of the purchase price.

REQUIRED:

Based on the information provided above, answer the following:

$4\mathrm{.}1.$ Using the Baumol model, calculate the optimal Rand amount of investments to be sold per

$(7$ Marks$)$ transaction, and determine the frequency of these transactions $($in days$).$

$4\mathrm{.}2.$ Calculate the Economic Order Quantity $($EOQ$)$ for product K for the upcoming year.

$(3$ Marks$)$

$4\mathrm{.}3.$ Calculate and compare the total annual costs associated with purchasing, ordering, and holding

$(10$ Marks$)$ product K under both the supplier's proposal and the Economic Order Quantity $($EOQ$)$ model. Based on this analysis, provide a recommendation to GCR$\text{'}$s management on the optimal course of action for the upcoming year.