The following incomplete manufacturing account has been prepared for Chima's business for the year ended 31 December 2024. $ $ Opening inventory of raw mate...

(a) Calculate the value of A (cost of raw materials consumed)

The question states that raw materials consumed were 60% of the prime cost. Prime cost equals the cost of raw materials consumed (A) plus direct wages ($30,000), so:

\( A = 0.6 \times (A + 30\,000) \) [1]

Expanding and solving for A:

\( A = 0.6A + 18\,000 \) [1]

\( A - 0.6A = 18\,000 \)

\( 0.4A = 18\,000 \) [1]

\( A = \frac{18\,000}{0.4} = \$45\,000 \) [1]

The algebraic approach is needed because both A and prime cost are unknown, but the percentage relationship between them allows us to form an equation with one unknown.

(b) Calculate the value of B (prime cost)

Prime cost is the total of all direct manufacturing costs: raw materials consumed plus direct wages.

\( B = A + \text{Direct wages} = 45\,000 + 30\,000 = \$75\,000 \) [1]

Verification: raw materials consumed ($45,000) as a percentage of prime cost ($75,000) = 60%, which confirms the answer. [1]

(c) Calculate the depreciation of plant

The plant cost $40,000 and is depreciated at 10% per annum using the straight-line method:

\( \text{Depreciation} = \$40\,000 \times 10\% = \$4\,000 \) [1]

The straight-line method charges an equal amount each year over the asset's useful life. [1]

This can be verified against the manufacturing account: total factory overheads are $9,800, comprising factory rent ($4,200), factory insurance ($1,600), and depreciation. So depreciation = $9,800 - $4,200 - $1,600 = $4,000.

(d) Calculate the closing inventory of raw materials

Using the raw materials formula: Opening inventory + Purchases - Closing inventory = Raw materials consumed.

\( \text{Closing inventory} = \text{Opening RM} + \text{Purchases} - A = 54\,800 - 45\,000 = \$9\,800 \) [1]

Opening raw materials ($6,800) plus purchases ($48,000) gives $54,800 available. Subtracting the $45,000 consumed leaves $9,800 as closing inventory. [1]

(e) Calculate the value of C

C represents the total of prime cost plus factory overheads (the manufacturing cost before adjusting for work in progress):

\( C = \text{Prime cost} + \text{Total factory overheads} = 75\,000 + 9\,800 = \$84\,800 \) [1]

This is sometimes called the total factory cost or the production cost before work-in-progress adjustments. [1]

(f) Calculate the value of D (closing work in progress)

The cost of production is determined by taking C, adding opening work in progress, and deducting closing work in progress (D):

\( C + \text{Opening WIP} - D = \text{Cost of production} \) [1]

\( 84\,800 + 3\,400 - D = 85\,000 \) [1]

\( 88\,200 - D = 85\,000 \) [1]

\( D = 88\,200 - 85\,000 = \$3\,200 \) [1]

(g) Difference between prime cost and cost of production

Prime cost includes only the direct costs of production: direct materials (raw materials consumed), direct labour (direct wages), and any direct expenses. These are costs that can be traced directly to the specific units of goods being manufactured. [1]

These direct costs represent the minimum cost that would not exist if production did not take place. [1]

Cost of production includes prime cost plus all factory overheads (indirect manufacturing costs such as factory rent, factory insurance, and depreciation of production equipment). These are costs necessary for production but which cannot be traced to specific units. [1]

Cost of production also incorporates adjustments for changes in work in progress, so it reflects only the cost of goods that were actually completed during the period, not partly finished items still in the factory. [1]