Calculation of WDV (Written Down Value) of Machine:

To calculate the WDV (Written Down Value) of the machine, we need to consider the initial cost of the machine, the depreciation rate, and any subsequent purchases or sales of the machine.

Initial Cost of the Machine:
On 1 October, a machine was purchased for $40,000.

Purchase of Machine:
On 31 January, a quarter of the machine was sold for $5,600. On the same day, a new machine was purchased for $15,000.

Depreciation Rate:
The depreciation rate is given as 10%.

Calculation Steps:

1. Calculate the depreciation for the period from 1 October to 31 January:

Depreciation for 3 months = (10% / 12) * $40,000 = $333.33

2. Calculate the adjusted cost of the machine on 31 January:

Adjusted cost = Initial cost - Depreciation for the period = $40,000 - $333.33 = $39,666.67

3. Calculate the depreciation on the new machine purchased on 31 January:

Depreciation on new machine = 10% * $15,000 = $1,500

4. Calculate the total depreciation for the year:

Total depreciation = Depreciation for 3 months + Depreciation on new machine = $333.33 + $1,500 = $1,833.33

5. Calculate the WDV of the machine on 31 January:

WDV = Adjusted cost - Total depreciation = $39,666.67 - $1,833.33 = $37,833.34

Summary:

The written down value (WDV) of the machine on 31 January is $37,833.34. This value represents the net book value of the machine after accounting for the initial cost, depreciation, and any subsequent purchases or sales. Depreciation is a systematic allocation of the cost of an asset over its useful life, and it helps in determining the value of the asset at any given point in time. By calculating the WDV, we can assess the remaining value of the machine and make informed decisions regarding its replacement, repair, or disposal. This information is essential for financial reporting, tax purposes, and decision-making within an organization.