# 12 QUESTIONS ON DEPRECIATION AND DISPOSAL OF FIXED ASSETS

One thing that is common with most long-term assets is depreciation.

Depreciation is the systematic allocation of the cost of a fixed asset over the number of periods it will use.

Depreciation is required because physical deterioration and obsolescence cause the fixed asset to lose its usefulness.

In this post, we will be dealing with questions on Depreciation and disposal of assets.

Forthwith, let's get started.

#### Question 1

Samuel PLC purchased a machine worth N100,000. It is estimated that the machine is expected to last for 5 years but no salvage value is assigned to the asset.

Determine the annual depreciation expense using straight-line depreciation.

solution:

To calculate straight-line annual depreciation, the formula is as follows:

$Dep=\frac{Cost-\text{Salvage value}}{\text{useful years}}$

$Dep=\frac{100,000-0}{5}$

$Dep=N20,000$

#### Question 2

On October 1, 2020, Daniel and Co Limited purchased a piece of equipment worth N250,000. The asset is expected to last for eight years.

Determine the depreciation expense for the year 2020 under the assumption that depreciation would occur in a straight line and the asset will be worth N10,000 at the end of its useful life

Solution:

The annual depreciation expense for the equipment in 2020 is

$Dep=\frac{250,000-10,000}{8}$

$Dep=\frac{240,000}{8}$

$Dep=N30,000$

But because the asset was only acquired on October 1, it was only utilized for three months October, November, and December, or one quarter of a year.

Therefore, the 2020 depreciation charges are as follows:

$\frac{1}{4}×N30,000=N7,500$

#### Question 3

A corporation spends N300,000 on a machine that can manufacture 3 million units of goods before wearing out.

The business anticipates producing 1 million units in the first year. Given that salvage value is not assigned to the asset, calculate the depreciation expense for the first year using the unit-of-production depreciation.

Solution:

You can calculate depreciation expenses per unit(DEPU) in units of production method as follows:

$DEPU=\frac{Cost-\text{residual value}}{\text{estimated number of units}}$

$DEPU=\frac{300,000-0}{3,000,000}$

$DEPU=0.10$

So, in the first year, when the company will produce 1 million units, the depreciation charge will be:

$Dep=0.10×1,000,000$

$Dep=N100,000$

#### Question 4

Equipment purchased on January 1 for N48,000 also has a salvage value of N3,000.

The current year's depreciation expense is N5,000 and the balance of the accumulated depreciation account, after adjustment, is N20,000.

If the company use straight-line depreciation, What are the asset's remaining useful years?

Solution:

We need to first determine the asset's total useful years.

$5,000=\frac{48,000-3,000}{n}$

$5,000n=45,000$

$n=9$

The total number of years is 9.

Now we need to prepare a depreciation table to know the current year of the asset which is expected to have an accumulated depreciation balance of N20,000,

Year Book value (year start) depreciationAccumulated depreciation Book value (year-end)
Year 1 N48,000N5,000N5,000N43,000
Year 2 N43,000N5,000N10,000N38,000
Year 3 N38,000N5,000N15,000N33,000
Year 4 N33,000N5,000N20,000N28,000
Year 5 N28,000N5000N25000N23,000
Year 6 N23,000N5,000N30,000N18,000
Year 7 N18,000N5,000N35,000N13,000
Year 8 N13,000N5,000N40,000N8,000
Year 9 N8,000N5,000N48,000N3,000

As you can see, it is in the fourth year that the balance of the accumulated depreciation account after adjustment is N20,000,

Therefore,  the asset is now in its fourth year of use, and the asset remaining useful is 9 minus 4, which is 5 years.

#### Question 5

A motor van was bought for N20,000 on 1 September 2020. Depreciation was charged at 20% using reducing balance depreciation.

The asset was sold for N18,0000 after being used for three years. Determine the gain or loss from the asset's disposal.

Solution:

Note: Profit or loss of fixed asset disposal is calculated as the selling price less the net book value of the asset at the time the asset was sold.

When the selling price of an asset exceeds its net book value, the company makes a profit on the asset's disposal.

When an asset is sold for less than its net book value, the company suffers a loss on asset disposal.

As you might probably imagine, reducing balance depreciation is calculated as follows:

Depreciation=depreciation rate × Net book value

For the first year, the depreciation charge will be:

$Dep=\frac{20}{100}×20,000=4,000$.

The closing net book value will be:

$NBV_1=20,000-4,000=16,000$

The annual depreciation charges for the second year are:

$Depreciation=\frac{20}{100}×16,000=3,200$

The Second year net book value is:

$NBV_2=16,000-3,200=12,800$.

For the third year, the depreciation charge will be:

$\frac{20}{100}×12,800=2,560$

The net book value of the asset is:

$NBV_3=12,800-2560=10,240$.

The asset was sold at the end of the third year for N18,000, which means the company earned a profit of 18,000-10,240, or 7,760.

#### Question 6

Equipment purchased by a firm worth N250,000 is expected to have a scrap value of N90,000 at the end of its useful life of 4 years.

However, at the end of the third year, the equipment was sold for N150,000. Calculate the profit or loss that the firm earned from selling the asset given that depreciation was made on a straight-line basis

Solution:

$Dep=\frac{250,000-90,000}{4}=40,000$

Now, let's draw the depreciation schedule

Year Book value (year start) depreciationAccumulated depreciation Book value (year-end)
Year 1 N250,000N40,000N40,000N210,000
Year 2 N210,000N40,000N80,000N170,000
Year 3 N170,000N40,000N120,000N130,000
year 4N130,000N40,000N160,000N90,000

At the end of the third year, the equipment has a net book value of N130,000.

So, the profit earned at the end of the third year, when the equipment was sold, is N20,000 (N150,000-130,000).

#### Question 7

A company bought a machine for N2,400,000 on January 1, 2020. The company initially estimated the useful life to be 3 years with no salvage value, and that straight-line depreciation will be used.

But, on January 1, 2021, the company decides that the equipment will now be used for 5 years. What is the depreciation charge for 2021?

Solution:

Initially, the company predicted a 3-year useful life. Using straight-line depreciation, it can be calculated as follows:

$Dep=\frac{2,400,000-0}{3}=800,000$

Hence, the depreciation charge for 2020 will be 800,000.

However, at the beginning of 2021, the company decides that the machine will be for five years. However, we have already depreciated the machine for one year, using straight-line depreciation.

As a result, the machine's remaining balance will be 2,400,000-800,000, or 1,600,000.

Now, the depreciation expenses for 2021 will be:

$Dep=\frac{1,600,000}{4}=N400,000$

#### Question 8

A machine costs N10,000 and has a scrap value of N1,000 at the end of its five years. It is estimated that the machine can produce 90,000 units. Using production methods,

1. Calculate the depreciation per unit.

2. If we assumed that the machine was used to produce 20,000 units of goods for the first year, 30,000 for the second and 10,000 units for the third year, what will be the carrying value at the end of the third year

Solution:

1. The depreciation per unit is calculated as follows:

$Dep=\frac{N10,000-N1,000}{90,000}=N0.10 \text{per unit}$.

2. Since the depreciation per unit is 0.10, and 20,000 units of goods were produced in the first year, then the depreciation charge for the first year is:

$Depreciation=0.10×20,000=2,000$.

The net book value will be 10,000-2,000=8,000.

For the second year,

$Depreciation=0.10×30,000=3,000$.

The net book value will be 8,000-3,000=5,000.

For the third year.

$Depreciation=0.10×10,000=1,000$.

The net book value will be 5,000-1,000=4,000.

Therefore, the carrying value at the end of the third year is N4,000.

#### Question 9

A fixed asset with a cost of N30,000 was sold for N6,000. At the date of disposal, the net book value of the asset is N3,000. Calculate the profit or loss earned on the disposal of the asset.

Solution:

As I have consistently emphasized, a company makes a gain on the disposal of an asset if the selling price is greater than the net book value of the asset at the date of disposal.

The reverse is also true. If the selling price is less than the asset's net book value at the time of disposal, the company incurs a loss.

In relation to this question, N3000 is the asset book value as of the disposal date. The asset was sold for N6,000, signifying a gain of N3,000.

Hence, the company make N3,000 on the disposal of the asset.

#### Question 10

A motor vehicle with a cost of N1,000,000 and accumulated depreciation of N900,000 is sold for N80,000. What is the gain or loss on disposal of the motor vehicle?

Solution:

Net book value is the asset's cost minus accumulated depreciation

Accordingly, the net book value of the motor vehicle is N1,000,000 - N900,000 or N100,000.

This time, the asset was sold for N80,000. As a result, a loss of N20,000 is incurred on the disposal of the asset.

#### Question 11

Eighteen years ago, Company XYZ bought a plant asset worth N1,000,0000. The asset has a scrap value of 100,000. Currently, the asset has an accumulated depreciation of N900,000. Calculate the rate on which depreciation has been charged since it was bought assuming depreciation is on a straight-line basis.

Solution:

Straight line basis means the depreciation rate is constant.

To calculate the depreciation rate on a straight-line basis. The formula is:

$\text{Depreciation rate}=\frac{\text{Annual Depreciation Amount} \times 100}{\text{Asset's cost}}$

Given that the asset has been used for 18 years and has accumulated N900,000 in depreciation, the annual depreciation is N50,000.

Accordingly, the depreciation rate is:

$\text{Depreciation rate}=\frac{50,000 \times 100}{1,000,000}=5\%$.

#### Question 12

A equipment worth N360,000 has a useful life span of n years and an expected disposal value of N12,000 with annual depreciation of N69,600. Using the reducing balance method, what will be the depreciation charges for Year 2 (ignore residual value)?

Solution:

We have to determine the rate and number of years using straight-line depreciation before we can solve using reducing the balance.

The number of years is as follows:

$n=\frac{360,000-12,000}{69,600}=5$

The rate of depreciation is annual depreciation divided by the depreciable value

$R=\frac{69,600}{348,000}$

$R=0.2$

Expressed in percentage,

R=20%

Since we know the rate of depreciation, we can solve it using reducing the balance depreciation

For the first year, depreciation will be calculated as follows:

$\frac{20}{100}×360,000=72,000$

Net book value will be 360,000-72,000 or 288,000.

For the second year, depreciation charges are

$\frac{20}{100}×288,000=57,600$

Therefore, the depreciation charge for the second year is 57,600.

That will be all for now. Meanwhile, remember to subscribe to our telegram channel so that you can access free quizzes like the one below.

Which of the following is not a depreciable asset?

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