Question

13. A machine that cot Birr 855 when it was new has an estimated trade - in value of Birr 129, if the monthly straight-line depreciation is Birr 7, what is the estimated life of the machine in years? ​

Answer 1

The straight-line depreciation method assumes that the value of an asset decreases at a constant rate over its useful life. The formula for straight-line depreciation is:

`$$\text{Depreciation} = \frac{\text{Cost of the asset} - \text{Salvage value}}{\text{Useful life of the asset}}$$`

In this case, the cost of the machine is 855 Birr, the trade-in value (which we can consider as the salvage value) is 129 Birr, and the monthly depreciation is 7 Birr. We can rearrange the formula to solve for the useful life of the asset:

`$$\text{Useful life of the asset} = \frac{\text{Cost of the asset} - \text{Salvage value}}{\text{Depreciation}}$$`

Substituting the given values:

`$$\text{Useful life of the asset} = (855 - 129)/(7)$$`

This will give us the life of the machine in months. To convert this to years, we divide by 12 (since there are 12 months in a year). Let's calculate this.

The estimated life of the machine, calculated using the straight-line depreciation method, is approximately 8.64 years.

Answer 2

To find the estimated life of the machine in years, we need to first calculate the total depreciation of the machine.

Total depreciation = Cost of machine - Estimated trade-in value

Total depreciation = 855 - 129

Total depreciation = 726

Next, we can use the monthly straight-line depreciation to find the number of months it takes for the machine to depreciate by 726.

Monthly depreciation = 7

Number of months to depreciate = Total depreciation / Monthly depreciation

Number of months to depreciate = 726 / 7

Number of months to depreciate = 103.71

Finally, we can convert the number of months to years by dividing by 12.

Estimated life of machine = Number of months to depreciate / 12

Estimated life of machine = 103.71 / 12

Estimated life of machine = 8.64 years (rounded to two decimal places)

Therefore, the estimated life of the machine is approximately 8.64 years.