The cost of a machine is Rs. 20,000 and its estimated useful life is 10 years. The scrap value of the machine, when its value depriciates at 10% p.a, is: use (0.9)10 = 0.35
Rs. 7000
Understanding Machine Depreciation and Scrap Value
Depreciation is the decrease in the value of an asset over time due to wear and tear, obsolescence, or usage. Scrap value, also known as salvage value or residual value, is the estimated value of an asset at the end of its useful life.
There are different methods to calculate depreciation, such as the Straight-Line Method and the Reducing Balance Method. The question specifies depreciation at a percentage of the written down value each year, indicating the use of the Reducing Balance Method.
Reducing Balance Method Explained
The Reducing Balance Method (also known as the Diminishing Balance Method or Written Down Value Method) calculates depreciation on the book value (or written down value) of the asset each year, rather than on its original cost. This results in higher depreciation charges in the initial years and lower charges in later years.
Calculating Scrap Value using Reducing Balance Method
The formula to calculate the value of an asset (scrap value) after 'n' years using the Reducing Balance Method is:
\( V_n = P(1 - r)^n \)
Where:
- \( V_n \) = Value of the asset after 'n' years (Scrap Value)
- \( P \) = Original Cost of the asset
- \( r \) = Annual rate of depreciation (as a decimal)
- \( n \) = Useful life of the asset in years
Step-by-Step Calculation
Let's apply the formula using the given information:
- Original Cost (\( P \)) = Rs. 20,000
- Annual Depreciation Rate (\( r \)) = 10% = \( \frac{10}{100} \) = 0.10
- Useful Life (\( n \)) = 10 years
We need to calculate the Scrap Value (\( V_{10} \)) after 10 years.
Using the formula:
\( V_{10} = 20000 \times (1 - 0.10)^{10} \)
\( V_{10} = 20000 \times (0.9)^{10} \)
The question provides the value of \( (0.9)^{10} \) as 0.35.
\( V_{10} = 20000 \times 0.35 \)
Now, we perform the multiplication:
\( V_{10} = 7000 \)
So, the scrap value of the machine after 10 years, depreciating at 10% per annum using the reducing balance method, is Rs. 7000.
Summary of Calculation
| Description | Value |
|---|---|
| Original Cost (P) | Rs. 20,000 |
| Depreciation Rate (r) | 10% or 0.10 |
| Useful Life (n) | 10 years |
| Factor \( (1-r)^n = (0.9)^{10} \) | 0.35 |
| Scrap Value \( V_n = P \times (1-r)^n \) | \( 20000 \times 0.35 \) = Rs. 7000 |
The calculated scrap value matches option 2.
Revision Table: Key Depreciation Concepts
| Term | Definition | Relevance to Question |
|---|---|---|
| Depreciation | Allocation of the cost of an asset over its useful life. | The process applied to the machine's value. |
| Original Cost | The purchase price of the asset plus installation costs. | The initial value (Rs. 20,000) used in calculation. |
| Useful Life | The estimated period an asset is expected to be used. | Given as 10 years for the machine. |
| Scrap Value | Estimated residual value at the end of useful life. | The value we needed to calculate. |
| Reducing Balance Method | Depreciation calculated on the book value each year. | The method implied by the question's rate format. |
Additional Information: Depreciation Methods
Apart from the Reducing Balance Method, another common method is the Straight-Line Method.
Straight-Line Method
In the Straight-Line Method, the depreciation expense is the same amount each year. The formula is:
\( \text{Annual Depreciation} = \frac{\text{Original Cost} - \text{Scrap Value}}{\text{Useful Life}} \)
This method is simpler but doesn't reflect the potentially higher usage or efficiency of an asset in its early years compared to later years, which the Reducing Balance Method attempts to do.
The choice of depreciation method can impact the reported profit of a company each year because the depreciation expense is deducted from revenue.
Important Questions from Mathematics
Let C be the circle of radius π/4, centered at z = \(\frac{1}{4}\) in the complex z-plane that is traversed counter-clockwise. The value of the contour integral ∮c\(\frac{{{{\rm{z}}^{\rm{2}}}}}{{{\rm{si}}{{\rm{n}}^{\rm{2}}}{\rm{4z}}}}\)dz is
Let X be a real-valued random variable such that E[eX] < ∞ and E[eX] = eE[X]. Then which of the following is correct?
There are three urns U1, U2, U3, each with balls of two colours. U1 contains 2 white balls and 3 black balls, U2 contains 3 white balls and 2 black balls and U3 contains 5 white balls and 5 black balls. An urn is chosen at random and a ball is drawn from that urn at random. What is the probability that U2 was chosen given that the ball picked is black in colour?
Let {Xn ∶ n ≥ 0} be a two state Markov chain with state space S = {0, 1} and transition matrix
P = \(\begin{bmatrix} \frac{1 }{2 }&\frac{ 1}{2 } \\\ \frac{1 }{ 3} &\frac{ 2}{3 } \end{bmatrix} \)
Assuming X0 = 0, the expected return time to 0 is
Let X and Y be independent Exponential random variables with means \(\rm \frac{1}{\lambda} \ and \ \frac{1}{\mu}\) respectively with λ ≠ μ. Let fz(z) denote the density function of Z = X + Y. Then for z > 0,
