A machine, the life of which is estimated to be 15 years, costs ₹40,000. Calculate the scrap value at the end

Exercise 7.7 · Q4

Q. A machine, the life of which is estimated to be 15 years, costs ₹40,000. Calculate the scrap value at the end of its life if it is depreciated at a constant rate of 10% per annum.

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Concept understanding — Straight Line Depreciation

Straight Line Depreciation: The Intuition

Imagine you buy a delivery van for your business. It costs ₹10,00,000. You expect to use it for 5 years, after which you'll sell it for ₹1,00,000 as scrap.

Does the van lose all its value in year 1? No. It loses value gradually, year after year, as you drive it, put miles on it, and it gets older. The van is an asset — something of value you own — and its value decreases over time. That decrease is called depreciation.

The simplest way to think about this loss is: the van loses the same amount of value every year. That's straight line depreciation. It's like slicing a cake into equal pieces — each year gets an equal share of the total loss in value.

The Precise Statement

\text{Annual Depreciation} = \frac{\text{Cost of Asset} - \text{Residual Value}}{\text{Useful Life}}

Where:

Cost of Asset = What you paid to buy and get it ready for use (purchase price + delivery + installation, etc.)
Residual Value (also called scrap value or salvage value) = What you expect to get when you sell it at the end of its useful life
Useful Life = How many years you expect to use the asset

Applying It to Our Van

Cost = ₹10,00,000

Residual Value = ₹1,00,000

Useful Life = 5 years

\text{Annual Depreciation} = \frac{10,00,000 - 1,00,000}{5} = \frac{9,00,000}{5} = ₹1,80,000

So every year, you record ₹1,80,000 as depreciation expense. After 5 years, the van's book value (original cost minus total depreciation) will be exactly ₹1,00,000 — its residual value.

The Depreciation Schedule

Year	Book Value at Start of Year	Depreciation Expense	Book Value at End of Year
1	₹10,00,000	₹1,80,000	₹8,20,000
2	₹8,20,000	₹1,80,000	₹6,40,000
3	₹6,40,000	₹1,80,000	₹4,60,000
4	₹4,60,000	₹1,80,000	₹2,80,000
5	₹2,80,000	₹1,80,000	₹1,00,000

Notice: the depreciation expense is constant every year. That's the "straight line."

Why Use This Method? …

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"Depreciated at a constant rate of 10% per annum" is the written-down-value method, so the scrap value after 15 years is $40000(0.90)^{15}=40000(0.205891)\approx ₹8235.65\ (\approx ₹8236)$ , agreeing with the textbook answer key of ₹8224 up to rounding.

Under the written-down-value (reducing-balance) method only a fixed percentage of the current book value is written off each year, so the book value stays positive and never goes negative. After $n$ years the book value is

V_n=C(1-r)^n,

with cost $C=₹40{,}000$ , rate $r=0.10$ and life $n=15$ years.

Set up the scrap value. $V_{15}=40000(1-0.10)^{15}=40000(0.90)^{15}.$ …

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Q.A machine, the life of which is estimated to be 15 years, costs ₹40,000. Calculate the scrap value at the end of its life if it is depreciated at a constant rate of 10% per annum.

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