Depreciation Methods

Depreciation is the systematic allocation of the depreciable amount of a tangible asset over its estimated useful life. It is an allocation process, not a direct measurement of market value.

Term	Meaning
Original cost ($C$)	Purchase price plus directly attributable acquisition, transport, installation, and commissioning cost
Residual / salvage value ($S$)	Estimated disposal value less disposal cost at the end of useful life
Useful life ($n$)	Expected service period or productive capacity
Depreciable amount	$C-S$ under the simplified model
Book value ($BV_t$)	Cost less accumulated depreciation at time $t$

Depreciation vocabulary

Straight-Line Method

Caution

Key Formula — Straight-line depreciation

$$\boxed{D=\frac{C-S}{n}}, \qquad \text{annual straight-line rate}=\frac{1}{n}\times100\%.$$

For a machine costing Rs. 500,000 with Rs. 50,000 residual value and a ten-year life,

$$D=\frac{500{,}000-50{,}000}{10}=\text{Rs.~}45{,}000\text{ per year}.$$

Declining-Balance Method

Caution

Key Formula — Constant-rate declining balance

$$D_t=rBV_{t-1}, \qquad r=1-\left(\frac{S}{C}\right)^{1/n}.$$

The rate is chosen so the theoretical year-$n$ book value reaches $S$.

For $C=\text{Rs.~}100{,}000$, $S=\text{Rs.~}10{,}000$, and $n=5$,

$$r=1-(0.1)^{1/5}=1-0.6310=0.369=36.9\%.$$

Year	Beginning $BV$	Depreciation	Ending $BV$
	100,000	36,900	63,100
2	63,100	23,284	39,816
3	39,816	14,692	25,124
4	25,124	9,271	15,853
5	15,853	5,850	$\approx 10{,}003$

Declining-balance schedule, rounded to rupees

The small residual difference arises from rounding the rate and annual charges; the final charge is adjusted in practice so book value does not fall below the estimated residual value.

Sum-of-Years’-Digits Method

Caution

Key Formula — SOYD depreciation

$$SYD=\frac{n(n+1)}{2}, \qquad \boxed{D_t=\frac{n-t+1}{SYD}(C-S)}.$$

For $C=\text{Rs.~}100{,}000$, $S=\text{Rs.~}10{,}000$, and $n=5$, $SYD=5(6)/2=15$.

Year	Fraction of Rs. 90,000	Depreciation (Rs.)
	$5/15$	30,000
2	$4/15$	24,000
3	$3/15$	18,000
4	$2/15$	12,000
5	$1/15$	6,000
Total		90,000

Sum-of-years’-digits schedule

Method	Expense pattern	Appropriate logic
Straight line	Equal charge each year	Benefits consumed relatively evenly
Declining balance	High early, decreasing later	Productivity or obsolescence is greater in early years
Sum-of-years’ digits	High early, decreasing by arithmetic weights	Accelerated allocation without a constant book-value rate

Depreciation patterns compared

Accelerated depreciation can bring tax deductions forward where tax rules allow, but financial-reporting method selection should reflect the pattern in which economic benefits are consumed and applicable standards.