Question

Make a schedule for all the examples provided for the following Depreciation Methods a. Straight Line Method b. Sinking Fund Method C: Matheson's Formula (2 problems) d. Double Declining Balance Method e, Sum of the Years Digit Method

Answer 1

Example 1 for Straight Line Depreciation:In this method it is assumed the book value of the asset decreases at a linear rate with the time period.

a)The initial cost of a piece of construction equipment is Rs.35000. It has useful life of 5 years. The estimated salvage value of the equipment at the end of useful life is Rs.5000. Calculate the annual depreciation and book value of the construction equipment using straight-line method.

Solution:

Initial cost of the construction equipment = Vo = Rs.35000

Estimated salvage value = SV = Rs.5000

Useful life = n = 5 years

For straight-line method, the depreciation amount for a given year is calculated using

$D=\frac{Vo-SV}{n}$ Where,Vo= initial cost of the asset,SV= salvage value of equipment,n=useful life and D= depreciation amount,Therefore

$D=\frac{35000-5000}{5}=Rs.6000$

Book value at the end of 1st year=BV1=Vo-aD=35000-(1*6000)=Rs.29000

Example 2 for Sinking Fund Depreciation:In this method it is assumed that money is deposited in a sinking fund over the useful life that will enable to replace the asset at the end of its useful life. For this purpose, a fixed amount is set aside every year from the revenue generated and this fixed sum is considered to earn interest at an interest rate compounded annually over the useful life of the asset, so that the total amount accumulated at the end of useful life is equal to the total depreciation amount i.e. initial cost less salvage value of the asset. Thus the annual depreciation in any year has two components. The first component is the fixed sum that is deposited into the sinking fund and the second component is the interest earned on the amount accumulated in sinking fund till the beginning of that year.

b)The initial cost of a piece of construction equipment is Rs.35000. It has useful life of 10 years. The estimated salvage value of the equipment at the end of useful life is Rs.5000. calculate the annual depreciation and book value of the construction equipment using sinking fund method. The interest rate is 8% per year.

Solution:

Vo = Rs.35000

SV = Rs.5000

n = 10 years

The interest rate per year = i = 8%

the depreciation amount for a given year is calculated using,

Dm = (Vo-SV)* i(1 + i)-1 (1 + i)" - 1

on putting values gives,D1=Rs.2070.88

Book value at the end of 1st year

$BVm=Vo-(Vo-SV)*\frac{[(1+i)^{m}-1]}{[(1+i)^{n}-1]}$

on putting values gives,BV1=Rs.32929.11

Example 3 on Matheson Formula/Declining Balance Method:In this method the annual depreciation is expressed as a fixed percentage of the book value at the beginning of the year and is calculated by multiplying the book value at the beginning of each year with a fixed percentage.

c)The initial cost of a piece of construction equipment is Rs.35000. It has useful life of 5 years. The estimated salvage value of the equipment at the end of useful life is Rs.5000. Calculate the annual depreciation and book value of the construction equipment using Matheson formula of Depreciation.

Solution:

Initial cost of the construction equipment = Vo = Rs.35000

Estimated salvage value = SV = Rs.5000

Useful life = n = 5 years

For Matheson Method, the depreciation amount for a given year is calculated using

$Dm=Vo(1-f)^{m-1}*f$

where ,$f=1-\left ( \frac{SV}{Vo} \right )^{\frac{1}{n}}$

therefore, f=0.32,The depreciation in 1st year is=Rs.11200

Similarly the generalized expression for book value at the end of 1st year is given as

$BVm=Vo(1-f)^{m}$

BV1=Rs.23800

Example 4 on Double Declining Balance Method:The ratio of depreciation amount in a given year to the book value at the beginning of that year is constant for all the years of useful life of the asset. When this ratio is twice the straight-line depreciation rate i.e 2/n , the method is known as double declining balance (DDB) method.

d)The initial cost of a piece of construction equipment is Rs.3500000. It has useful life of 10 years. The estimated salvage value of the equipment at the end of useful life is Rs.500000. Calculate the annual depreciation and book value of the construction equipment using double-declining balance method.

Solution:

Initial cost of the construction equipment = Vo = Rs.3500000

Estimated salvage value = SV = Rs.500000

Useful life = n = 10 years

For double-declining balance method, the constant annual depreciation rate ‘f’ is given by;

$f=\frac{2}{n}=\frac{2}{10}=0.2$

The depreciation amount for a given year is calculated using equation

$Dm=Vo(1-f)^{m-1}*f$

On putting values we get,

D1=Rs.700000

Similarly the generalized expression for book value at the end of 1st year is given as

$BVm=Vo(1-f)^{m}$

on putting values,we will get

Book value at the end of 1st year = BV1=Rs.2800000

Example 5 on Sum Year Digit Method:In this method the annual depreciation rate for any year is calculated by dividing the number of years left (from the beginning of that year for which the depreciation is calculated) in the useful life of the asset by the sum of years over the useful life.

e)The initial cost of a piece of construction equipment is Rs.3500000. It has useful life of 10 years. The estimated salvage value of the equipment at the end of useful life is Rs.500000. Calculate the annual depreciation and book value of the construction equipment using sum-of-years-digits method.

Solution:

For sum-of-years-digits method, the depreciation amount for a given year is calculated using equation

$Dm=\frac{(n-m+1)}{SOY}*(Vo-SV)$

SOY = sum of years’ digits over the useful life =n(n+1)/2=10(10+1)/2=55

on putting values we have,

Depreciation for 1st year =D1=Rs.545454.55

Book value is calculated using

where P=Vo=original value of asset,m=for paticular year and on putting values we have,

(P-SV) BV = P - X 101 SOY m(m-1)] 2 .

Book value at the end of 1st year will be=Rs.2954545.45