Farm Power & Machinery Management 3(2+1)

Lesson 11. Cost of Operation of Farm Equipment - continued

The following steps determine the amount of depreciation by the sum-of-the years digits method:

1) Add up the numbers representing the years covered by the depreciation method.

2) Divide the total depreciation by sum of the digits of the years for the depreciation period.

3) Proportion the depreciation in reverse of the years over which the depreciation occurs.

Example: Suppose a new tractor is purchased for Rs. 3,00,000.00 and its life is 15 years. Assume salvage value as 10% of the purchase price. Find the depreciation.

Solution:

Step 1: The sum-of-the-digits for 15 years is

15+14+13+12+11+10+9+8+7+6+5+4+3+2+1 =  120

Step II: Total depreciation = 300000.00 – 10% x 300000.00 = 270000.00

Step III: Each year depreciation would be calculated as follows:

             First years’ depreciation = (L – n) x 2250.00

             For first year   n = 0

             First years’ depreciation          = (15 – 0) x 2250.00 = 33750.00

             Second years’ depreciation     = (15 – 1) x 2250.00 = 31500.00

             Third years’ depreciation        = (15 – 2) x 2250.00 = 29250.00

             Fourth years’ depreciation      = (15 – 3) x 2250.00 = 27000.00

             And so on

Comparison of depreciation cost by different methods taking life of machine 15 years, price of machine P and salvage value 10% of P is given in Table 1.

Table 1: Comparison of depreciation cost by different methods.

     (Life of machine = 15 years; Price of machine = P; Salvage value = 10% of P)

End of year	Straight-line method	Declining-balance method	Sum-of-the-years digits method
1	0.06 P	0.1153 P	0.1125 P
2	0.06 P	0.1000 P	0.1050 P
3	0.06 P	0.0867 P	0.0975 P
4	0.06 P	0.0751 P	0.0900 P
5	0.06 P	0.0651 P	0.0825 P
6	0.06 P	0.0565 P	0.0750 P
7	0.06 P	0.0490 P	0.0675 P
8	0.06 P	0.0425 P	0.0600 P
9	0.06 P	0.0368 P	0.0525 P
10	0.06 P	0.0319 P	0.0450 P
11	0.06 P	0.0277 P	0.0375 P
12	0.06 P	0.0240 P	0.0300 P
13	0.06 P	0.0208 P	0.0225 P
14	0.06 P	0.0180 P	0.0150 P
15	0.06 P	0.0156 P	0.0075 P

 

Sinking-Fund Method

Sinking fund depreciation method is primarily advantageous for use with a planned replacement internal policy. By formula the values for the sinking fund annual payment (SFP) and the value at the end of the year n are:

Where,

D_n+1         =         amount of depreciation charged for year n+1, Rs./year

V_n              =        remaining value at the end of the year n, Rs.

V_n+1           =       remaining value at the end of the year n+1, Rs.

P            =         purchase price, Rs.

S            =         salvage value, Rs.

i             =         interest rate, fraction

L            =         life of machine, years