Farm Power & Machinery Management 3(2+1)

Lesson 12. Interest on Investment

Where,

I  =  annual interest charge, Rs./year

P =  purchase price, Rs.

S =  salvage value, Rs.

i  =  interest rate, per cent

Insurance and Shelter

Insurance and shelter charges together are taken @ 2% of the purchase price per year.

Consideration of Inflation in Depreciation Analysis of Farm Equipment

Any consideration of cash flows in today’s economy must include an effect of inflation. Inflation can be defined in terms of an annual percentage that represents the rate at which current years prices have increased over the previous year’s prices. It has a compounding effect. Because of inflation, the cost of farm equipment or any other product continues to rise. Hence, inflation affects adversely the purchasing power of money. The future prices of farm equipment in the n^th year at constant inflation rate can be represented by

F  =  P (1 + I)ⁿ                                                         ----------------  (1) 

Where.

F = Future price in the n^th year, Rs.

P = Purchase price, Rs.

I  = Inflation rate, fraction

If the inflation changes in each year, then the future price of the farm equipment would be

F  =  P (1 + I₁) (1 + I₂)   ----------   (1 + I_n)           ---------------   (2)

If constant inflation rate is taken as 10%, then the future price of the product after 10 years would be (using equation 1)

F  =  P (1 + 0.1)¹⁰       =    2.59 P

i.e. the future price of the product will inflate to 2.59 times the purchase price in 10 years.

The effect of inflation can be included in the depreciation analysis. The depreciation of a machine under constant inflationary condition using straight-line method can be written as

Where,

CD_n =  Cumulative depreciation charges up to n^th year, Rs.

n     =  Number of years elapsed after the purchase of the machine

L     =  Life of machine, years

P    =  Purchase price, Rs.

S    =  Salvage value of the machine

Annual depreciation charge (D_n) in the n^th year will be

D_n  =  CD_n - CD_n-1

and future value of machine at the end of n^th year (V_n)

V_n  =  Future price at the end of n^th year - CD_n

      = P (1 + I)ⁿ n  -  n/L  [ P (1 + I)ⁿ - S ]

Taking life of the machine as 15 years and salvage value as 10% of the inflated price of the machine, equation (3) reduces to

Similarly, cumulative depreciation charge up to (n-1)^th year may be written as

CD_n-1  =  0.06 (n-1) P ( 1 + I)^n-1                     ---------------   (5 )

Annual depreciation charge (D_n) in the n^th year will be

D_n  =  CD_n - CD_n-1

      =  0.06 n P  (1 + I)ⁿ  -   0.06 (n-1) P ( 1 + I)^n-1

      =  0.06  P  [ n (1 + I)ⁿ  -   (n-1)  ( 1 + I)^n-1   ]        -------------   (6)

The remaining value of the machine after n^th year (V_n ) may be obtained as

V_n  =  Future price at the end of n^th year  -  cumulative depreciation value up to n^th year

=  P (1 + I)ⁿ  -  D_n

=  P (1 + I)ⁿ  -  0.06 n P (1 + I)ⁿ

=  P (1 + I)ⁿ [ 1 -  0.06 n ]                               --------------   (7)

Variation in future price, total depreciation cost and remaining value of a machine as a function of purchase price P at constant 10% annual inflation rate under straight-line method for total life of machine 15 years are given in Table 2.

Table 2:  Comparison of future price, depreciation cost and remaining value of machine as a function of purchase price.

End of year	Future price	Total depreciation	Remaining value
1	1.100 P	0.0660 P	1.0340 P
2	1.210 P	0.1452 P	1.0648 P
3	1.331 P	0.2396 P	1.0914 P
4	1.464 P	0.3514 P	1.1126 P
5	1.611 P	0.4833 P	1.1277 P
6	1.772 P	0.6379 P	1.1341 P
7	1.949 P	0.8186 P	1.1304 P
8	2.144 P	1.0291 P	1.1149 P
9	2.358 P	1.2733 P	1.0847 P
10	2.594 P	1.5564 P	1.0376 P
11	2.853 P	1.8830 P	0.9700 P
12	3.138 P	2.2594 P	0.8786 P
13	3.452 P	2.6926 P	0.7594 P
14	3.797 P	3.1895 P	0.6075 P
15	4.177 P	3.7593 P	0.4177 P