Farm Power & Machinery Management 3(2+1)

Lesson 19. Replacement of farm machinery

The time of replacement decisions depends on the accumulated costs over a period of years. The annual cost curve as well as the accumulated average cost curve for a machine is shown in Fig. 1. Both the curves intersect at a point. Theoretically, the time to replace a machine is when the annual cost starts to exceed the average accumulated cost. However, machine repair rate really determines the time of replacement. One method of establishing the time of replacement is to determine that the cost per unit of use has reached its lowest value.

Case I: Repair is proportional to use

Total cost,       C         = FC + RC X

Where,

C         = Total repair cost

FC       = Fixed cost

RC       = Repair cost

X         = Number of ha of machine used

In this case, the lowest cost/ha can only be attained with indefinite use of machine as shown in Fig. 1.

Case II: Repair cost increases with use

C = FC + R₁ C X + R₂ C X²

Where,

C         = Total repair cost

FC       = Fixed cost

R₁C     = Repair cost rate proportional to use

R₂C     = Repair cost rate that increases with use

X         = Number of hectare of machine use

Repair cost per hectare is given by

 C             FC

----       = ------- + R₁C + R₂C X 

 X              X

The time of replacement is defined by the minimum cost point. If replacement is delayed beyond this point, costs are expected to rise due to the increasing repair cost.

For minimum cost

  dC                    dC           FC

------     = 0, i.e. -------  = - ------- + 0 + R₂C = 0

  dX                    dX            X²

 

i.e.       X²        = FC/ R₂C

 

Or,       X         = [ FC/R₂C ]^1/2

The accumulated repair cost will depend upon the type of repair rate. For constant repair rates, the effect of repair on replacement is ignored. For implements, which have an increasing repair rate, the repair cost is given by

Where,

Cr        = Accumulated repair cost up to Year n, Rs

Rr        = Value of repair rate at a given accumulated hours of use, expressed 

                in %P/100 hours

P          = Purchase price, Rs

Ah       = Accumulated hours

H         = Average hourly use per year

Obsolescence should be considered in determining the proper time of replacement. Accumulated cost of obsolescence can be expressed as

Co = 1/2 (Fo n²)

Where,

Co       = Accumulated cost of obsolescence, Rs

Fo        = Obsolescence factor, Rs/year

N         = Number of years

In this case, the depreciation can be expressed in terms of percentage of purchase price at the beginning of year n as

Vn       = 68 - 4.2 n                  for tractors

Vn       = 60 - 4.6 n                  for other implements

Where,

Vn       = Remaining value at any time, Rs

n          = Number representing age of machine in years at the beginning of year in question

The accumulated depreciation cost can be calculated as

Cd       = (100 -Vn) %P

Where,

Cd       = Accumulated depreciation cost up to year n, Rs

P          = Purchase price, Rs

Optimum replacement time would be in the year when the total accumulated cost of depreciation; repair and obsolescence per year would be the minimum.

Total cost (Ct) can be written as

 

Example: Find the optimum replacement time for the mould board plough.

Given,

Rr        = 1.5% P/100 hours

Ah       = 2500 hours

Fo        = Rs 150/year

P          = Rs 18000.00

H         = 200 hours

For implements

 

Therefore, the mould board plough should be replaced after about 9 years of use with the conditions given in the example.