SKEDSOFT
Introduction:
Replacement model is the part of operation research mostly used in the industries when a purchased items like machinery, buildings efficiency is reduced or wear out due to much usage.
Comparing of replacement alternative:
Sometimes a business man may come across a problem, when he wants to purchase a machine or a vehicle for his business. He may have different models with comparatively equal price and with different maintenance and other expenses. In such cases, he can use present worth concept to select the right type of machine or a vehicle. Here the present value of all future expenditures and revenues is calculated for each alternative and the one for which the present value is minimum is preferred. Let
Q = Annual cost or purchase price in Rs.
i = Annual interest rate.
t = Period in years.
P = Principal amount in Rs.
S = Scrap value or salvage value in Rs.
The present value of total cost is given by:
P Q (Pwfs for i % interest rate for n years) – S (Pwf for i % interest for n years)
Similarly, if the annual operating costs vary for different years then the present value of these costs will be calculated on the basis of time period for which these expenditures are made. i.e. say for example, if Q1, Q2, Q3…….Qn is the operating costs for different years, then the present value of the operating cost during 'n' years will be given by:
Q1(Pwfs at i % interest for 1 year) Q2 (Pwfs at i % for 2 years) ……….. Qn (Pwfs at i % interest for n years).
Now present value of total cost will be:
P Q1 (Pwfs at i % interest for 1 year) Q2 (Pwfs at i % interest rate for 2 years) Q3 (Pwfs at i % rate of interest for 3 years) ………… Qn (Pwfs at i% interest for n years) – S (Pwf at i % interest for n years).
Example .
An entrepreneur is considering purchasing a machine for his factory. The related data for alternative machines are as
As an advisor of the company, you have been asked to select the best machine considering 12 % normal rate of return per year. Given that: Present worth factor series @ 12 % for 10 years is 5.650 Present worth factor @ 12 % for 10 th year is 0.322
Solution
Machine B is having less present value of total cost. Hence to purchase the machine B.
