Comparison of alternatives by future worth method:

In the future worth method for comparison of mutually exclusive alternatives, the equivalent future worth (i.e. value at the end of the useful lives of alternatives) of all the expenditures and incomes occurring at different periods of time are determined at the given interest rate per interest period. As already mentioned, the cash flow of the mutually exclusive alternatives may consist of expenditures and incomes in different forms. Therefore the equivalent future worth of these expenditures and incomes will be determined using different compound interest factors namely single payment compound amount factor, uniform series compound amount factor and future worth factors for arithmetic and geometric gradient series etc.

The use of future worth method for comparison of mutually exclusive alternatives will be illustrated in the following examples. Similar to present worth method, first the comparison of equal life span alternatives by future worth method will be illustrated followed by comparison of different life span alternatives. Some of the examples already worked out by the present worth method will be illustrated using the future worth method in addition to some other examples.

Example -6 (Using data of Example-1)

There are two alternatives for purchasing a concrete mixer. Both the alternatives have same useful life. The cash flow details of alternatives are as follows;

Alternative-1: Initial purchase cost = Rs.300000, Annual operating and maintenance cost = Rs.20000, Expected salvage value = Rs.125000, Useful life = 5 years.

Alternative-2: Initial purchase cost = Rs.200000, Annual operating and maintenance cost = Rs.35000, Expected salvage value = Rs.70000, Useful life = 5 years.

Using future worth method, find out which alternative should be selected, if the rate of interest is 10% per year.

Solution:

The future worth of the mutually exclusive alternatives will be compared over a period of 5 years. The equivalent future worth of the alternatives can be obtained either by multiplying the equivalent present worth of each alternative already obtained by present worth method with the single payment compound amount factor or determining the future worth of expenditures and incomes individually and adding them to get the equivalent future worth of each alternative.

The equivalent future worth of Alternative-1 is obtained as follows;

PW₁ is the equivalent present worth of Alternative-1 which is equal to - Rs.298203 (referring to Example-1). (F/P, i, n) is the single payment compound amount factor.

Now putting the value of single payment compound amount factor in the above expression;

FW₁ = -Rs.480256