Example -7

There are two alternatives for a construction firm to purchase a road roller which will be used for the construction of a highway section. The cash flow details of the alternatives are as follows;

Alternative-1: Initial purchase cost = Rs.1500000, Annual operating cost = Rs.35000 starting from the end of year ‘2' (negligible in the first year) till the end of useful life, Annual revenue to be generated = Rs.340000 for first 4 years and then Rs.320000 afterwards till the end of useful life, Expected salvage value = Rs.430000, Useful life = 8 years.

Alternative-2: Initial purchase cost = Rs.1800000, Annual operating cost = Rs.25000, Annual revenue to be generated = Rs.365000, Expected salvage value = Rs.550000, Useful life = 8 years.

Find out the most economical alternative on the basis of equivalent future worth at the interest rate of 9.5% per year.

Solution:

The cash flow diagram of Alternative-1 is shown in Fig. 2.17.

Fig. 2.17 Cash flow diagram of Alternative-1

From Fig. 2.17, it is observed that there are two uniform amount series for the annual income i.e. first series with Rs.340000 from end of year ‘1' till end of year ‘4' and second one with Rs.320000 from end of year ‘5' till end of year ‘8'. For the first series, the equivalent present worth at time ‘0' will be calculated first and then it will be multiplied with single payment compound amount factor i.e. (F/P, i, n) to calculate its equivalent future worth . For the second uniform series with Rs.320000, the future worth will be calculated by multiplying the uniform amount i.e. Rs.320000 with uniform series compound amount factor by taking the appropriate ‘ n' i.e. number of years.

The annual operating cost is in the form of a uniform amount series, which starts from end of year ‘2' till the end of useful life i.e. the uniform amount series is shifted by one year.

The equivalent future worth of the Alternative-1 i.e. FW₁ is computed as follows;

Putting the values of different compound interest factors in the above expression results in the following;

FW₁ = Rs.728849