Future worth method

In most of the practical decision environments, executives will be forced to select the best alternative from a set of competing alternatives.

Let us assume that an organization has a huge sum of money for potential investment and there are three different projects whose initial outlay and annual revenues during their lives are known. The executive has to select the best alternative among these three competing projects.

There are several bases for comparing the worthiness of the projects. These bases are:

1.   Present worth method

2.   Future worth method

3.   Annual equivalent method

4.   Rate of return method

FUTURE WORTH METHOD

ü  In the future worth method of comparison of alternatives, the future worth of various alternatives will be computed.

ü  Then, the alternative with the maximum future worth of net revenue or with the minimum future worth of net cost will be selected as the best alternative for implementation.

i.Revenue-Dominated Cash Flow Diagram

A generalized revenue-dominated cash flow diagram to demonstrate the future worth method of comparison is presented in Fig.

In Fig. P represents an initial investment, Rj the net-revenue at the end of the jth year, and S the salvage value at the end of the nth year.

The formula for the future worth of the above cash flow diagram for a given interest rate, i is

FW(i) = –P(1 + i)n  + R1(1 + i)n–1  + R2(1 + i)n–2  + ...

+ R j(1 + i)n–j  + ... + Rn + S

In the above formula, the expenditure is assigned with negative sign and the revenues are assigned with positive sign.

ii.Cost-Dominated Cash Flow Diagram       

A generalized  cost-dominated  cash      flow  diagram       to  demonstrate  the  future worth method

of comparison is given in Fig.

In Fig. 5.2, P represents an initial investment, Cj the net cost of operation and maintenance at the end of the j th year, and S the salvage value at the end of the nth year.

The formula for the future worth of the above cash flow diagram for a given interest rate, i is

FW(i) = P(1 + i)n + C1(1 + i )n–1 + C2(1 + i)n–2 + ...  + Cj(1 + i)n–j  + ... + Cn – S

EXAMPLE

Consider the following two mutually exclusive alternatives:

At i = 18%, select the best alternative based on future worth method of comparison.

Solution Alternative A

Initial investment, P = Rs. 50,00,000

Annual equivalent revenue, A = Rs. 20,00,000

Interest rate, i = 18%, compounded annually

Life of alternative A = 4 years

The cash flow diagram of alternative A is shown in Fig.

The future worth amount of alternative B is computed as

FWA(18%)  = –50,00,000(F/P, 18%, 4) + 20,00,000(F/A, 18%, 4)

=  –50,00,000(1.939) + 20,00,000(5.215)

 = Rs. 7,35,000

Alternative B

Initial investment, P = Rs. 45,00,000

Annual equivalent revenue, A = Rs. 18,00,000

Interest rate, i = 18%, compounded annually

Life of alternative B = 4 years

The cash flow diagram of alternative B is illustrated in Fig..

The future worth amount of alternative B is computed as

FWB(18%) = – 45,00,000(F/P, 18%, 4) + 18,00,000 (F/A, 18%, 4)

=  – 45,00,000(1.939) + 18,00,000(5.215)

=  Rs. 6,61,500