    # Net Present Value Method The net present value NPV method is an important criterion for project appraisal. Profitability of a project is evaluated by this method. It is also called as present value method. Net present value is calculated by using an appropriate rate of interest which is the capital cost of a firm. This is the minimum rate of expected return likely to be earned by the firm on investment proposals.

To find out the present value of cash flows expected in future periods, all the cash outflows and cash inflows are discounted at the above rate. Net present value is the difference between total present value of cash outflows and total present value of cash inflows occurring in periods over the entire life of project. When the net present value is positive, the investment proposal is profitable and worth selecting. But if it is negative, the investment proposal is non-profitable and rejectable. The method to compute the net present value index of different investment proposals is as under.

NPV                =                      Total Present Value of All Cash Flows
Initial Investment

NPV method considers the time value of money. it compares time value of cash flows.

NPV = Present Value of Gross Earnings – Net Cash Investment

NPV can be found out from the following:

NPV    =          A1                    +          A2        ……    +          An         - C
(1+r)^1                         (1+r)^2                        (1+r)^n

Where A1, A2 are cash inflows at the end of first year and second year respectively, n is the expected life of investment proposals, r is Rate of discount which is equal to the cost of capital, C is present value of costs.

Thus NPV = Sum of Discounted Gross Earnings - Sum of Discounted Value of Cost.

Illustration 3

Let us have the initial investment cost of a project as \$200 million, cash inflows in the forth coming years is \$250 million and the market rate of interest is 20 % pa. Determine the NPV

NPV                =                          250              - 200
(1+0.20)^1

=                            250             - 200
1.2

=                      208.33             - 200   =          8.33

Hence NPV is 8.33

1. Internal Rate of Return Method

This method refers to the percentage rate of return implicit in the flows of benefits and costs of projects A. Margin defines the internal rate of return IRR “as the discount rate at which the present value of return minus costs is zero”. In other words, the discount rate which equates the present value of project with zero, is known as IRR.

Thus, IRR is the discounted rate which equates the present value of cash inflows with the present value of cash outflows. IRR is also based on discount technique like NPV method. Under this technique, the future cash inflows are discounted in such a way that their total present value is just equal to the present value of total cash outflows. It is assumed that the management has knowledge of the time schedule of occurrence of future cash flows but not of the rate of discount. IRR can be measured as:

IRR     =        A1                   +          A2        ……    +          An         - C     = 0
(1+r)^1                       (1+r)^2                     (1+r)^n

Where, A1, A2 are the cash inflows at the end of the first and second years respectively. And the rate of return is computed as follows.

C         =                    A1
(1 + r)^n

Where, 1 is the cash outflow or initial capital investment, A1 is the cash inflow at the end of first year, r is the rate of return from investment.

Illustration 4

Let us assume Capital invested in a project as \$100 million. They become \$150 million at the end of first year. Determine the rate of return.

100      =             150
(1+r)^1

100 + 100r       =         150

100r                 =          50

r                       =          50
100

=          50%

Hence the rate of return is 50%

The Certainty Equivalent Method

This method helps to ascertain the uncertainty in the investments of the project. According to this method, the estimated cash flows are reduced to a conservative level by applying a correction factor termed as certainty equivalent co-efficient. The correction factor is the ration of riskless cash flow to risky cash flow.

Certainty Equivalent Co-efficient      =       Riskless Cash Flow
Risky Cash Flow

Illustration 5

Suppose if a project is expected to generate a cash of \$24,000 and the project is risky. But the management senses that it will get atleast a cash flow of \$16,800. Determine the Certainty equivalent co-efficient.

Certainty Equivalent Co-efficient      =     16,800
24,000

=     0.7

Hence the Certainty Equivalent Co-efficient is 0.7

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