# 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 =__ A____1 __ + __ A____2 __…… + __ An __ -
C

(1+r)^1 (1+r)^2 (1+r)^n

Where A_{1}, A_{2} 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**

__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 =

__A__+_{1}__A__…… +_{2}__A__- C = 0_{n}

(1+r)^1 (1+r)^2 (1+r)^nWhere, A

**1**, 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 =

__A___{1}

(1 + r)^nWhere, 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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**Other topics under Factor Pricing:**

- Break Even Analysis
- Concept of Factor Cost
- Contribution Margin, Limitations of Break Even Analysis
- Criticism, Clark's Product Exhaustion Theorem
- Distributive Shares: The Product Exhaustion Theorem
- Inequality of Income, Effects of Inequality
- Interest, Gross and Pure Interest
- Investment Analysis and Social Cost Benefit
- Measurement of Inequality, Lorenz Curve
- Meaning of Minimum Wages, Benefits of Minimum Wages
- National Income Meaning and Measurement
- Price Level, Social Prestige, Conditions of Work
- Profit, Gross Profit and Net Profit
- Rent, Meaning of Economic Rent
- Time Preference Theory
- Theories of Distribution
- Theories of Profit, Rent Theory of Profit
- Value Added Approach to GNP
- Quasi Rent, Distinction Between Rent and Quasi Rent