Before going into the detail of **Net Present Value** (NPV) and **Internal Rate of Return** (IRR), few of the basic concepts are important to know.

**Present Value:**

The present value is an important concept of **Financial Management**. It is concerned with the present value of cash flows that are taking place in some future. In short the apples are compared with apples. This means that all the cash flows taking place at different time interval must be compared at one point of time in order to determine their present value. For example if one has $ 100 in his hand and after ten years he may also possess $ 100. As both amounts are equal but their actual value is different, which means that the present value of today’s $ 100 is more than the ten years after $ 100.

**Discounting:**

To bring the future cash flow back to the present is called discounting. In order to compare the two cash flows taking place at different time intervals, first of all both of these should be discounted back at some common present time. For this purpose, there should be some interest rate (opportunity cost) that helps in the discounting process.

**Net Present Value (NPV):**

Net present value is the most important concept and technique of the **Capital Budgeting** area of financial management. All the future cash flows are discounted back at the present and subtracted from the initial investment to give the value of net present value. If one wants to start a new project then how can he measure the feasibility and profitability of that project? The simple and effective way is through net present value calculation. In net present value calculation, all the expected cash flows are forecasted and discounted with a certain discount rate or interest rate. If the net present value of a project is more than zero then that project is favorable for the investor. The formula of net present value is given below.

**Net Present Value Formula**

Net Present Value = -I_{o}+∑CF_{t} / (1+i)^{t}

In the above equation “I_{o}” means the initial investment that is in the shape of cash outflow.

“CF_{t}” are the cash flows that are occurring at different time intervals.

“i” is the interest rate.

“t” is the year in which cash flow occur.

Although, the net present value is very powerful technique of capital budgeting, but still, it has certain drawbacks. The main reason is that the cash flows are the estimated values that are not actually real, also the discount rate is determined subjectively. But, still net present value is using frequently in the financial management in ascertaining the value of any investment or even the whole company. Moreover if there are more 2 or 3 projects available to invest, then the project that has higher net present value is the better one.

**Example:**

Suppose David wants to start a retail store in a certain market. He makes estimation of initial investment of $ 200,000, the revenue of the first year is $ 12,000 per month and the second year is $ 18,000 per month. The discount rate is based on expected rate of return that your business must generate. Suppose the discount rate is 10%, so if the new business of retail store of David return him less than the discount rate then it is not feasible for him to invest in that business as he can easily earn 10% return by putting his amount into the bank. Now David need to know whether this new project is feasible for him or not. For this purpose he needs to calculate the NPV of the project.

**Solution:**

Initial Investment = I_{o} = $ 200,000

Cash inflow in the first year = CF_{1}= 144,000

Cash inflow in the second year = CF_{2}= 216,000

Putting values in the formula of NPV

NPV = -I_{o}+CF_{1} / (1+i)^{1} + CF_{2} / (1+i)^{2}

NPV = -200,000 + 144,000 / (1.1) + 216,000 / (1.1)^{2}

NPV = -200,000 + 130,909 + 178,512

NPV = 109,421

As the answer of net present value is more than zero. So, this project of starting a new retail store is favorable for David.

**Internal Rate of Return (IRR)**

Another important technique of capital budgeting is the Internal Rate of Return (IRR). It is similar in calculation with the net present value, but IRR is expressed in percentage. Due to this fact it can be compared with the other interest rates, cost of capital and inflation rate etc.

Another feature of IRR is that it remains constant throughout the life of the project. This means the IRR for the first year of a project is the same for the second year and so on. IRR is actually break-even point of the project. At this rate, the project returns all the initial investment throughout its life.

The formula of IRR is similar to NPV, but there is a small difference in its calculation. The equation of NPV is used for the determination of IRR, but in that equation the value of NPV is considered to be zero. After keeping the NPV equal to zero, the value of “i” is determined that gives the value of IRR, because IRR is actually a rate of return on the investment. In simple words, the IRR is that value of “i” at which the NPV value is equal to zero.

In the calculation of IRR the **Trial and Error** method or iteration method is used, because it is much effort and time consuming to solve the higher degree polynomial equations. In trial and error method the value of “i” is set to make the equation equal to zero. Mostly the calculation demands more than one try. So if the equation does not result in the zero answer, another value of “i” is set and again the calculation is made to get the answer equal to zero. This process repeats a number of times unless the equation becomes zero. The rate of “i” at which the equation becomes zero is gives the IRR.

There is a big difference between the “i” of the NPV and the “i” of IRR equation. The “i” in the NPV is the external required rate of return based on the opportunity cost of capital that must be desired by an investor in investing any new project. This required rate of return comes from the risk free rate of return given by the banks on the deposited money. On the other hand the “i” in the IRR equation is the forecasted rate of return that comes from the expected cash flows of the project, so the “i” is not set externally.

**Example:**

Considering the above NPV example, David has to find the value of IRR for his new retail store project. The other data is same.

**Solution:**

By using the formula of IRR

NPV = 0 = -I_{o}+CF_{1} / (1+i)^{1} + CF_{2} / (1+i)^{2}

By keeping the value of “i” at 10%, the answer of equation become 109421, which is much higher than zero. So the rate of “i” is increased to 15%. Then

NPV = 0 = -I_{o}+CF_{1} / (1+0.15)^{1} + CF_{2} / (1+0.15)^{2}

NPV = 0 = 88,544

This answer is again much higher than zero. If “i” is set to 45% then the answer become 2045 which is slightly above zero. So by keeping the “i” equal to 46% the equation gives approximately zero answer. So the IRR is 46% based on the future cash flows of the new project.

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