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Net Present Value

 

The net present value of a project is equal to the sum of the present value of all the cash flows associated with the project. One of the most important concepts originating from the time value of money, NPV is calculated by subtracting the present value of the cash outflows (investment) from the present value of the cash inflows (income).

 

Suppose you are making an investment of Rs 1 lac today and are expecting that you will get Rs 1.1 lacs one year from now. You will only invest if the present value of Rs 1.1 lac that you are getting one year hence is more than Rs 1 lac you have invested today. Using the table for present value of Rs 1, the multiplying factor for one year at 10% is 0.909. If we multiply Rs 1.1 lac with .909 we get approx. Rs 1 lac. This means that we are getting a return of 10%  from the project.

 

If you again look at the same table, the value gets lowered as the interest rate increases, which means that for an interest rate of more than 10% we will be getting a present value which will be lower than the investment we are making. So if we are expecting a return of 15% for one year, we will not invest as the present value of Rs 1.1 lac at 15% discount rate is lower than the investment of Rs 1 lac we are making today.

 

The formula for calculating the NPV is:

                                               

where           NPV    =        net present value

                             CF_t      =        cash flow occurring at the end of year

                             C₀       =        Initial cash outflow or investment

                             t        =        (t = 0 ......n), A cash inflow has a  positive sign,
                                                whereas a cash outflow has a negative sign

                                                n        =        life of the project

                                                k        =        cost of capital used as the discount rate

Here C₀ is the initial investment we are making into the project and the rest is the present value of the cash flows we are expecting in the future. So NPV is the difference between the two at the expected rate of return.

With NPV the acceptance rule is

                      NPV > 0  Accept

                                                = 0  Indifferent

                                                < 0  Reject

If the NPV is greater than zero we accept the project because we are getting a rate of return which exceeds our desired rate of return, if it is equal to zero we may or may not accept the project as we are getting a return which is exactly equal to our desired rate of return, and if it is less than zero we reject the project proposal because the rate of return we are getting is less than our desired rate of return.

Features of Net Present Value

 

Two features of the net present value method to be emphasized:

1.       The NPV method is based on the assumption that the intermediate cash inflow of the project is reinvested at a rate of return equal to the firm's cost of capital.

2.       The NPV of a simple project monotonically decreases as the discount rate increases; the decrease in NPV, however, is at a decreasing rate.

 

Evaluation

Conceptually sound, the net present value criterion has considerable merits:

• It takes into account the time value of money.
• It considers the cash flow stream in its entirety.
• It squares neatly with the financial objective of maximization of the wealth of stockholder. The net present value represents the contribution to the wealth of stockholders.
• The net present value of various projects, measured as they are in today's rupees, can be added. For example, the present value of package consisting of two projects A and B, will simply be the sum of the net present value of these projects individually:

           NPV (A+B) = NPV (A) + NPV (B)

The additivity property of net present value ensures that a poor project (one which has a negative net present value) will not be accepted just because it is combined with a good project (which has a positive net present value).

The limitations of the net present value criteria are:

• The ranking of projects on the net present value dimension is influenced by the discount rate. To illustrate, consider two mutually exclusive projects – A and B which have the following cash flow streams:

                                           Year                       A                            B

                                                0                  -3,00,000                -3,00,000

                                                1                      60,000                1,30,000

                                                2                  1,00,000                 1,00,000

                                                3                  1,20,000                     80,000 

                                                4                  1,50,000                     60,000

The net present value of A and B for various rates of discounts is given below. 

                    Discount rate       NPV (A)             NPV (B)

                         10%                 36,622                 29,180

                         12%                 20,390                 17,658

                         14%                   5,318                   6,828

                         15%                  -1,826                  1,654

                         16%                  -8,702                 -3,350

Looking at the behavior of net present value, we find that: (i) when the discount rate is 12 per cent, the net present value of A is greater than the net present value of B; and (ii) when the discount rate is 14 per cent the net present value of B is greater than the net present value of A.

• The net present value measure, an absolute measure, does not appear very meaningful to businessmen who want to think in term of rate of return measures.

 

Profitability Index (PI)

 

Profitability Index relates the present value of benefits to the initial investment. It is also known as Benefit-Cost Ratio (BCR).

 

        where , PI = Profitability Index

                     PVCF = present value of cash flows

                          I  = initial investment

To illustrate the calculation of these measures, let us consider a project which is being evaluated by a firm that has a cost of capital of 12 per cent.

Initial investment :                Rs.   1,00,000

          Year 1                              25,000

          Year 2                              40,000

          Year 3                              40,000

          Year 4                              50,000

The profitability index for this project is:

 

With PI the acceptance rule is

                         PI           > 1  Accept

                                                = 1  Indifferent

                                                < 1  Reject

 

If PI is greater than one we accept the project because we are getting a rate of return which exceeds our desired rate of return. If it is equal to one we may or may not accept the project as we are getting a return which is exactly equal to our desired rate of return. If it is less than one we reject the project proposal because the rate of return we are getting is less than our desired rate of return.

 

Putting it simply PI is an adaptation of the NPV rule because through it uses the same figures it only helps in ranking of the project.

Evaluation

 

The proponents of profitability index argue that since this criterion measures net present value per rupee of outlay it can discriminate better between large and small investments and hence is preferable to the net present value criterion. How valid is this argument? Theoretically, it can be very easily verified that:

(i)                 Under unconstrained conditions, the PI criteria will accept and reject the same projects as the net present value criteria. 

(ii)               When the capital budget is limited in the current period, the benefit cost ratio criteria may rank projects correctly in the order of decreasingly efficient use of capital.  However, its use is not recommended because it provides no means for aggregating several smaller projects into a package that can be compared with a large project. 

(iii)              When cash outflows occur beyond the current period, PI criteria is unsuitable as a selection criteria.

 

Internal Rate Of Return

 

When the present value of cash inflows are exactly equal to the present value of cash outflows we are getting a rate of return which is equal to our discounting rate. In this case the rate of return we are getting is the actual return on the project. This rate is called the IRR.

                                     

Using the same formula as given in the NPV above, IRR will be the return when the NPV is equal to zero as only then the present value of cash inflows will be equal to the present value of the cash outflows.

 

                     here CF_t  = cash flow at the end of year t

                       r  = discount rate

                       n  = life of the project

 

In the net present value calculation we assume that the discount rate (cost of capital) is known and determine the net present value of the project. In the internal rate of return calculation, we set the net present value equal to zero and determine the discount rate (internal rate of return), which satisfies this condition.

 

Both the discounting methods NPV and IRR relate the estimates of the annual cash outlays on the investment to the annual net of tax cash receipt generated by the investment. As a general rule, the net of tax cash flow will be composed of revenue less taxes, plus depreciation. Since discounting techniques automatically allow for the recovery of the capital outlay in computing time-adjusted rates of
return, it follows that depreciation provisions implicitly form part of the cash inflow.

 

Internal rate of return method consists of finding that rate of discount that reduces the present value of cash flows (both inflows and outflows attributable to an investment project to zero. In other words, this true rate is that which exactly equalizes the net cash proceeds over a project's life with the initial investment outlay.

 

If the IRR exceeds the financial standard (i.e. cost of capital), then the project is prima facie acceptable. Instead of being computed on the basis of the average or initial investment, the IRR is based on the funds in use from period to period.

 

The actual calculation of the rate is a hit-and-miss exercise because the rate is unknown at the outset, but tables of present values are available to aid the analyst. These tables show the present value of future sums at various rates of discount and are prepared for both single sums and recurring annual payments.

What Does IRR Mean?

 

There are two possible economic interpretations of internal rate of return: (i) Internal rate of return represents the rate of return on the unrecovered investment balance in the project. (ii) Internal rate of return is the rate of return earned on the initial investment made in the project.

Evaluation

 

A popular discounted cash flow method, the internal rate of return criteria has several virtues:

• It takes into account the time value of money.
• It considers the cash flow stream in its entirety.
• It makes sense to businessmen who want to think in terms of rate of return and find an absolute quantity, like net present value, somewhat difficult to work with.

 

The internal rate of return criteria, however, has its own limitations.

• It may not be uniquely defined. If the cash flow stream of a project has more than one change in sign, there is a possibility that there are multiple rates of return.
• The internal rate of return figure cannot distinguish between lending and borrowing and hence a high internal rate of return need not necessarily be a desirable feature.
• The internal rate of return criterion can be misleading when choosing between mutually exclusive projects that have substantially different outlays. Consider projects P and Q.

        Cash Flows      Internal rate            Net present value

        -------------- of return (%)           (assuming k = 12%)

          Period                     0                           1

P  - 10,000  + 20,000         100                        7,857

Q  - 50,000  + 75,000        50                          16,964

 

Both the projects are good, but Q, with its higher net present value, contributes more to the wealth of the stockholders.   Yet from an internal rate of return point of view P looks better than Q.  Hence, the internal rate of return criterion seems unsuitable for ranking projects of different scale.