## Measurement and Decision-Making Under Discounted Cash Flow Techniques

The discounted cash flow method determines the cash inflow and outflow over the asset’s lifetime. After that, a discounting factor is applied to them. After that, discounted cash inflows and outflows are contrasted. This method considers the interest rate as well as the return after the payback period.

### Net Present Value (NPV)

The sum of the current values of all the cash flows associated with a project is the project’s net present value. NPV is determined by subtracting the present value of the cash outflows (investment) from the present value of the cash inflows. It is one of the most fundamental principles derived from the time value of money.

Suppose you are making an investment of ₹1 lac today and are expecting that you will get ₹1.1 lacs one year from now. You will only invest if the present value of ₹1.1 lac that you are getting one year hence is more than ₹1 lac you have invested today. Using the table for present value of ₹1, the multiplying factor for one year at 10% is 0.909. If we multiply ₹1.1 lac with .909, we get approx. ₹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 1.1 lac at a discount rate of 15% is lower than the investment of 1 lac we are making today.

The formula for calculating the NPV is:

Where NPV = net present value

CFt = cash flow occurring at the end of year

C0 = Initial cash out flow 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 represents the initial investment in the enterprise, and the remainder represents the current value of potential cash flows. So, at the estimated rate of return, NPV is the difference between the two.

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 the rate of return is higher than our desired rate of return; if it is equal to zero, we can or may not accept the project because the return 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 is lower than our desired rate of return.

Net Present Value (NPV) = Present Value of Cash Inflows – Present Value of Cash Outflows

The discounting is done by the entitiy’s weighted average cost of capital

The discounting factors is given by: ( )

1

1 n

Where i = rate of interest per annum

n = no. of years over which discounting is made.

Advantages of net present value (NPV) are as follows:

- It recognises the Time Value of Money.
- It considers total benefits during the entire life of the Project.
- This is applicable in case of mutually exclusive Projects.
- Since it is based on the assumptions of cash flows, it helps in determining Shareholders Wealth.

Limitations of net present value (NPV) are as follows:

- Net present value is not an absolute measure.
- In net present value desired rate of return may vary from time to time due to changes in cost of capital.
- Net present value Method is not effective when there is disparity in economic life of the projects.
- More emphasis on net present values. Initial investment is not given due importance.

**Example:** M Ltd. has two projects under consideration A & B, each costing ₹60 lacs. The projects are mutually exclusive. Life for project A is 4 years & project B is 3 years. Salvage value NIL for both the projects. Tax Rate 33.99%. Cost of Capital is 15%.

Net Cash Inflow (₹Lakhs)

At the end of the year | Project A | Project B | P.V. @ 15% |
---|---|---|---|

1. | 060 | 100 | 0.870 |

2. | 110 | 130 | 0.756 |

3. | 120 | 050 | 0.685 |

4. | 050 | – | 0.572 |

**Solution:**

Computation of Net Present Value of the Projects.

**Project A (₹lakhs)**

Particular | Yr. 1 | Yr. 2 | Yr. 3 | Yr. 4 |
---|---|---|---|---|

1. Net Cash Inflow | 60.00 | 110.00 | 120.00 | 50.00 |

2. Depreciation | 15.00 | 15.00 | 15.00 | 15.00 |

3. PBT (1-2) | 45.00 | 95.00 | 105.00 | 35.00 |

4. Tax 33.99 | 15.30 | 32.29 | 35.70 | 11.90 |

5. PAT (3-4) | 29.70 | 62.71 | 69.30 | 23.10 |

6. Net Cash Flow (PAT+Dep^{n}) | 44.70 | 77.71 | 84.30 | 38.10 |

7. Discounting Factor | 00.870 | 00.756 | 00.685 | 00.572 |

8. P.V. of Net Cash Flows | 38.89 | 58.75 | 57.75 | 21.79 |

9. Total P.V. of Net Cash Flow | = 177.18 | |||

10. P.V. of Cash outflow (Initial Investment) | = 60.00 | |||

Net Present Value | = 117.18 |

**Project B**

Particular | Yr. 1 | Yr. 2 | Yr. 3 |
---|---|---|---|

1. Net Cash Inflow | 100.00 | 130.00 | 50.00 |

2. Depreciation | 20.00 | 20.00 | 20.00 |

3. PBT (1-2) | 80.00 | 110.00 | 30.00 |

4. Tax 33.99 | 27.19 | 37.39 | 10.20 |

5. PAT (3-4) | 52.81 | 72.61 | 19.80 |

6. Net Cash Flow (PAT+Dep) | 72.81 | 92.61 | 39.80 |

7. Discounting Factor | 0.870 | 0.756 | 0.685 |

8. P.V. of Net Cash Flows | 63.345 | 58.75 | 57.75 |

9. Total P.V. of Net Cash Flow | = 160.621 | ||

10. P.V. of Cash outflow (Initial Investment) | = 60.000 | ||

Net Present Value | = 100.621 |

As Project “A” has a higher Net Present Value, it has to be taken up.

### Profitability Index (PI)

Profitability index (PI) is a financial tool that helps in making a decision of whether an investment should be accepted or rejected. It measures the ratio between the present value of future cash flows and the initial investment. The index is a useful tool for ranking investment projects and showing the value created per unit of investment. If PI is greater than 1, the investment is accepted. If PI is less than 1, the investment is rejected and if PI = 1, then indifferent (may accept or reject the decision). Profitability Index relates the present value of benefits to the initial investment.

It is also known as Benefit-Cost Ratio (BCR). It uses the time value concept of money and is calculated by the following formula:

PI =

PVCF

I

Where, PI = Profitability Index

PVB = present value of cash flows

I = initial investment

Consider a project that is being assessed by a company with a cost of capital of 12% to demonstrate how these metrics are calculated.

Initial investment | ₹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:

PI = ( ) ( ) ( ) ( )

25,000 40,000 40,000 50,000

1.12 1 1.12 2 1.12 3 1.12 4

1,00,000

+++

= 1.145

With PI the acceptance rule is

PI > 1 Accept

PI = 1 Indifferent

PI < 1 Reject

If the PI is greater than one, we approve the project because the rate of return is higher than what we expected. If it equals one, we will approve or reject the project since the return is exactly equal to our desired rate of return. If it’s less than one, we’ll reject the project plan because the rate of return isn’t as high as we’d like. Simply put, the PI rule is an adaptation of the NPV rule since it uses the same figures but only aids in project ranking.

#### Advantages of Profitability Index (PI)

- PI considers the time value of money.
- PI considers analysis all cash flows of entire life.
- PI makes the right in the case of different amount of cash outlay of different project.
- PI ascertains the exact rate of return of the project.

#### Limitations of Profitability Index (PI)

- There is no getting around the fact that facts are not used to calculate the profitability index.
- The NPV creates an investment figure that is based on short-term projects more than long-term results.
- The cash inflows and outflows are not the only estimates which are used when calculating a profitability index figure.
- A profitability index is usually calculated by people or teams that are close to the projects or companies being examined.

**Example:** Calculate Profitability Index from the following information:

- Initial investment ₹20 lacs.
- Expected annual cash flows ₹6 lacs for 10 years.
- Cost of Capital @ 15%.

**Solution:**

Cumulative discounting factor @ 15% for 10 years = 5.019

P.V. of inflows = 6.00 × 5.019 = ₹30.114 lacs.

Profitability Index = P.V. of Inflows

P.V. of Outflows =

30 114

20 = 1.51

**Decision:** The project should be accepted.

### Internal Rate of Return (IRR)

We get a rate of return equal to our discounting rate when the present value of cash inflows is exactly equal to the present value of cash outflows. In this scenario, the rate of return we’re getting is the project’s return. The IRR stands for Internal Rate of Return.

IRR is the return when the NPV is equal to zero, since only then can the present value of cash inflows equal the present value of cash outflows, using the same formula as in the NPV above.

Here CFt = cash flow at the end of year t

r = discount rate

n = life of the project

The net present value estimate assumes that the discount rate (cost of capital) is calculated, and it is used to calculate the project’s net present value. We calculate the internal rate of return by setting the net present value to zero and then determining the discount rate (internal rate of return) that meets 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. The internal rate of return approach involves determining the rate of discount that decreases the current value of cash flows (both inflows and outflows attributable to an investment project) to nil.

In other words, this true rate is the rate at which the net cash flows over the life of a project are exactly equal to the initial investment outlay. The project is prima facie permissible if the IRR reaches the financial standard (cost of capital).

The IRR is calculated based on the funds in use from time to period, rather than the average or initial investment. Since the rate is uncertain at the start, the actual estimation of the rate is a hit-or-miss exercise, but tables of present values are available to assist the analyst. These tables, which are prepared for both single amounts and regular annual payments, display the present value of potential sums at different discount rates.

#### Advantages of Internal Rate of Return (IRR)

- It possesses the advantages, which are offered by the NPV criterion such as it considers time value of money and takes into account the total cash inflows and outflows.
- IRR is easier to understand. Business executives and non-technical people understand the concept of IRR much more readily that they understand the concepts of NPV
- It does not use the concept of the required cost of return (or the cost of capital). It itself provides a rate of return which is indicative of the profitability of the proposal. The cost of capital enters the calculation, later on.
- It is consistent with the overall objective of maximising shareholders wealth since the acceptance or otherwise of a project is based on comparison of the IRR with the required rate of return.

#### Limitations of Internal Rate of Return (IRR)

- It involves tedious calculations.
- It produces multiple rates, which can be confusing.
- When comparing mutually exclusive proposals, the project with the highest IRR would be chosen above the rest. However, in practise, it may not turn out to be the most profitable and consistent with the firm’s aims, namely, maximising of shareholder value.
- All intermediate cash flows are supposed to be reinvested at the IRR rate in the IRR technique. It is illogical to believe that the same company is capable of reinvesting cash flows at different rates. It goes without saying that accurate and dependable findings must be based on realistic estimations of the interest rate at which the revenue will be re-invested.

**Example**: Calculate the Internal Rate of Return from the following information:

Project Cost ₹1,10,000

Cash Inflows:

Year 1 | 60,000 |

Year 2 | 20,000 |

Year 3 | 10,000 |

Year 4 | 50,000 |

**Solution:**

Internal Rate of Return will be calculated by the trial-and-error method. The cash flow is not uniform. To have an approximate idea about such rate, we can calculate the “Factor”. It represents the same relationship of investment and cash inflows in case of payback calculation:

Where,

F = I/C

F = Factor

I = Original investment

C = Average Cash inflow per annum

Factor for the project =

110,000

35,000 = 3.14

The factor will be located from the table “P.V. of an Annuity of ` 1” representing number of years corresponding to estimated useful life of the asset. The approximate value of 3.14 is located against 10% in 4 years. We will now apply 10% and 12% to get (+) NPV and (–) NPV [Which means IRR lies in between]

Year | Cash Inflows | P.V. @ 10% | DCFA | P.V. @ 12% | DCFAT |
---|---|---|---|---|---|

1. | 60,000 | 0.909 | 54,540 | 0.893 | 53,580 |

2. | 20,000 | 0.826 | 16,520 | 0.797 | 15,940 |

3. | 10,000 | 0.751 | 7,510 | 0.712 | 7,120 |

4. | 50,000 | 0.683 | 34,150 | 0.636 | 31,800 |

P.V. of Inflows | 1,12,720 | 1,08,440 | |||

Less: Initial Investment | 1,10,000 | 1,10,000 | |||

NPV | 2,720 | (1,560) |

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