# Net Present Value (NPV)

Net present value (NPV) of a project represents the change in a company's net worth/equity that would result from acceptance of the project over its life. It equals the present value of the project net cash inflows minus the initial investment outlay. It is one of the most reliable techniques used in capital budgeting because it is based on the discounted cash flow approach.

Net present value calculations require the following three inputs:

- Projected net after-tax cash flows in each period of the project.
- Initial investment outlay
- Appropriate discount rate i.e. the hurdle rate.

Net after-tax cash flows equals total cash inflow during a period, including salvage value if any, less cash outflows (including taxes) from the project during the period.

The initial investment outlay represents the total cash outflow that occurs at the inception (time 0) of the project.

The present value of net cash flows is determined at a discount rate which is reflective of the project risk. In most cases, it is appropriate to start with the weighted average cost of capital (WACC) of the company and adjust it up or down depending on the difference between the risk of the specific project and average risk of the company as a whole.

## Formulas and calculation

The first step involved in the calculation of NPV is the estimation of net cash flows from the project over its life. The second step is to discount those cash flows at the hurdle rate.

The net cash flows may be even (i.e. equal cash flows in different periods) or uneven (i.e. different cash flows in different periods). When they are even, present value can be easily calculated by using the formula for present value of annuity. However, if they are uneven, we need to calculate the present value of each individual net cash inflow separately.

Once we have the total present value of all project cash flows, we subtract the initial investment on the project from the total present value of inflows to arrive at net present value.

Thus we have the following two formulas for the calculation of NPV:

*When net cash flows are even, i.e. when all net cash flows are equal:*

NPV = R × | 1 − (1 + i)^{-n} |
− Initial Investment |

i |

In the above formula,

*R* is the net cash inflow expected to be received in each period;

*i* is the required rate of return per period (i.e. the hurdle rate, discount rate);

*n* are the number of periods during which the project is expected to operate and generate cash inflows.

*When net cash flows are uneven, i.e. when net cash flows vary from period to period:*

NPV = | R_{1} |
+ | R_{2} |
+ | R_{3} |
+ ... − Initial Investment |

(1+i)^{1} |
(1+i)^{2} |
(1+i)^{3} |

Where,

*i* is the hurdle rate (also called discount rate);

*R _{1}* is the net cash inflow during the first period;

*R*is the net cash inflow during the second period;

_{2}*R*is the net cash inflow during the third period, and so on ...

_{3}These formulas ignore the effect of taxes and inflation. Read further: NPV and taxes, NPV and inflation and international capital budgeting.

## Decision rule

In case of standalone projects, accept a project only if its NPV is positive, reject it if its NPV is negative and stay indifferent between accepting or rejecting if NPV is zero.

In case of mutually exclusive projects (i.e. competing projects), accept the project with higher NPV.

## Examples

### Example 1: Even net cash flows

Calculate the net present value of a project which requires an initial investment of $243,000 and it is expected to generate a net cash flow of $50,000 each month for 12 months. Assume that the salvage value of the project is zero. The target rate of return is 12% per annum.

#### Solution

We have,

Initial Investment = $243,000

Net Cash Inflow per Period = $50,000

Number of Periods = 12

Discount Rate per Period = 12% ÷ 12 = 1%

Net Present Value

= $50,000 × (1 − (1 + 1%)^{-12}) ÷ 1% − $243,000

= $50,000 × (1 − 1.01^{-12}) ÷ 0.01 − $243,000

≈ $50,000 × (1 − 0.887449) ÷ 0.01 − $243,000

≈ $50,000 × 0.112551 ÷ 0.01 − $243,000

≈ $50,000 × 11.2551 − $243,000

≈ $562,754 − $243,000

≈ $319,754

### Example 2: Uneven net cash flows

An initial investment of $8,320 thousand on plant and machinery is expected to generate net cash flows of $3,411 thousand, $4,070 thousand, $5,824 thousand and $2,065 thousand at the end of first, second, third and fourth year respectively. At the end of the fourth year, the machinery will be sold for $900 thousand. Calculate the net present value of the investment if the discount rate is 18%. Round your answer to nearest thousand dollars.

#### Solution

PV Factors:

Year 1 = 1 ÷ (1 + 18%)^{1} ≈ 0.8475

Year 2 = 1 ÷ (1 + 18%)^{2} ≈ 0.7182

Year 3 = 1 ÷ (1 + 18%)^{3} ≈ 0.6086

Year 4 = 1 ÷ (1 + 18%)^{4} ≈ 0.5158

The rest of the calculation is summarized below:

Year | 1 | 2 | 3 | 4 |

Net Cash Inflow | $3,411 | $4,070 | $5,824 | $2,065 |

Salvage Value | 900 | |||

Total Cash Inflow | $3,411 | $4,070 | $5,824 | $2,965 |

× Present Value Factor | 0.8475 | 0.7182 | 0.6086 | 0.5158 |

Present Value of Cash Flows | $2,890.68 | $2,923.01 | $3,544.67 | $1,529.31 |

Total PV of Cash Inflows | $10,888 | |||

− Initial Investment | − 8,320 | |||

Net Present Value | $2,568 | thousand |

## Strengths and weaknesses of NPV

### Strengths

Net present value accounts for time value of money which makes it a better approach than those investment appraisal techniques which do not discount future cash flows such as payback period and accounting rate of return.

Net present value is even better than some other discounted cash flow techniques such as IRR. In situations where IRR and NPV give conflicting decisions, NPV decision should be preferred.

### Weaknesses

NPV is after all an estimation. It is sensitive to changes in estimates for future cash flows, salvage value and the cost of capital. NPV analysis is commonly coupled with sensitivity analysis and scenario analysis to see how the conclusion changes when there is a change in inputs.

Net present value does not take into account the size of the project. For example, say Project A requires initial investment of $4 million to generate NPV of $1 million while a competing Project B requires $2 million investment to generate an NPV of $0.8 million. If we base our decision on NPV alone, we will prefer Project A because it has higher NPV, but Project B has generated more shareholders’ wealth per dollar of initial investment ($0.8 million/$2 million vs $1 million/$4 million).

by Irfanullah Jan, ACCA and last modified on