# Net Present Value (NPV)

Net present value (NPV) of a project is the potential change in an investor's wealth caused by that project while time value of money is being accounted for. It equals the present value of net cash inflows generated by a project less the initial investment on the project. It is one of the most reliable measures used in capital budgeting because it accounts for time value of money by using discounted cash flows in the calculation.

Net present value calculations take the following two inputs:

- Projected net cash flows in successive periods from the project.
- A target rate of return i.e. the hurdle rate.

Where,

Net cash flow equals total cash inflow during a period, including salvage value if any, less cash outflows from the project during the period.

Hurdle rate is the rate used to discount the net cash inflows. Weighted average cost of capital (WACC)is the most commonly used hurdle rate.

## Calculation Methods and Formulas

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 cash inflows are even:**

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;

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

**When cash inflows are uneven:**

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

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

Where,**i** is the target rate of return per period;**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}## 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 Cash Inflows:** Calculate the net present value of a project which requires an initial investment of $243,000 and it is expected to generate a cash inflow 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 Cash Inflows:** An initial investment of $8,320 thousand on plant and machinery is expected to generate cash inflows 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 sounder approach than other investment appraisal techniques which do not discount future cash flows such payback period and accounting rate of return.

Net present value is even better than some other discounted cash flows 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.

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 shareholdersâ€™ wealth per dollar of initial investment ($0.8 million/$2 million vs $1 million/$4 million).

Written by Irfanullah Jan