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 =

R1

+

R2

+

R3

+ … – Initial Investment

(1 + i)1 (1 + i)2 (1 + i)3

Where,

i is the target rate of return per period;

R1 is the net cash inflow during the first period;

R2 is the net cash inflow during the second period;

R3 is the net cash inflow during the third period, and so on …

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 × Present Value Factor |
$3,411 0.8475 |
$4,070 0.7182 |
$5,824 0.6086 |
$2,965 0.5158 |

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

Total PV of Cash Inflows – Initial Investment |
$10,888 – 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

shareholders’ wealth per dollar of initial investment ($0.8 million/$2 million vs $1 million/$4

million).

** Why Choose HelpHub**

**Quality Researched Papers**

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

**Qualified Writers**

We have hired a team of professional writers experienced in academic and business writing. Most of them are native speakers and PhD holders able to take care of any assignment you need help with.

**Unlimited Revisions**

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account.

**On Time Delivery**

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. We will always strive to deliver on time.

**Original & Confidential**

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text.

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

HelpHub Writing Services

No need to work on essay at night. Sleep tight, we will cover your back. We offer all kinds of essay writing services.

Essays

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Editing

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Revision

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied.