Net Present Value (NPV) Calculator

What is Net Present Value (NPV)?

Net Present Value (NPV) is one of the key financial parameters that help to know whether or not an investment or project will be profitable. NPV helps investors decide on investments by knowing if the future cash inflows and outflows have a present value greater than zero. It gives a clear picture of whether investment adds value.

Net Present Value Calculator

NPV can be calculated manually, but using a Net Present Value Calculator will make it time-efficient. Simply enter your investment’s cash flows, discount rate, and initial cost, and you’ll receive the results in a matter of seconds. You can access an easy-to-use tool at Net Present Value Calculator.

Future Cash Flows NPV (Net Present Value)

The NPV of future cash flows shows their equivalent value today, taking into account the time value of money. So, if a project has been generating $15,000 a year for the next 5 years, and the discount rate is 12%, then NPV calculation discounts each and every one of those payments to current value and sums them. As a result, the analysis effectively captures the accurate value of the investment.

Future Payments = Net Present Value

NPV isn’t only for cash inflows—it’s also used to determine the present value of future outflows. You can also use NPV when comparing loan options with different payments; by bringing future payments to the present, you’re able to identify which loan option will cost you the least.

Examples and Solutions of Net Present Value

Example 1: Positive NPV

A $60,500 investment is made by the company in a project, with an expected return of $15,000 per year for the next 5 years. It assumes a 12% discount rate.

Solution: The discounted cash inflows are greater than the initial investment when plugged into the formula or calculator above which results in a positive NPV. This means the project is profitable and should be pursued.

Example 2: Negative NPV

Example: A person is thinking of buying an investment property that will require $200,000 in the beginning and is expected to return $12,000 a year for the next 20 years at a discount rate of 12%

Answer: The calculations produce a negative NPV, which indicates that the company will likely not earn back the amount spent on the rock samples.

In what ways are Net Present Value and Present Value different?

Though NPV and Present Value (PV) are closely related, they have distinct roles:

PV considers only the value today of a future income, ignoring the initial cost.
Net Present Value (NPV) calculates the present value of cash flows net of the initial investment, so it gives a measure of net profit.
NPV provides a comprehensive view, which makes it a better metric for investment analysis.

FAQs on Net Present Value

Q1. So why is a positive NPV significance?

NPV greater than 0 indicates the investment is providing more value than it costs, which translates to being profitable.

Q2. What discount rate do I apply?

Typically, the discount rate represents your cost of capital, desired return, or the rate of a different investment opportunity.

Q3. Is NPV good for comparing loans/mortgages?

Yes! By calculating the NPV of all payments, you can find the most cost-effective option by comparing loans.

Q4. How does NPV differ from IRR?

NPV gives a dollar value of profitability, whereas the Internal Rate of Return (IRR) represents the return expressed as a percentage by which NPV = 0.

Use the Net Present Value Calculator to analyze the profitability, or financial decisions, of your projects. It works super fast and is very reliable and easy to use!

Net Present Value (NPV) Formulas

Basic NPV Formula

$ \text{NPV} = \sum_{t=1}^{N} \frac{C_t}{(1 + r)^t} - C_0 $

Where:

$ C_t $ = Cash flow at time $ t $
$ r $ = Discount rate
$ N $ = Number of time periods
$ C_0 $ = Initial investment (cash outflow at time 0)

Alternative NPV Formula (Expanded)

An expanded form of the NPV formula is:
$ \text{NPV} = \frac{C_1}{(1 + r)^1} + \frac{C_2}{(1 + r)^2} + \dots + \frac{C_N}{(1 + r)^N} - C_0 $

NPV with Continuous Compounding

If cash flows are compounded continuously, the formula becomes:
$ \text{NPV} = \sum_{t=1}^{N} C_t \cdot e^{-rt} - C_0 $

Where:

$ e $ = Euler's number (approximately 2.71828)
$ -rt $ = Negative exponent of the discount rate times the time period

Net Present Value (NPV) Problems and Solutions

Problem 1

Calculate the NPV of a project with an initial investment of $510,000 and cash flows of $150,000, $180,000, $120,000, and $240,000 over the next 4 years. The discount rate is 8%.

Solution:
$ \text{NPV} = -510,000 + \frac{150,000}{(1 + 0.08)^1} + \frac{180,000}{(1 + 0.08)^2} + \frac{120,000}{(1 + 0.08)^3} + \frac{240,000}{(1 + 0.08)^4} $
After calculation, $ \text{NPV} = \$56,049.69 $.

Problem 2

A project has an initial investment of $200,000 with cash flows of $60,000, $80,000, $100,000, and $120,000 over the next 4 years. If the discount rate is 10%, should you invest in this project?

Solution:
$ \text{NPV} = -200,000 + \frac{60,000}{(1 + 0.10)^1} + \frac{80,000}{(1 + 0.10)^2} + \frac{100,000}{(1 + 0.10)^3} + \frac{120,000}{(1 + 0.10)^4} $
After calculation, $ \text{NPV} = \$11,348.59 $. The positive NPV suggests that this project is financially viable and worth pursuing.

Problem 3

Calculate the NPV of a project with an initial investment of $1,000,000 and a series of irregular cash flows: $250,000, $300,000, $400,000, and $500,000 over the next 4 years. The discount rate is 7%.

Solution:
$ \text{NPV} = -1,000,000 + \frac{250,000}{(1 + 0.07)^1} + \frac{300,000}{(1 + 0.07)^2} + \frac{400,000}{(1 + 0.07)^3} + \frac{500,000}{(1 + 0.07)^4} $
After calculation, $ \text{NPV} = \$140,223.95 $.

Problem 4

A business project requires an upfront investment of $850,000 and is expected to produce consistent cash inflows of $120,000 each year for a duration of 8 years. Calculate the Net Present Value (NPV) of the project if the annual discount rate is 5%.

Solution:
$ \text{NPV} = -850,000 + \sum_{t=1}^{8} \frac{120,000}{(1 + 0.05)^t} $
Annuity formula:
$ \text{NPV} = -850,000 + 120,000 \times \frac{1 - (1 + 0.05)^{-8}}{0.05} $
After calculation, $ \text{NPV} = \$28,777.57 $.

Problem 5

Calculate the NPV of a project with an initial investment of $300,000 and cash flows of $75,000 for 6 years. The discount rate is 6%.

Solution:
$ \text{NPV} = -300,000 + \sum_{t=1}^{6} \frac{75,000}{(1 + 0.06)^t} $
After calculation, $ \text{NPV} = \$24,388.87 $.

Problem 6

A project has an initial cost of $1,500,000 with a 4-year cash flow stream of $400,000, $450,000, $500,000, and $600,000. The discount rate is 9%. Calculate the NPV.

Solution:
$ \text{NPV} = -1,500,000 + \frac{400,000}{(1 + 0.09)^1} + \frac{450,000}{(1 + 0.09)^2} + \frac{500,000}{(1 + 0.09)^3} + \frac{600,000}{(1 + 0.09)^4} $
After calculation, $ \text{NPV} = -\$12,050.47 $.

Problem 7

Consider a project with an initial investment of $250,000, generating cash flows of $50,000, $75,000, $100,000, and $125,000 over 4 years. If the discount rate is 8% with continuous compounding, calculate the NPV.

Solution:
$ \text{NPV} = -250,000 + \sum_{t=1}^{4} 50,000 \cdot e^{-0.08 \cdot t} $
After calculation, $ \text{NPV} = \$15,205.54 $.

Problem 8

Calculate the NPV of a project with a cost of $600,000, cash flows of $150,000, $180,000, and $200,000 for 3 years, and a discount rate of 12%.

Solution:
$ \text{NPV} = -600,000 + \frac{150,000}{(1 + 0.12)^1} + \frac{180,000}{(1 + 0.12)^2} + \frac{200,000}{(1 + 0.12)^3} $
After calculation, $ \text{NPV} = -\$16,526.72 $.

Problem 9

A project requires an initial outlay of $1,200,000 and produces cash flows of $300,000 each year for 5 years. Calculate the NPV if the discount rate is 7%.

Solution:
$ \text{NPV} = -1,200,000 + \sum_{t=1}^{5} \frac{300,000}{(1 + 0.07)^t} $
After calculation, $ \text{NPV} = \$52,396.80 $.

Problem 10

Calculate the NPV of a project with an investment of $400,000 and annual cash flows of $100,000 for 8 years with a discount rate of 6%.

Solution:
$ \text{NPV} = -400,000 + \sum_{t=1}^{8} \frac{100,000}{(1 + 0.06)^t} $
After calculation, $ \text{NPV} = \$157,393.32 $.