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# Net Present Value Explained – Definition, Formula & Examples

Investment is the key to every business. From inception to development of the business and expansion, capital is required. Based on the capital investment, the company will decide to expand. When doing so business needs to calculate the Net Present Value of future cash.

## Definition of Net Present Value

As the name implies it is the net worth of the present cash flow including the cash inflow, cash outflow, discounted at a particular rate. NPV is the popular form by which is known in the accounting world.

It is important to calculate the net present value as it keeps the company informed about the value that any business adds keeping in the account about the money available to spend and the money that the business will generate.

NPV is a method used to estimate the worth of investment in any project.

## How To Calculate Net Present Value?

There are different formulas used by people in corporate finance to calculate the NPV. It can be either done with the cash inflow or the cash outflow.

Calculated using the cash inflow

NPV = ∑ (P / (1+i)t) – C

• C – Initial cost
• T – Time
• P – Cash inflow
• i – Discount rate

Calculated using the cash outflow

When cash outflow is first used, use one of the present value formula to calculate the PV and then find the Net Present Value.

NPV = PV – Cash outflow
PV = FV / (1+r)n

• PV – Present value
• FV – Future value
• r – interest rate
• n – number of periods

NPV = PV – Cash outflow
PV = FV / (1+i)t)

## What Inputs are Required to Calculate NPV?

From the above net present value formula, you can understand that there are a couple of ways it can be calculated. It requires the following basic details

• Initial investment
• Discount rate
• Net cash flows (after tax) for every project

### What does NPV convey?

• Positive NPV is an indication to accept the project as there is a scope of getting profit.
• On the other hand, a negative NPV indicates a loss.

### Examples of NPV calculation

Find some examples to understand NPV better.

NPV formula =  ∑ (P / (1+i)t) – C

• The cost of the project is \$2000(C) and offers four cash flows namely 500, 900, 1200, and 700 (P)  for the next 4 years (t). The rate of return is 10% (i).

NPV = (500 / (1+0.10) + 900 / (1+0.10)2 + 1200 / (1+0.10)3 + 700/ (1+0.10)4) – 2000

The return rate is the discount rate (discount rate formula)  i = 10
Period – 1, 2, 3, 4 (years)
P – Cash flow – 500, 900, 1200, and 700
C – Initial cost – 2000
Calculation

Find some examples to understand NPV better.

 Cash Flow (P) i (1+i) (1+i)^n Calculation 500 1 0.1 1.1 1.1 454.54545 900 1 0.1 1.1 1.21 743.80165 1200 1 0.1 1.1 1.331 901.57776 700 1 0.1 1.1 1.4641 478.10942 Total 2578.0343

NPV = (454.5 + 743.8 + 901.5 + 478.1) – 2000
2578.0343 – 2000
578.0343

In the above example, the Net Present Value is positive and thus seems to be a beneficial project.

• The initial cost is \$50000 with a net cash flow of \$5000 every month for 10 months. The rate of return is 10% yearly.

Initial Investment = \$50000
Cash Inflow = \$5000
Total Number of Periods = 10
Discount Rate/ Period = 10% ÷ 10 = 1%

= 5000 X (1 – (1+1%)-10/ 1%  –  50000
=  5000 X (1 – 1.01-10) / 0.01 – 50000
= 5000 X (1-0.9053)/0.01 – 50000
= 5000 X (0.0947/0.01) – 50000
= 47356 – 50000
= – 2643

In the above case, it is not beneficial as the net worth value is negative and hence this investment is a loss to the business.

## Discount Formula and Net Present Value

There is another scenario in which the discount formula is used to calculate the discount rate. It either uses

• the weighted average cost of capital (WACC)

WACC = E/V x EC + DC/V x Cd x (1-T)

E – Equity Value
D – Debt Value
EC – Equity cost
DC – Debt cost
V – E + D
T – Tax rate

APV  = NPV + PV

• Example – One company is looking at opening a new branch and the details of their investment are provided below. The initial investment is \$5000

E – Equity Value – 2%
D – Debt Value – 8%
EC – Equity cost – 3.5%
DC – Debt cost – 1.5%
V – E + D
T – Tax rate – 3.2%

Cash flow

 Year 1 2 3 4 5 6 7 -1200 1000 1100 1200 1300 1400 1500

Calculation

WACC = E/V x EC + DC/V x DC x (1-T)

= 1.08 x 0.035 + 0.81 x (1-3.2%)
= 1.08 x 0.035 + 0.81 x (0.968)
= 0.8122%

NPV formula =  ∑ (P / (1+i)t) – C

1+i = 1.008

= -1200/1.008 + 1000/(1.008)2 + 1100 / (1.008)3 + 1200 / (1.008)4 + 1300 / (1.008)5 + 1400/(1.008)6 + 1500 / (1.008)7

∑ (P / (1+i)t)

C = 5000

 Cash Flow (P) i (1+i) (1+i)^n Calculation -1200 1 0.008 1.008 1.008 -1190.4762 1000 1 0.008 1.008 1.01606 984.18997 1100 1 0.008 1.008 1.02419 1074.0168 1200 1 0.008 1.008 1.03239 1162.3559 1300 1 0.008 1.008 1.04065 1249.2251 1400 1 0.008 1.008 1.04897 1334.6422 1500 1 0.008 1.008 1.05736 1418.6248 Total 6032.5785

NPV =  6032.5785 – 5000
NPV = \$1032.5785

This investment is profitable for the business.

## Observation

From the above scenarios, you can see that the same NPV formula is used to calculate the value but with a difference.

• In the first and third example the cash flow is different and the second one the cash flow remains the same.
• In the first and second example discount rate was given and in the third example discount rate was calculated using the discount formula

Therefore, the calculation steps varied. Based on the different inputs available in your business you need to calculate the Net Present Value.

## Bottom Line

Net Present Value is the best tool that takes the time value of money to calculate business profitability. It is a comprehensive tool that takes care of all the components of investment. The only drawback with this method is when it comes to calculating the discount rate which sometimes might mislead showing false profitability. But this can be overruled by using the right calculating app.

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