Net Present Value (NPV)

In finance, the net present value (NPV) or net present worth (NPW) is defined as substructing present values (PV) of cash outflows (including initial cost) from the present values of cash inflows over a period of time. We can call incoming cash flows as benefit cash flows. We can also call outgoing cash flows as cost cash flows [1].

Internal Rate of Return (IRR)

The internal rate of return (IRR) is described as calculating rate of return. The term internal means that its calculation is not related with environmental factors like the interest rate or inflation. If NPV becomes zero, a rate of return is internal rate of return [2].

Let

= Net cash inflow during the period i

= Discount rate

= Number of Periods

We have

One can use numerical methods to calculate by approximating in the equation .

**Example 1**

*Input*

Period = 4

Discount Rate = 10%

Cash Flow 0 = -2000

Cash Flow 1 = 100

Cash Flow 2 = 100

Cash Flow 3 = 2600

*Output*

Net Present Value = 126.972

Internal Rate of Return = 12.382%

**Example 2**

*Input*

Period = 4

Discount Rate = 5%

Cash Flow 0 = -123400

Cash Flow 1 = 36200

Cash Flow 2 = 54800

Cash Flow 3 = 48100

*Output*

Net Present Value = 2331.994

Internal Rate of Return = 5.962%

1. Net present value (n.d.). Retrieved August 18, 2016, from https://en.wikipedia.org/wiki/ Net_present_value

2. Internal rate of return (n.d.). Retrieved August 18, 2016, from https://en.wikipedia.org/wiki/ Internal_rate_of_return