NET PRESENT VALUE

Net present value

X corporation must decide whether to introduce a new product line. The new product will have startup costs, operational costs, and incoming cash flows over six years. This project will have an immediate (t=0) cash outflow of 0,000 (which might include machinery, and employee training costs). Other cash outflows for years 1-6 are expected to be ,000 per year. Cash inflows are expected to be ,000 per year for years 1-6. All cash flows are after-tax, and there are no cash flows expected after year 6. The required rate of return is 10%. The present value (PV) can be calculated for each year:

T=0 -0,000/ 1.100 = -0,000 PV.

T=1 (,000 – ,000) / 1.101 = ,727 PV.

T=2 (,000 – ,000) / 1.102 = ,661 PV.

T=3 (,000 – ,000) / 1.103 = ,783 PV.

T=4 (,000 – ,000) / 1.104 = ,075 PV.

T=5 (,000 – ,000) / 1.105 = ,523 PV.

T=6 (,000 – ,000) / 1.106 = ,112 PV.

The sum of all these present values is the net present value, which equals ,881. Since the NPV is greater than zero, the corporation should invest in the project.

The same example in an Excel formulae:

NPV(rate,net_inflow)+initial_investment

PV(rate,year_number,yearly_net_inflow)

 

Internal rate of return

The internal rate of return (IRR) is a capital budgeting metric used by firms to decide whether they should make investments. It is an indicator of the efficiency of an investment, as opposed to net present value (NPV), which indicates value or magnitude.

The IRR is the annualized effective compounded return rate which can be earned on the invested capital, i.e., the yield on the investment.

A project is a good investment proposition if its IRR is greater than the rate of return that could be earned by alternate investments (investing in other projects, buying bonds, even putting the money in a bank account). Thus, the IRR should be compared to any alternate costs of capital including an appropriate risk premium.

Mathematically the IRR is defined as any discount rate that results in a net present value of zero of a series of cash flows.

In general, if the IRR is greater than the project’s cost of capital, or hurdle rate, the project will add value for the company.

 

Method

To find the internal rate of return, find the value(s) of r that satisfies the following equation:

(See net present value for details on this formula.)

[edit] Example

Calculate the internal rate of return for an investment of 100 value in the first year followed by returns over the following 4 years, as shown below:

Year

Cash Flow

0

-100

1

39

2

59

3

55

4

20

Solution:

We use an iterative solver to determine the value of r that solves the following equation:

The result from the numerical iteration is .

 

 

Credit:ivythesis.typepad.com