
Net Present Value And Internal Rate Of Return  Net Present Value
The net present value approach is the most intuitive and accurate valuation approach to capital budgeting problems. Discounting the aftertax cash flows by the weighted average cost of capital allows managers to determine whether a project will be profitable or not. And unlike the IRR method, NPVs reveal exactly how profitable a project will be in comparison to alternatives. The NPV rule states that all projects which have a positive net present value should be accepted while those that are negative should be rejected. If funds are limited and all positive NPV projects cannot be initiated, those with the high discounted value should be accepted.
In the two examples below, assuming a discount rate of 10%, project A and project B have respective NPVs of $126,000 and $1,200,000. These results signal that both capital budgeting projects would increase the value of the firm, but if the company only has $1 million to invest at the moment, project B is superior.
Investment 
Inflows 

Year 0 
Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
1,000,000 
300,000 
300,000 
300,000 
300,000 
300,000 
Investment 
Inflows 

Year 0 
Year 1 
Year 2 
Year 3 
Year 4 
Year 5 
1,000,000 
300,000 
300,000 
300,000 
300,000 
3,000,000 
Some of the major advantages of the NPV approach include the overall usefulness and easy understandability of the figure. NPV provides a direct measure of added profitability, allowing one to simultaneously compare multiple mutually exclusive projects and even though the discount rate it subject to change, a sensitivity analysis of the NPV can typically signal any overwhelming potential future concerns. Although the NPV approach is subject to fair criticisms that the valueadded figure does not factor in the overall magnitude of the project, the profitability index (PI), a metric derived from discounted cash flow calculations, can easily fix this concern. We'll discuss the profitability index in a later section. (It's never too early to start learning about money. Read 5 Ways To Teach Your Kids The Value Of A Dollar.)
Here is another example of how companies use NPV.
Using the company's cost of capital, the net present value (NPV) is the sum of the discounted cash flows minus the original investment.
Projects with NPV > 0 increase stockholders\' return Projects with NPV < 0 decrease stockholders\' return 
Example: Net Present Value
Assume Newco is deciding between two machines (Machine A and Machine B) in order to add capacity to its existing plant. Using the cash flows in the table below, let's calculate the NPV for each machine and decide which project Newco should accept. Assume Newco's cost of capital is 8.4%.
Expected aftertax cash flows for the new machines
Calculation and Answer:
NPV_{A} = 5,000 + 500 + 1,000 + 1,000 + 1,500 + 2,500 + 1,000 = $469
(1.084)^{1} (1.084)^{2} (1.084)^{3} (1.084)^{4} (1.084)^{5} (1.084)^{6}NPV_{B} = 2,000 + 500 + 1,500 + 1,500 + 1,500 + 1,500 + 1,500 = $3,929
(1.084)^{1} (1.084)^{2} (1.084)^{3} (1.084)^{4} (1.084)^{5} (1.084)^{6}
Given that both machines have NPV > 0, both projects are acceptable. However, for mutually exclusive projects, the decision rule is to choose the project with the greatest NPV. Since the NPV_{B} > NPV_{A}, Newco should choose the project for Machine B.
We'll discuss additional applications of NPV in the following pages.


Budgeting
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Personal Finance
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Investing
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Economics
Explaining Appreciation
Appreciation refers to an increase over time in the value of an investment or asset. 
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