NPV is short for Net Present Value and it makes difference between the present value and cost of a project. In addition, NPV takes into account all cash flows through out the whole life of the projects, as well as the time value of money. And it compares like with like as all inflows and outflows are discounted to today¡¯s date. Also, the cost of capital is very unlikely to be changed over a period of time. To judge if the NPV is good, we should see the value of it, and the rule is the high the better. But, there is a rule for NPV, which is When NPV is greater than 0 we accept it, when the NPV is less than 0 we reject it. What is more, the net present value rule states that managers increase shareholders¡¯ wealth by accepting all projects that are worth more than they cost. Therefore, they should accept all projects with a positive net present value. When choosing between mutually exclusive projects, the decision rule is simple. Calculate the NPV of each project and, from those options that have a positive NPV, choose the one whose NPV is highest. In Fisher¡¯s separation theorem, it states that companies can make their investment decisions independently of individual shareholders¡¯ consumption decision by using the NPV rule. Moreover, the formula of NPV is NPV=PV-required investment, and there is a traditional way to calculate NPV, which is to use DCF, but, with real investment options DCF is not the appropriate way of calculating NPV. Sometimes, sunk costs are thought to be considered when calculating NPV, but, this is improper because sunk costs are past and irreversible outflows, e.g. cost of research for a new project. Furthermore sunk costs remain the same whether or not you accept the project. Therefore, they do not affect project NPV.

...Net Present Value
Net present value (NPV) and Internal rate of return (IRR) are used to determine whether to accept a project or not.Net Present Value (NPV)Net present value is the difference between the present value of cash inflows and the present value of cash outflows. It is used in capital budgeting to analyze the profitability of an investment or project.
NPV= sum[CFt/(1+r)t]-C0
CFt– cash flow in the time t
C0 – initial investment
r – periodic interest rate
NPV rule:
Accept all independent projects with NPV greater than 0 as they add value to shareholder. In case of mutually exclusive projects, the project with the highest NPV should be chosen
Advantages:
Direct measure of the dollar contribution to the stockholders.
NPV method is preferable for non-normal cash flows (e.g. negative cash flows)
Disadvantage:
Does NOT measure the project size.
Internal Rate of Return (IRR)
The discount rate makes the net present value of all cash flows from a project equal to zero. The higher a project's internal rate of return, the more desirable it is to undertake the project. IRR can be used to rank several prospective projects a firm is considering.
NPV= Sum[CFt/(1+r)t]–C0
r = internal rate of return (IRR)
IRR rule:
Accept all independent projects with IRR greater than cost of capital. In case of mutually exclusive projects, the project with...

...“THE ADVANTAGES AND DISADVANTAGES OF USINFG NPV (NET PRESENT VALUE) AND IRR (INTERNAL RATE OF RETURN)”
NPV (NET PRESENT VALUE)
The difference between the present value of cash inflows and the present value of cash outflows. NPV is used in capital budgeting to analyze the profitability of an investment or project. NPV analysis is sensitive to the reliability of future cash inflows that an investment or project will yield.NPV compares the value of a dollar today to the value of that same dollar in the future, taking inflation and returns into account. If the NPV of a prospective project is positive, it should be accepted. However, if NPV is negative, the project should probably be rejected because cash flows will also be negative.
Net present value, or NPV, is one of the calculations business managers use to evaluate capital projects. A capital project is a long-term investment or improvement, such as building a new store. The NPV calculation determines the present value of the project's projected future income. In the calculation, the present value of the project's cost is subtracted from the present value of future income. A positive net present value usually means you should accept or implement the project. Business owners who compare two or more projects tend to favor the one with the higher net present value.
ADVANTAGES OF NET PRESENT...

...government regulations. There are three categories of investment decisions: acceptance or rejection, ranking of projects, and choosing between projects. To assess whether it is viable to invest or not the NPV technique can be used to compare the present value of returns and costs. If the NPV is negative it implies that costs exceed returns and hence it would not be advisable to invest in such projects. There are also other investment appraisal techniques that are employed apart from the NPV; these are the pay back method, accounting rate of return and internal rate of return method.
Net present value (NPV) is generally considered as the most correct method for investment
appraisal because it focuses on cash and takes into account the time value of money and riskiness
of the investment project. The method is hence consistent with the objective of shareholder
wealth maximization (Shapiro, 2005). The net present value of an investment project is the
present value of the net cash inflows less the project’s initial investment outlay. If the resulting
NPV is positive, the company should accept the investment project; if it’s negative, the project
should be rejected. In mutually exclusive projects, the investment with higher net present value
should be accepted (Drury, 2004).
The use of NPV technique, which is the most appropriate to evaluate investment projects, require the identification of a...

...Comparing Net Present Value and Internal Rate of Return
by Harold Bierman, Jr
Executive Summary
• • • Net present value (NPV) and internal rate of return (IRR) are two very practical discounted cash flow (DCF) calculations used for making capital budgeting decisions. NPV and IRR lead to the same decisions with investments that are independent. With mutually exclusive investments, the NPV method is easier to use and more reliable.
Introduction
To this point neither of the two discounted cash flow procedures for evaluating an investment is obviously incorrect. In many situations, the internal rate of return (IRR) procedure will lead to the same decision as the net present value (NPV) procedure, but there are also times when the IRR may lead to different decisions from those obtained by using the net present value procedure. When the two methods lead to different decisions, the net present value method tends to give better decisions. It is sometimes possible to use the IRR method in such a way that it gives the same results as the NPV method. For this to occur, it is necessary that the rate of discount at which it is appropriate to discount future cash proceeds be the same for all future years. If the appropriate rate of interest varies from year to year, then the two procedures may not give identical answers. It is easy to use the NPV method correctly. It is much more difficult to...

...Advanced Time Value of Money Problems
Professor A. Spieler
Question 1 (mortgage problem)
(Try to work this question WITHOUT using Excel)
You purchase a house that costs $625,000 with an 8%, 30-year mortgage. You make a 20% down payment to avoid PMI insurance.
1. What is your monthly payment?
2. Amortize the first and second payments.
3. What is the mortgage balance after 5 years?
4. What percentage of the principal is paid off after 5 years?
5. Suppose after 5 years you refinance at 6% the remaining balance at a cost of $10,000, for 30 years. What is your new monthly payment?
6. Further, suppose you maintain the same payments as in (1), i.e. pre-pay on the principal, how many YEARS until you payoff the mortgage?
Question 2 (2nd mortgage problem)
You are considering the purchase of a $500,000 home. You plan to take a 30-year fixed mortgage after making a 20% downpayment to avoid PMI. Payments are to be made monthly (at the end of the month) and the APR is 8%.
1. What is the monthly payment?
2. During what month does the principal portion first exceed the interest portion? Are you surprised by your answer?
3. How long does it take to pay off your mortgage if you pay an additional $300 towards principal each payment?
4. How long does it take to pay off your mortgage if you pay an additional amount each month equal to the current month’s principal?
Question 3 (College planning)
Your child was just born and you are planning for his/her college education....

...How do the results of the NPV technique relate to the goal of maximizing shareholder wealth?
The NPV technique measures the present value of the future cash flows that a project will produce. A positive NPV means that the investment should increase the value of the firm and lead to maximizing shareholder wealth. A positive NPV project provides a return that is more than enough to compensate for the required return on the investment. Thus, using NPV as a guideline for capital investment decisions is consistent with the goal of creating wealth.
In theory, why is NPV the most appropriate technique for making capital budgeting decisions?
The NPV method is theoretically the most appropriate method for making capital budgeting decisions because it measure wealth creation, which is the assumed goal of financial management. NPV is an absolute measure of a project’s profitability and indicates the expected change in owners’ wealth from a capital investment. As an evaluation technique, NPV considers all expected future cash flows, the time value of money, and the risk of the future cash flows. Thus, NPV can help identify projects that maximize shareholder wealth.
If a firm selects a project with an NPV of $75,000, what impact should this decision have on shareholder wealth?
If the estimated cash flows and discount rate are...

...Examples Of Net Present Value (NPV), ROI and
Payback Analysis
Introduction
Terms and Definitions
Net Present Value - Method of calculating the expected net monetary gain or loss from a project by discounting all expected future cash inflows and outflows to the present point in time.
Discount Rate - Also known as the hurdle rate or required rate of return, is the rate that a project must achieve in order to be accepted rather than rejected.
Return on Investment – Expected income divided by the amount originally invested
Payback Analysis – The number of years needed to recover the initial cash outlay.
Formulas
Net Present Value = (t=1..n A * (1+r)-t OR (t=1..n A/ (1+r)t
Where A = Cash flow
r = Required rate of return
t = year of cash flow
n = the nth year
Return On Investment = (Discounted Benefits – Discounted Costs) / Discounted Costs
Payback Period = Years taken to repay initial outlay .
Eg. Project Z Outlay = $ 4000
Yearly cash flows = $2000
Payback period = 2yrs
Examples
• Required rate of Return = 10%
|Project A | Year 1...

...Net Present Value
Net Present Value (NPV) is used in capital budgeting to analyze the profitability of an investment or project. NPV is found by subtracting the present value of the after-tax outflows from the present value of the after-tax inflows. Investments with a positive NPV increase shareholder value and those with a negative NPV reduce shareholder value. In order to compute the NPV for Worldwide Paper Company, we have to calculate the cash flow in capital budgeting of the project as below.
| | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | Terminal Cash flow |
A | Fixed Assets | | | | | | | | |
| Cost of Investment | -$16 | -$2 | | | | | | |
| Sales of Fixed Asset | | | | | | | | $1.08 |
B | Working Capital | | | | | | | | |
| Incremental Sales | | $4 | $6 | | | | | |
| Change in Working Capital (10%) | | $0.4 | $0.6 | | | | | |
| Cash flow of investment in working capital | | -$0.4 | -$0.6 | | | | | $1.0 |
C | Operating Cash Flow | | | | | | | | |
| Revenue of Investment | | $4 | $10 | $10 | $10 | $10 | $10 | |
- | Cost of Good Sold (75%) | | -$3 | -$7.5 | -$7.5 | -$7.5 | -$7.5 | -$7.5 | |
- | SG&A expenses (5%) | | -$0.2 | -$0.5 | -$0.5 | -$0.5 | -$0.5 | -$0.5 | |
| Net Income | | $0.8 | $2 | $2 | $2 | $2 | $2 | |
+ | Operating Saving | | $2 | $3.5 | $3.5 | $3.5 | $3.5 | $3.5 | |
- |...