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Thursday, March 31, 2011

How Net Present Value is calculated

The Net Present Value (NPV) calculation makes use of an important time variable to tell you 1) the value of an investment at present time given future cash flows and 2) if the investment is worthwhile. Net Present Value is important in valuation of projects and investments because the combination of estimated value based on cost, yields and cash flow can sometimes paint an inaccurate financial mirage without quantification of the variables.

Another reason why Net Present Value calculations are useful is because they can help determine if an investment or project is more profitable than it actually is in less uncertain terms. With numerical figures entered into a proven formula, the only factors that may be questionable are the future cash flows and cost of capital. Moreover, if these can be reliably estimated, the resulting NPV stands a greater chance of accurately predicting present value.


When NPV calculations are used 


If you buy a bond and know the periodic interest rate, and will receive the face value of the bond at a specific point in time like 10 years, then fair valuation would price the bond at the present value of all future payments. Present value adds up all the interest payments, and the difference between the initial purchase price of the bond and the future reimbursement to arrive at a present value. In another circumstance maybe a bond is bought from someone else several years after it was originally issued and you want to know the price. Net Present Value would factor in additional costs if the bond investment were considered as a project.

Perhaps you are a project manager and are attempting to illustrate the value of a project to another executive. The Net Present Value calculation will mathematically give you the total value of an investment's returns that are in the future and are based on key variables including 1) the cost of capital, 2) time, and 3) negative and positive cash flow. Two more examples of circumstances in which NPV calculations may be used are below:

• Example 1: Your business purchases tax free bonds with some of its earnings. The bonds pay 5% every 6 months for 10 years at which time the face amount of the bond is either redeemable without penalty or rolled over. You are trying to calculate how much you should pay for the bond not to be overcharged and use a NPV calculation to do so.

• Example 2: Your company is thinking about investing in a project and wants to know if the opportunity cost is lower than the rate of return for the project. You know how much the initial investment is and have a good idea of what your annual returns will be and how much, if any, the financing of the project will cost. The NPV calculation can help you with the decision.

NPV calculations and methods of calculation


Net Present Value can be calculated in a number of ways and a number of different NPV calculations exist for varying circumstances. In other words, due to differences in variables used, Net Present Value calculations can differ. For example, a bonds can provide either fixed or variable rates of return. Both cases require different calculations. Additionally, cash flows can vary from year to year due to changes in project success and/or cost. NPV can be calculated manually, with regular or financial calculators or with financial software. Examples of NPV calculations are below:

Calculating Net Present Value against costs of capital and opportunity cost for a fixed rate bond 


Variables: Term of the bond 10 years
Fixed rate of return 5% annual
Future Face Value: $ 5000.00
Interest payments: Bi-annual

Step 1: Calculate present value:
$5000.00 x 5%= $250.00 x 10/20=$125.00
$125.00 x 20=$2,500 + $5000.00 =$7,500.00
The bond is worth $7,500 at present with all cash flow included

Step 2: Reduce value by cost of capital
Cost of capital, inflation + opportunity cost
3.35% (est .avrg)+2% (est. return after risk reduction)
=5.35% = $3210.00+$5000.00=$8,210.00

Step 3: Subtract present values for net present value
$8,210-$7,500= -$720.00
NPV= - $720.00

Conclusion: The bond is a bad investment based on cost of capital and opportunity cost discounting.

Calculating Net Present Value with inconsistent cash flow


Variables: Project down payment $5000.00
Cost of financed capital (Annual project yield -Annual project cost): 12% per year
Time period: 10 years
Cash flows: Between 12-18% ascending return per year

Step 1: Calculate present value of each individual estimated cash flow
Y1: $600.00 Y2: $625.00 Y3: $650.00 Y4: $675.00 Y5: $700.00 Y6: $825.00 Y7: $850.00 Y8: $875.00 Y9: $900.00 Y10: $900

Step 2: Present value for each future year's payment equals percentage yield plus value to which that yield can be added to amount to the future yield. EX: $600 =$535.71 x 12%., $625.00 =$498.246 x 12% for 2 years.

Step 3: For each year add the present value to arrive at Net Present Value. Ex. $535.71 + 498.25= $1033.96 for 2 year Net Present Value.

Source:

Brigham and Houston. 'Fundamentals of Financial Management 9th ed.' Mason, Ohio. South-Western, 2001, Chapters 8 + 11.

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