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38WGfd̙ԔԔ?Net Present Value Made EasyImpact$
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LThe ability to perform net present
value calculations is a great skill to have.
The applications are limitless and net present
value is very flexible. Research indicates that it
is one of the best financial decision tools available.
Fortunately, once you see how it works it is a very
simple tool to use.
Use your Arrow Keys to navigate the slides. J3H
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38WGfd̙ԔԔ?Net Present Value Made EasyImpact$
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KTwo Keys to Success
There are two keys to success when doing net present value:
cash flows
and interest rate
When doing NPV problems, the two keys to success are guesses (estimates). They are important guesses because they affect the outcome of the NPV analysis and your decision.
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ACash Flows
Usually, a business project or business investment will have cash flows. That is, sometimes an entity doing a project will be spending money and sometimes the business entity will be receiving money. Money going out of the entity is called a negative cash flow and money received by the entity is called a positive cash flow.
The focus of a NPV analysis is cash flows. A primary job of a person doing a NPV analysis is determining the amount and the timing of cash flows. As mentioned before, cash flows are usually an estimate. 73.3
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TInterest Rate
In order to do a NPV analysis, you need to have an interest rate. Interest rates vary depending on what you want to do. Credit cards offer various interest rates, and mortgages, savings accounts, etc will offer even different interest rates. In addition, interest rates change frequently.
As with cash flows, the interest rate used in a NPV analysis is a guess. Although just an estimate, the interest rate used in the analysis will have a huge impact on the outcome of the analysis and therefore the business decision.
So what interest rate should be used? VG %33
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What Interest Rate Should be Used?
Since the interest rate used in a NPV analysis is a guess, there are many different ways to choose an interest rate. The interest rate should be chosen carefully because the interest rate will affect the decision in a very big way. In fact, unprofitable projects can be made to look profitable, simply by the the interest rate used in the analysis. Of course, the opposite can occur also.
Here is one common way to choose an interest rate:
Usually a business will have a rate of return on investments and projects that the organization strives to achieve. That rate might be 15%, 20%, 25%, etc. It depends on the business and the policy of the management. Start with the desired rate of return and add a percentage point or two if the project is not too risky. If the project is very risky, add several percentage points to the desired rate of return. 6#^#^
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:The Timing of Cash Flows
As said before, the amounts and timing of cash flows need to be estimated. Since NPV is a method of analyzing future alternatives, and the future is usually quite uncertain, there is a limit as to how precise the timing of cash flows can be determined. For example, a person could try to forecast future cash flows to the day and hour, but that would be too impractical and the person would probably be wrong anyway.
Most people believe the tradeoff between accuracy and practicality is a year. That is, when people do NPV, they only attempt to estimate cash flows to the nearest year. For example, any cash flows taking place in a given year are assumed to take place on the last day of that given year. A very rough estimate, but it works in most cases and it simplifies the NPV analysis. 6""
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+Recognizing Some Cash Flow Patterns
There are only two types of cash flow patterns used in NPV analysis.
Lump Sum
and Annuity
A lump sum is just what the name implies. A lump sum of money, received or paid, on a certain date. For example: a person receives (or pays out) $1,000,000 at the end of year 2018.
An annuity is a series of equal payments over equal periods of time. For example: a person receives (or pays out) $10,000 at the end of each year for the next 20 years.
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The key to solving NPV problems is the time line. A time line looks as follows:6RR
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You place the estimated cash flows onto the time line in order to gain a clear understanding of the cash flow patterns. The following is an example:6
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gEverything Needed to Solve the NPV Problem
The last thing to enter is the interest rate being used in the analysis. This problem is going to use 15%
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=Everything Needed to Solve the NPV Problem (really)
Last slide I said that we had everything we needed to solve the problem. I forgot one important thing: either a calculator that can do cash flows or present value tables.
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.Problem #1: Solving an Annuity Problem
By looking at the time line below, it is easy to see that the cash flows represent an annuity (equal payments & equal periods of time). You need to look at the Present Value of an Annuity Table to get the factor.
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8Looking at the Present Value of an Annuity Table you see Interest Rates along the top of the table and Periods down the left side of the table. In problem #1, the interest rate is 15% and the number of periods is 5. The payments happen each and every year, starting at the end of year 1 and terminating at the end of year 5.
The appropriate factor from the table should be 3.35216 or something close to it. :z3
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!Problem #1: Solving an Annuity Problem
On the last slide we found the factor to be 3.35216
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Present Value = 3.25216 x $1,000
Present Value = $325.22 (negative number)
That is all you do to find the PV of an annuity.zQ%331
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JProblem #2: Solving a Lump Sum Problem
Here is a lump sum problem. Lump sum problems are pretty easy. Again, you need to look up a factor. Be sure to look up the factor on a Present Value of a Lump Sum table. Sometimes those tables are called Present Value of $1.
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Present Value = .65752 x $5,000
Present Value = $3,287.60 (positive cash flow) L" .`
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%Problem #3: Mixing An Annuity and a Lump Sum
Check out the following cash flows. If you look carefully, you will see that there is an annuity for years 16 and a lump sum at the end of the 7th year. The interest rate has been changed to 12%.
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Solution: Find the present value of the annuity (12% & 6 periods)
Present Value = 4.11141 x $3,000 = $12,334.23
Next: find the present value of the lump sum ($12% & 7th period)
Present Value = .45235 x $10,000 = $452.35
Finally: simply add the two present values together for the final answer.
$12,334.23 + $452.35 = $12,786.58C>6 9J?
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Although it looks different, this problem is similar to the problem we just did. Below we have an annuity (equal payments & equal periods of time), but the annuity begins at the end of year 3 and extends to the end of year 7. If you count the number of payments, you would see that there are 5 payments of $5,000 each. The first step is to find the present value of the annuity.
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3Solution: Find the present value of the annuity (12% & 5 periods, not 7 periods)
Present Value = 3.60478 x $5,000 = $18,023.90
We are left with a lump sum of $18,023.90. Notice that it is placed at the end of year 2. Now, just find the present value of a lump sum $18,023.90, 12%, period 24833=,K
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Sometimes there will be cash flows that occur in different amounts and at different times. The key is to treat them as separate lump sums and then add each present value together.
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Present Value of $2,500, end of year 2, 12% = .79719 x $2,500 = $1,992.98
Present Value of $4,000, end of year 3, 12% = .71178 x $4,000 = $2,847.12
Present Value of $3,500, end of year 5, 12% = .56743 x $3,500 = $1,986.01
Grand total and final answer = $6,826.11 <w
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mProblem #6: Mixing Positive and Negative Cash Flows
Often times when analyzing business opportunities, there are a combination of positive and negative cash flows. For example, perhaps a business must invest $3,000 for the first three years in order to receive $10,000 at the end of the 4th and 5th years. Again, all cash flows are assumed to take place at the end of each year.
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9Solution:
PV of $3,000 Annuity, 3 years, 12% = 2.40183 x $3,000 = $7,205.49
PV of $10,000, end of year 4, 12% = .63552 x $10,000 = $6,355.20
PV of $10,000, end of year 5, 12% = .56743 x $10,000 = $5,674.30
Grand total and final answer = $4,824.01 3.3 3
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ePutting it All Together
So what does this all mean? How do you use it to solve business problems?
Here are the steps:
#1. Determine the cash flows in regard to the business opportunity you are analyzing and place the cash flows on a time line.
#2. Determine a rate of interest. A good place to start is the rate of return you would like to earn. Add percentage points if the opportunity is very risky.
#3. Find the present value of all cash flows. Do not forget to distinguish positive and negative cash flows.
#4. If the final result of your present value calculations is greater than zero, the project might be worth doing. If the final result of your present value calculations is less than zero, the business opportunity fails the NPV test and the project might not be worth further consideration.
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dPractice Problem #1: Converting to a Company Wide Software System
During years one and two, a company is spending $5,000 each year on a new computer software system. The company expects to save (positive cash flow) $8,000 each year for years 3, 4, 5, & 6. Is the project worthy of consideration if the company expects a 15% return on its investments? FE E
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wPractice Problem #1: Solution
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PV of $5,000 Annuity, 2 years, 15% = 1.62571 x $5,000 = $8,450.25
PV of $8,000 Annuity, 4 years, 15% = 2.85498 x $8,000 = $22,839.84
(The $22,839.84 is lands at the end of year 2 and must be treated as a lump sum)
PV of $22,839.84, end of year 2, 15% = .75614 x $22,839.84 = $17,270.12
Add up the results inside the boxes for the final total = $8,819.87
Since the end result is positive (greater than zero) the project passes the NPV test and might be worthy of further consideration.93'33[I
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rPractice Problem #2: Adding a New Technology Department
A company has decided to add a new technology department. During year one the cost will be $10,000. During years 2 7 the cost of operating the department is expected to be $5,000 each year. During year 5, the department will be upgraded. The upgrade will cost $4,000. This $4,000 upgrade is an additional cost over and above the normal operating cost of $5,000 during year 5.
The company expects to save (positive cash flow) $9,000 each and every year for years 1 7. The company expects to earn a 10% rate of return on this investment. Does the project pass the NPV test? 6;M;M
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wPractice Problem #2: Solution
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As indicated on the previous slide, here are the revised cash flows:
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rThere are a few different ways to go about this, but here is a straight forward approach:
PV of $1,000, lump sum, year 1, 10% = .90909 x $1,000 = $909.09
PV of $4,000 Annuity, years 2  4 (3 years), 10% = 2.48685 x $4,000 = $9,947.40
(the PV of the annuity lands at the end of year 1 and must be treated as a lump sum)
PV of $9,947.40, year 1, 10% = ,90909 x $9,947.40 = $9,043.08
PV of $4,000 Annuity, years 6 7 (2 years), 10% = 1.73554 x $4,000 = $6,942.16
(the PV of the annuity lands at the end of year 5 and must be treated as a lump sum)
PV of $6,942.16, lump sum, year 5, 10% = .62092 x $6,942.16 = $4,310.53
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VPV of $1,000, lump sum, year 1, 10% = .90909 x $1,000 = $909.09
PV of $4,000 Annuity, years 2  4 (3 years), 10% = 2.48685 x $4,000 = $9,947.40
(the PV of the annuity lands at the end of year 1 and must be treated as a lump sum)
PV of $9,947.40, year 1, 10% = ,90909 x $9,947.40 = $9,043.08
PV of $4,000 Annuity, years 6 7 (2 years), 10% = 1.73554 x $4,000 = $6,942.16
(the PV of the annuity lands at the end of year 5 and must be treated as a lump sum)
PV of $6,942.16, lump sum, year 5, 10% = .62092 x $6,942.16 = $4,310.53
Combining the numbers in the boxes equals $12,444.52
$12,444.52 is greater than zero and so the project passes the NPV test and should be considered further.
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The moral of the story is that when a cash flow is listed at the beginning of the time line, the amount is already at the present value and no additional calculation are required for that first $1,000. See the next slide for more infoH
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