Capital budgeting (or investment appraisal) is the planning process used to determine whether a firm's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing. It is budget for major capital, or investment, expenditures.

Many formal methods are used in capital budgeting, including the techniques such as

Accounting rate of return Net present value Profitability index Internal rate of return Modified internal rate of return Equivalent annuity

These methods use the incremental cash flows from each potential investment, or project Techniques based on accounting earnings and accounting rules are sometimes used - though economists consider this to be improper - such as the accounting rate of return, and "return on investment." Simplified and hybrid methods are used as well, such as payback period and discounted payback period.

I. Net Present Value (NPV) or net present worth (NPW) is defined as the sum of the present values (PVs) of the individual cash flows. In the case when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV). NPV is a central tool in discounted cash flow (DCF) analysis, and is a standard method for using the time value of money to appraise long-term projects. Used for capital budgeting, and widely throughout economics, finance, and accounting, it measures the excess or shortfall of cash flows, in present value terms, once financing charges are met.

Formula

Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore NPV is the sum of all terms,

where

t - the time of the cash flowi - the discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk.)

file: jakartaprofessional.wordpress.com 1

Rt - the net cash flow (the amount of cash, inflow minus outflow) at time t (for educational purposes, R0 is commonly placed to the left of the sum to emphasize its role as (minus) the investment.

The result of this formula if multiplied with the Annual Net cash in-flows and reduced by Initial Cash outlay will be the present value but in case where the cash flows are not equal in amount then the previous formula will be used to determine the present value of each cash flow separately. Any cash flow within 12 months will not be discounted for NPV purpose.

What NPV MeansNPV is an indicator of how much value an investment or project adds to the firm. With a particular project, if Rt is a positive value, the project is in the status of discounted cash inflow in the time of t. If Rt is a negative value, the project is in the status of discounted cash outflow in the time of t. Appropriately risked projects with a positive NPV could be accepted. This does not necessarily mean that they should be undertaken since NPV at the cost of capital may not account for opportunity cost, i.e. comparison with other available investments. In financial theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher no-no should be selected.

If... It means... Then...NPV > 0

the investment would add value to the firm the project may be accepted

NPV < 0

the investment would subtract value from the firm

the project should be rejected

NPV = 0

the investment would neither gain nor lose value for the firm

We should be indifferent in the decision whether to accept or reject the project. This project adds no monetary value. Decision should be based on other criteria, e.g. strategic positioning or other factors not explicitly included in the calculation.

Example

A 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 $100,000 (which might include machinery, and employee training costs). Other cash outflows for years 1-6 are expected to be $5,000 per year. Cash inflows are expected to be $30,000 each 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:

file: jakartaprofessional.wordpress.com 2

Year Cashflow Present Value

T=0 -$100,000

T=1 $22,727

T=2 $20,661

T=3 $18,783

T=4 $17,075

T=5 $15,523

T=6 $14,112

The sum of all these present values is the net present value, which equals $8,881.52. Since the NPV is greater than zero, it would be better to invest in the project than to do nothing, and the corporation should invest in this project if there is no mutualy exclusive alternative with a higher NPV.

Discount rate is an interest rate a central bank charges depository institutions that borrow reserves from it.

The term discount rate has two meanings:

the same as interest rate; the term "discount" does not refer to the common meaning of the word, but to the meaning in computations of present value, e.g. net present value or discounted cash flow

the annual effective discount rate, which is the annual interest divided by the capital including that interest; this rate is lower than the interest rate; it corresponds to using the value after a year as the nominal value, and seeing the initial value as the nominal value minus a discount; it is used for Treasury Bills and similar financial instruments

Annual effective discount rate

The annual effective discount rate is the annual interest divided by the capital including that interest, which is the interest rate divided by 100% plus the interest rate. It is the

file: jakartaprofessional.wordpress.com 3

annual discount factor to be applied to the future cash flow, to find the discount, subtracted from a future value to find the value one year earlier.

For example, suppose there is a government bond that sells for $95 and pays $100 in a year's time. The discount rate according to the given definition is

The interest rate is calculated using 95 as its base:

For every annual effective interest rate, there is a corresponding annual effective discount rate, given by the following formula:

or inversely,

where the approximations apply for small i and d; in fact i - d = id.

Payback period in capital budgeting refers to the period of time required for the return on an investment to "repay" the sum of the original investment. For example, a $1000 investment which returned $500 per year would have a two year payback period. The time value of money is not taken into account. Payback period intuitively measures how long something takes to "pay for itself." All else being equal, shorter payback periods are preferable to longer payback periods.

The time value of money is the value of money figuring in a given amount of interest earned over a given amount of time.

For example, 100 dollars of today's money invested for one year and earning 5 percent interest will be worth 105 dollars after one year. Therefore, 100 dollars paid now or 105 dollars paid exactly one year from now both have the same value to the recipient who assumes 5 percent interest; using time value of money terminology, 100 dollars invested for one year at 5 percent interest has a future value of 105 dollars.

file: jakartaprofessional.wordpress.com 4

Formula

Present value of a future sum

The present value formula is the core formula for the time value of money; each of the other formulae is derived from this formula. For example, the annuity formula is the sum of a series of present value calculations.

The present value (PV) formula has four variables, each of which can be solved for:

1. PV is the value at time=02. FV is the value at time=n3. i is the rate at which the amount will be compounded each period4. n is the number of periods (not necessarily an integer)

The cumulative present value of future cash flows can be calculated by summing the contributions of FVt, the value of cash flow at time=t

Note that this series can be summed for a given value of n, or when n is .

Payback Period Method for Capital Budgeting Decisions:Objectives:

1. Define and Explain payback period.2. Determine the payback period for an investment project.3. What are the advantages and disadvantages of Payback method?

Definition and Explanation:The payback is another method to evaluate an investment project. The payback method focuses on the payback period. The payback period is the length of time that it takes for a project to recoup its initial cost out of the cash receipts that it generates. This period is some times referred to as" the time that it takes for an investment to pay for itself." The basic premise of the payback method is that the more quickly the cost of an investment can be recovered, the more desirable is the investment. The payback period is expressed in years. When the net annual cash inflow is the same every year, the following formula can be used to calculate the payback period.

file: jakartaprofessional.wordpress.com 5

Formula / Equation:The formula or equation for the calculation of payback period is as follows:

Payback period = Investment required / Net annual cash inflow*

*If new equipment is replacing old equipment, this becomes incremental net annual cash inflow.

To illustrate the payback method, consider the following example:

Example:York company needs a new milling machine. The company is considering two machines. Machine A and machine B. Machine A costs $15,000 and will reduce operating cost by $5,000 per year. Machine B costs only $12,000 but will also reduce operating costs by $5,000 per year.

Required:

Calculate payback period. Which machine should be purchased according to payback method?

Calculation:

Machine A payback period = $15,000 / $5,000 = 3.0 years

Machine B payback period = $12,000 / $5,000 = 2.4 years

According to payback calculations, York company should purchase machine B, since it has a shorter payback period than machine A.

Evaluation of the Payback Period Method:The payback method is not a true measure of the profitability of an investment. Rather, it simply tells the manager how many years will be required to recover the original investment. Unfortunately, a shorter payback period does not always mean that one investment is more desirable than another.

To illustrate, consider again the two machines used in the example above. since machine B has a shorter payback period than machine A, it appears that machine B is more desirable than machine A. But if we add one more piece of information, this illusion quickly disappears. Machine A has a project 10-years life, and machine B has a projected 5 years life. It would take two purchases of machine B to provide the same length of service as would be provided by a single purchase of machine A. Under these circumstances, machine A would be a much better investment than machine B, even though machine B has a shorter payback period. Unfortunately, the payback method has no inherent mechanism for highlighting differences in useful life between investments. Such differences can be very important, and relying on payback alone may result in incorrect decisions.

file: jakartaprofessional.wordpress.com 6

Another criticism of payback method is that it does not consider the time value of money. A cash inflow to be received several years in the future is weighed equally with a cash inflow to be received right now. To illustrate, assume that for an investment of $8,000 you can purchase either of the two following streams of cash inflows: 

Years 0 1 2 3 4 5 6 7 8

Stream 1         $8,000 $2,000 $2,000 $2,000 $2,000

Stream 2   $2,000 $2,000 $2,000 $2,000 $8,000      

Which stream of cash inflows would you prefer to receive to receive in return for your $8,000 investment? Each stream has a payback period of four years. Therefore, if payback method alone were relied on in making the decision, you would be forced to say that the streams are equally desirable. However from the point of view of the time value of money, stream 2 is much more desirable than stream 1.

On the other hand, under certain conditions the payback method can be very useful. For one thing, it can help identify which investment proposals are in the "ballpark." That is, it can be used as a screening tool to help answer the question, "Should I consider this proposal further?" If a proposal does not provide a payback within some specified period, then there may be no need to consider it further. In addition, the payback period is often of great importance to new firms that are "cash poor." When a firm is cash poor, a project with a short payback period but a low rate of return might be preferred over another project with a high rate of return but a long payback period. The reason is that the company may simply need a faster return of its cash investment. And finally, the payback method is sometimes used in industries where products become obsolete very rapidly - such as consumer electronics. Since products may last only a year or two, the payback period on investments must be very short.

Extension of Payback Method:The payback period is calculated by dividing the investment in a project by the net annual cash inflows that the project will generate. If equipment is replacing old equipment then any salvage to be received on disposal of the old equipment should be deducted from the cost of the new equipment, and only the incremental investment should be used in payback computation. In addition, any depreciation deducted in arriving at the project's net operating income must be added back to obtain the project's expected net annual cash inflow. To illustrate consider the following data:

Example 2:

Goodtime Fun Centers, Inc., operates many outlets in the eastern states. Some of the vending machines in one of its outlets provide very little revenue, so the company is considering removing the machines and installing equipment to dispense soft ice cream. The equipment would cost $80,000 and have an eight-year useful life. Incremental annual revenues and costs associated with the sale of ice cream would be as follows:

file: jakartaprofessional.wordpress.com 7

Sales $150,000Less cost of ingredients 90,000 Contribution margin 60,000 Less fixed expenses:       Salaries 27,000     Maintenance 3,000     Depreciation 10,000 Total fixed expenses 40,000 Net operating income $20,000  ===========

The vending machines can be sold for a $5,000 scrap value. The company will not purchase equipment unless it has a payback of three years or less. Should the equipment be purchased? An analysis of the payback period for the proposed equipment is given below:

Step 1: Compute the net annual cash inflow

Since the net annual cash inflow is not given, it must be computed before the payback period can be determined:   Net operating income (given above) $20,000Add: Noncash deduction for depreciation 10,000 Net annual cash inflow $30,000  =========   Step 2: Compute the payback period

Using the net annual cash inflow figure from above, the payback period can be determined as follows:   Cost of the new equipment $80,000Less salvage value of old equipment 5,000 Investment required $75,000  =========   

Payback period = Investment required / Net annual cash inflow

= $75,000 / $30,000

= 2.5 years

Several things should be noted from the above solution. First, notice that depreciation is added back to net operating income to obtain the net annual cash inflow from the new equipment. Depreciation is not a cash outlay; thus, it must be

file: jakartaprofessional.wordpress.com 8

added back to net operating income to adjust it to a cash basis. Second, notice in the payback computation that the salvage value from the old machines has been deducted from the cost of the new equipment, and that only the incremental investment has been used in computing the payback period.

Since the proposed equipment has a payback period of less than three years, the company's payback requirement has been met.

Payback and Uneven Cash Flows:When the cash flows associated with an investment project changes from year to year, the simple payback formula that we outlined earlier cannot be used. To understand this point consider the following data:

Example:Year Investment Cash Inflow

1 $4,000 $1,0002   03   2,0004 2,000 1,0005   5006   3,0007   2,0008   2,000

What is the payback period on this investment? The answer is 5.5 years, but to obtain this figure it is necessary to track the unrecovered investment year by year. The steps involved in this process are shown below:

Year

Beginning Unrecovered Investment Investment Cash Inflow

Ending Unrecovered Investment

(1) + (2) - (3)1 $     0 $4,000 $1,000 $3,0002 3,000   0 3,0003 3,000   2,000 1,0004 1,000 2,000 1,000 2,0005 2,000   500 1,5006 1,500   3,000 07 0   2,000 08 0   2,000 0                  

By the middle of the sixth year, sufficient cash inflows will have been realized to recover the entire investment of $6,000 ($4,000 + $2,000)

In Business | Rapid Obsolescence

file: jakartaprofessional.wordpress.com 9

Intel Corporation invests a billion to a billion and half dollars to fabricate computer processor chips such as the Pentium IV. But the fab plants can only be used to make state-of-the-art chips for about two years. By the end of that time, the equipment is obsolete and the plant must be converted to making less complicated chips. Under such conditions of rapid obsolescence, the payback method may be the most appropriate way to evaluate investments. If the project does not pay back within a few years, it may never pay back its initial investment.

Source: "Pentium at a Glance," Forbes ASAP, February 26, 1996, p.66.

Internal Rate of Return (IRR) Method in Capital Budgeting Decisions:Objectives:

1. Define and explain the internal rate of return (IRR).2. Evaluate the acceptability of an investment project using the internal rate of

return (IRR) method.3. What are the advantages and disadvantages of internal rate of return?

Definition and Explanation:The internal rate of return (IRR) is the rate of return promised by an investment project over its useful life. It is some time referred to simply as yield on project. The internal rate of return is computed by finding the discount rate that equates the present value of a project's cash out flow with the present value of its cash inflow In other words, the internal rate of return is that discount rate that will cause the net present value of a project to be equal to zero.

Example:A school is considering the purchase of a large tractor-pulled lawn mower. At present, the lawn is moved using a small hand pushed gas mower. The large tractor-pulled mower will cost $ 16,950 and will have a useful life of 10 years. It will have only a negligible scrap value, which can be ignored. The tractor-pulled mower will do the job much more quickly than the old mower and would result in a labor savings of $ 3,000 per year.

To compute the internal rate of return promised by the new mower, we must find the discount rate that will cause the new present value of the project to be zero. How do we do this?

The simplest and most direct approach when the net cash inflow is the same every year is to divide the investment in the project by the expected net annual cash inflow. This computation will yield a factor from which the internal rate of return can be determined.

file: jakartaprofessional.wordpress.com 10

The formula or equation is as follows:

[Factor of internal rate of return = Investment required / Net annual cash inflow]  (1)

The factor derived from formula (1) is then located in the present value tables to see what rate of return it represents. Using formula (1) and the data for school's proposed project, we get:

Investment required / Net annual cash inflow

= $16,950 / $3,000

= 5.650

Thus, the discount factor that will equate a series of $ 3,000 cash inflows with a present investment of $16,950. Now we need to find this factor in the table to see what rate of return it represents. We would use the 10-period line in the table since the cash flows for the project continue for 10 years. If we scan along the 10-period line, we find that a factor of 5.650 represents a 12% rate of return. (See Future Value and Present Value Tables page - Table 4) We can verify this by computing the project's net present value using a 12% discount rate. This computation is made as follows: 

Initial costLife of the project (years)Annual cost savingsSalvage value

$16,50010$3,0000

ItemYears Amount of cash flow 12% factor Present value of

cash flows

Annual cost savingsInitial investment

Net present value

1―10Now

$3,000(16,950)

5.650*1,000

$16,950(16950)---------

0======

*From Future Value and Present Value Tables page - Table 4

Notice that using a 12% discount rate equates the present value of the annual cash inflows with the present value of the investment required in the project, leaving a zero net present value. The 12% rate therefore represents the internal rate of return promised by the project.

Salvage Value and Other Cash Flows:The technique just demonstrated works very well if a project's cash flow s are identical every year. But what if they are not? For example, what if a project will have some salvage value at the end of its life in addition to the annual cash inflows? Under these circumstances, a trial and error process may be used to find the rate of return that will equate the cash inflow with the cash outflows. The trial and error process can be carried out by hand; however, computer software programs such as

file: jakartaprofessional.wordpress.com 11

spreadsheets can perform the necessary computations in seconds. In short, erratic or uneven cash flows should not prevent a manager from determining a project's internal rate of return.

Using the Internal Rate of Return:Once the internal rate of return has been computed, what does the manager do with the information? The internal rate of return is compared to the company's required rate of return. The required rate of return is the minimum rate of return that an investment project must yield to be acceptable. If the internal rate of return is equal to or greater than the required rate of return, than the project is acceptable. If it is less than the required rate of return, then the project is rejected. Quite often the company's cost of capital is used as the required rate of return. The reasoning is that if a project cannot provide a rate of return at least as greater as the cost of the funds invested in it, then it is not profitable.

The Cost of Capital as a Screening Tool:The cost of capital often operates as a screening device, helping the manager screen out undesirable investment projects. This screening is accomplished in different ways, depending on whether the company is using the internal rate of return method or the net present value method in its capital budgeting analysis.

When the internal rate of return method is used, the cost of capital is used as the hurdle rate that a project must clear for acceptance. If the internal rate of return of a project is not great enough to clear the cost of capital hurdle, then the project is ordinarily rejected. We saw the application of this idea in the above example where the hurdle rate was set at 15%.

When the net present value method is used, the cost of capital is the discount rate used to compute the net present value of a proposed project. Any project yielding a negative net present value is rejected unless other factors are significant enough to require its acceptance.

file: jakartaprofessional.wordpress.com 12

The use of cost of capital as a screening tool is summarized below:

The Cost of Capital as a Screening ToolThe Net Present Value Method The Internal Rate of Return Method

The cost of capital is used as the discount rate when computing the net present value of a project. Any project with a negative net present value is rejected unless other factors dictate its acceptance.

The cost of capital is compared to the internal rate of return promised by a project. Any project whose internal rate of return is less than the cost of capital is rejected unless other factors dictate its acceptance.

 Average ROR

In finance, rate of return (ROR), also known as return on investment (ROI), rate of profit or sometimes just return, is the ratio of money gained or lost (whether realized or unrealized) on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or net income/loss. The money invested may be referred to as the asset, capital, principal, or the cost basis of the investment. ROI is usually expressed as a percentage rather than a fraction.

The rate of return can be calculated over a single period, or expressed as an average over multiple periods.

A. Single-period: Arithmetic return

The arithmetic return is:

is sometimes referred to as the yield. See also: effective interest rate, effective annual rate (EAR) or annual percentage yield (APY).

B. Multiperiod average returns: Arithmetic average rate of return

The arithmetic average rate of return over n periods is defined as:

file: jakartaprofessional.wordpress.com 13

Calculating the Rate of Return on Investments

Let's say you invest $100 in stock, which is called your capital. One year later, your investment yields $110. What is the rate of return of your investment? We calculate it by using the following formula:

((Return - Capital) / Capital) X 100% = Rate of Return

Therefore,

(($110 - $100) / $100) X 100% = 10%

Your rate of return is 10%.

There are two ways to measure the rate of return on an investment.

Average annual rate of return (also known as average annual arithmetic return)Compound rate of return (also called average annual geometric return)

A simple example below will show what these two yardsticks measure.

You initially invest $100. One year later, your investment grows to $200 in value. The year after that, the investment drops back to $100. The rate of return after the first year is

((Return - Capital) / Capital) X 100% = Rate of Return

(($200 - $100) / $100) X 100% = 100%

The rate of return after the second year is

file: jakartaprofessional.wordpress.com 14

(($100 - $200) / $200) X 100% = -50%

By using the formulas for calculating the average annual rate of return, we get a percentage that measures gains accurately over only a short period. Whereas, the geometric or compound rate of return is a better yardstick to measure your investment over the long run. The arithmetic mean or average return should be used to calculate return on investment only in the short-term.

Average annual return (arithmetic mean) = (Rate of Return for Year 1 + Rate of Return for Year 2) / 2 = (100% + (-50%)) / 2 = 25% (Arithmetic return = 25%)

Compound return (geometric mean) = (capital / return) ^ (1 / n) - 1 where n = number of years. The formula is (100 / 100) ^ .5 - 1 = 0%. (Geometric return = 0%)

Note : Mutual fund managers report the average annual rate of return (arithmetic) on the investments they manage. As shown in the above example, the arithmetic return of the investment is 25%, even though the value of the investment is the same as it was two years ago. Thus, mutual fund reports are somewhat deceptive.

How to Compute Average Annual Rate of Return (optional)

Computing the average annual rate of return (ROR) for a bond, stock, fund, or trading strategy should be straightforward, shouldn’t it? For example, to get the average annual ROR for the last five years, don’t you just sum up the 5 individual annual returns, and divide by 5?

Well yes, you can do it that way. But what you’ll end up with is the arithmetic average, which is probably not really what you’re after. Why not? Let’s look at an example.

Say we’re examining a stock that had the following closing prices on December 31 of the following years:

Table 1Year 2000 2001 2002 2003 2004 2005Priceper

Share$111.19 $97.80 $76.12 $97.82 $108.32 $113.49

This translates into the following annual returns:Table 2

Year 2001 2002 2003 2004 2005AnnualROR -12.0% -22.2% +28.5% +10.7% +4.8%

file: jakartaprofessional.wordpress.com 15

Now we’ll follow our original assumption and compute the arithmetic average:

[ (-12.0) + (-22.2) + (28.5) + (10.7) + (4.8) ] / 5 = +2.0%

What’s wrong with our computation? Well nothing technically, but the arithmetic mean can mistakenly lead you to assume that if you had invested money 5 years ago, your investment today would be worth the same as if the fund returned that average +2.0% for each of those 5 years. But didn’t it?

If we had initially invested $10,000:At the end of year 1 it would be worth: $10,000 x (1-.12) = $8,800At the end of year 2 it would be worth: $8,800 x (1-.222) = $6,846At the end of year 3 it would be worth: $6,846 x (1+.285) = $8,798At the end of year 4 it would be worth: $8,798 x (1+.107) = $9,739At the end of year 5 it would be worth: $9,739 x (1+.048) = $10,206

Note that this is quite a different return than if we’d made that arithmetic average 2% each year:

At the end of year 1 it would be worth: $10,000 x (1+.02) = $10,200At the end of year 2 it would be worth: $10,200 x (1+.02) = $10,404At the end of year 3 it would be worth: $10,404 x (1+.02) = $10,612At the end of year 4 it would be worth: $10,612 x (1+.02) = $10,824At the end of year 5 it would be worth: $10,824 x (1+.02) = $11,041

Of course the problem with the arithmetic mean is that it doesn’t take into account the compounding effect of each yearly ROR. This would be fine if we invested say $10,000 each year and whether we made money or lost money, we still set our principal back to $10,000 for each subsequent year.

But most of us don’t invest that way. If we put money in a fund for a number of years, the amount invested in any particular year is what was leftover from the previous year.

Assuming this is the way we’re investing, if we wanted to figure out what equivalent yearly average return would give us what our investment is worth today, we have to use the geometric mean.

To compute the geometric mean, multiply each of the yearly returns (rather than summing them) and then take the nth root of the product (rather than dividing by n), where n is the number of years we’re averaging over.

For our n=5 years this would work out to be:

[(1-.12) x (1-.222) x (1+.285) x (1+.107) x (1+.048)](1/5) = 1.0041 or 0.41%

file: jakartaprofessional.wordpress.com 16

And in fact if we compound our initial principal at this geometric average, we do get what our investment is worth today:

At the end of year 1: $10,000 x (1+.0041) = $10,041At the end of year 2: $10,041 x (1+.0041) = $10,082At the end of year 3: $10,082 x (1+.0041) = $10,124At the end of year 4: $10,124 x (1+.0041) = $10,165At the end of year 5: $10,165 x (1+.0041) = $10,207

Actually you’ll see we’re off by one dollar, due to round-off error.

There is a simpler way to compute the geometric mean, and that is to use the beginning and ending prices in Table 1, but annualize the gain, again by taking the nth root where n is the number of years between beginning and end prices.

If we do this, we get the same as the geometric mean:

(113.49 / 111.19)(1/5) = 1.0041 or 0.41%

Apart from the calculation being simpler, the nice thing about annualizing is that you can get a yearly geometric mean, even when you have a non-integer number of years.

For example, let’s say that instead of annual prices we’re examining quarterly prices:

Table 3Quarter Q1 2005 Q2 2005 Q3 2005 Q4 2004 Q1 2006

Priceper

Share$64.08 $67.77 $81.02 $80.85 $83.52

We have 5 quarters, or 1.25 years worth of data, so we annualize to compute the following effective annual ROR:

(83.52 / 64.08) (1/1.25) = 1.2361 or 23.6%

So by annualizing, when computing average ROR we don’t have to restrict ourselves to periods where we have a complete year’s worth of data. This is helpful because chances are the stock or fund was not created on January 1 of its inception year and usually we’re part of the way into a new year.

By annualizing we can therefore include all price data available to us to get an average ROR – including fractional years.

file: jakartaprofessional.wordpress.com 17