# Back to basics: Mastering investment performance measurement.

It's back to basics for many businesses struggling to manage
their way through today's economic recession. Real estate
management firms are no exception. They understand that in order to
survive the current downturn they must master the essentials of basic
business acumen including financial fundamentals.

Measuring investment performance is one such critical business skill for today's real estate managers. Understanding how to accurately calculate net present value (NPV) and the internal rate of return (IRR) is essential to developing effective decision-making criteria. Typically, the management of income-producing properties involves three phases of real estate investment.

Part I: The "Going In" Phase

In this phase, the investor acquires the property for which a price is paid. Although there are some investors who may pay cash for the property; the majority of investors acquire properties with the use of two types of funds--mortgage funds and the investor's cash equity portion. The mortgage portion is typically based on a Loan to Value Ratio (LTV) imposed by the lender. This LTV ratio is applied against the total purchase price or the appraised value, which ever is least, in many cases. (Example: 75% LTV or 80% LTV.) The investor would need to provide the balance in the form of cash equity. This is generally referred to as "Investment Base." (See Chart A.)

In addition to the traditional terms of lending (i.e.; interest rare, LTV ratio, the amortization term, payment periods), the lender most often will use another judgement criteria called the debt coverage ratio (DCR). This is the ratio of net operating income to the annual debt service. It measures the ability of a property to meet its debt service out of net operating income. It is also referred to as the debt service coverage ratio (DSCR). Thus, for a property with a net operating income of $60,000 and annual debt service of $49,275, the debt coverage ratio is calculated as: NOI $60,000 / ADS $49,275 = DCR 1.22 (rounded). The .22 represents the cash flow position as well as the lender's margin of safety.

After considering the mortgage position, the balance of the purchase price must be paid by the borrower in the form of cash equity. In order to place these equity funds (investment base) into an income-producing property, investors want to receive an adequate return on their invested capital. This is called a "cash-on-cash return to equity", an "equity dividend rate", or even a "cash flow" rate. It might also be referred to as a "reinvestment rate", if used in conjunction with a FMRR "Financial Management Rate of Return" calculation.

The selection of the appropriate annual cash-on-cash return may come from various sources. First, the investor either may have owned a similar investment at one time, and received a certain annual return. This may become the benchmark for this new investment.

Second, national economic indicators, such as those from the American Council of Life Insurance Companies, Korpacz Real Estate Investor Survey, Pricewaterhouse-Coopers, LLP, or the Valuation Insight & Perspectives, published by the Appraisal Institute, might indicate that the range of cash-on-cash returns for this property type might, hypothetically, be from 10 percent to 12 percent. Thus, the investor might select a rate that is commensurate with these indicators.

Third, the investor might select a rate based on the "build up" method. Consider, for example, that prior to the acquisition, the $1,250,000, which will be used for the down payment, lies in an interest bearing account, drawing 4.5 percent per annum. This is considered a "safe rate" or return on capital. (See Chart B.)

Whether the owners funds are currently deposited into a 90-day Certificate of Deposit or Corporate Aaa Bond, consideration must be given to the anticipated holding period should the owner acquire this particular property. For example: If the anticipated holding period is five years, the "safe rate" should be commensurate with a return on capital received from a similar holding period. In this case, it might be a five-year Treasury Security of 4.32 percent (for purposes of this example, a safe rate of 4.50 percent).

To withdraw these funds and place them in a real estate venture, further consideration needs to be given to the following issues:

* Lack of Liquidity: An apartment complex, for example, cannot be liquidated overnight. It must first be placed on the open market for a reasonable period of time, before it will (hopefully) sell for the asking price. It cannot be immediately converted into M1 cash (i.e., cash on hand). The investor might consider adding a point or two to the safe rate, in order to build up his or her desired annual return on equity.

* Risk: There is always some risk attached to a real estate venture. The older the property, the greater the risk. The more deferred maintenance and upkeep, the greater the risk. Even tenant mix and lease terms might increase the risk. With an income-producing property, the quantity, quality, and durability of the income stream is extremely important. Therefore, it is essential that these elements be considered prior to the commencement of ownership. If these three factors are favorable, then there is less risk. If the leases are below the indicated market, or the terms are shorter than the terms in the market, then this might add additional risk to the venture. The inverse of this is that the newer the property and the more favorable the lease terms, the less risk.

* Burden of Management: Owners may be involved to some degree with the day-to-day management of the asset. This might consist of periodically visiting the property, spending time conversing with the manager, or consulting on such issues as operational and capital expenditure budgets.

* Profit: Entrepreneurial profit may also be an issue for the investor. (See Chart C.)

Part II: The "Holding Period"

Holding periods will likely vary according to geographic area and property type. In one local apartment market, the typical holding period might be seven years, while the holding period for a suburban office building might range from six to eight years. For purposes of this article, however, let's assume that the typical holding period is five years. During this holding period, the owner wishes to receive a healthy net operating income (NOI) in order to comfortably service the debt. The residual, after servicing the debt, is the pre-tax cash flow position. (See Chart D.)

Part III:

The "Going Out" Phase

In this final phase, the investor will sell the property and pay off the mortgage balance. The remainder is known as the "reversion" to the equity position. Let's assume that the sales price at the end of Year 5 is $6 million. From this amount, a sales commission of 3% was deducted, which left $5.82 million.

Sales Price: $6,000,000

Less Cost of Sale 3% $180,000

Total $5,820,000

From this amount, the loan balance at the end of Year 5 was deducted which resulted in the following:

Sales Price: $6,000,000

Less Cost of Sale 3% $180,000

Less Loan Balance $3,418,581

Reversion

(Sales Proceeds) $2,401,419

(See Chart E)

Net Present Value Calculations

Understanding how to perform a net present value calculation is essential for today's real estate managers. According to the Appraisal of Real Estate, 12th Edition, (the Appraisal Institute), net present value (dollar reward) "is the difference between the present value of all positive cash flows and the present value of all negative cash flows, or capital outlays. When the net present value of the positive cash flows is greater than the net present value of the negative cash flows or capital outlays, an investment is deemed viable. If the reverse relationship exists, the investment is not considered feasible."

As an example, let's assume that the pro-forma indicated earlier has been presented to the owner who desires a pre-tax internal rate of return of 16 percent. When using the HP 19BII to determine the NPV, it should be kept in mind that any time you rake money "out of pocket," you need to change its sign in order to make it a negative number. Thus, the model in the cash flow menu would be set up as follows: (See Chart F.)

In order to test the owner's desired return, the following keystrokes should be utilized:

Calc. 16 I

(The owner's desired return)

NPV $521,390

(will appear on display)

If the number that appears is a positive number, it denotes that the true internal rate of return is higher than the owner's desired return of 16 percent. If the number on display were negative, it would denote that the true internal rate of return is below the owner's desired return of 16 percent, thus falling short of the desired goal. If the number were zero, it would denote that the true internal rate of return was exactly 16 percent. (The IRR key displays: 26.028801).

The internal rate of return is the annualized yield rate or rate of return on capital that is generated or capable of being generated within an investment or portfolio over a period of ownership. This rate is similar to the equity yield rate. According to the Appraisal of Real Estate, the IRR is defined as "the rate of discount that produces a profitability index of one and a net present value of zero. It is often used to measure profitability after income taxes, i.e., the after-tax equity yield rate."

A way to test the internal rate of return is by using the following keystrokes (See Chart G) on the HP19BII (assuming an IRR of 26.028801).

This supports the definition that "it is that rate that will discount all cash flows plus the reversion, back to an amount that is equal to the original investment base."

Returning to the NPV calculation, with a NPV being a positive $521,390, it further denotes that by adding this amount to the original investment base of $1.25 million for a total of $1,771,390, the internal rate of return would be exactly 16 percent. (See Chart H.)

If the previously calculated NPV were a negative number, it would further denote that the investor put that much more down than he or she should have to get a 16 percent IRR.

Returning to the original model, if the cash flows were even, you could use the "financial keys" rather than the cash flow menu. It's only when the cash flows are uneven that you must use the cash flow menu. Thus, the HP19BII would have to be in the "end" mode and at "1 payment per year". The keystrokes would be those indicated in Chart I.

It is also important to keep in mind that when calculating the IRR, multiple answers can be achieved depending upon any changes that occur in the cash flows, the investment base, or the reversion. The only way to obtain an accurate IRR is to sell the property, and be aware of the exact amount of the original investment base, each annual cash flow, and the reversion. Thus, if the seller claims that the property will produce a particular internal rate of return, it must perform exactly as stated. If there are any changes in the projected cash flows or the reversion, the internal rate stated by the seller or agent will change.

In summary, understanding how to perform and analyze both NPV and IRR calculations is essential in order to effectively measure investment performance of today's real estate assets.

Is is only by utilizing such criteria that real estate professionals can make intelligent and sound decisions on behalf of their owners and investors.

Bodie J. Beard, CPM[R], SRA[R], SRPA[R] resides in The Woodlands, Texas where he is Director of the Houston Regional Office of Nationwide Consulting Company. Inc. He is a member of the IREM National Faculty, REM's Academy of Authors, and has served at the local, regional, and national levels within IREM.

Chart (A)

EXAMPLE: Determining Investment Base

Purchase Price: $5,000,000

Mortgage Position (75% LTV): -$3,750,000

Equity Position (Investment Base): $1,250,000

Chart (B)

Return on Capital

According to U.S. Financial Data, published by the Federal Reserve Bank of St. Louis, as of January 25, 2002, the return on capital from selected securities is as follows:

Federal Funds: 1.74

3-Month Treasury Bill: 1.68

2-Year Treasury Securities: 3.02

5-Year Treasury Securities: 4.32

10-Year Treasury Securities: 5.01

30-Year Treasury Securities: 5.44

30-Day Commercial Paper: 1.68

90-Day CDs: 1.74

90-Day Euro Dollars: 1.73

Corporate Aaa Bonds: 6.47

Corporate Baa Bonds: 7.81

Chart (C)

Calculating the Build-Up Method

Safe Rate: 4.5%

Risk: 2.0%

Lack of Liquidity: 2.0%

Burden of Management: 1.0%

Profit: 2.5%

Total: 12%

* In this case, the investor would require an annual "cash on cash" return of $150,000.

(Equity Portion: $1,250,000 x .12 = $150,000).

Chart (D)

Example: Five-Year Cash Flow Projections

Year 1

NOI: $468,051

Debt Service: -$318,051

Cash Flow: $150,000

* $3,750,000 loan financed at 7% interest for 25 years.

The following is based on an annual increase in the Net Operating Income of 5% over the holding period.

Year 2

NOI: $491,454

Debt Service: -$318,051

Cash Flow: $173,403

Year 3

NOI: $516,026

Debt Service: -$318,051

Cash Flow: $197,975

Year 4

NOI: $541,828

Debt Service: -$318,051

Cash Flow: $223,777

Year 5

NOI: $568,919

Debt Service: -$318,051

Cash Flow: $250,868

Chart (E)

Three-Phase Investment Model

"Going In"

Sales Price: $5,000,000

Mortgage: -$3,750,000

Investment

Base: $1,250,000

"Holding Period"

NOI: $468,051

Debt/Yr: -$318,051

Cash Flow: $150,000

"Going Out"

Sales Price: $6,000,000

Sales Cost: -$180,000

Mtg. Bal.: -$3,418,581

Reversion: $2,401,419

Cash Flow Yr. 2: $173,403

Cash Flow Yr. 3: $197,975

Cash Flow Yr. 4: $223,777

Cash Flow Yr. 5: $250,868......Plus...Reversion $2,401,419

Chart: (F)

(To round to six decimals, hit "disp," "grey variable key under fix," 6 input)

CFLO Menu:

Gold Clear Data

Clear the List?

Yes

Initial Flow: $1,250,000 +/- Input

Flow 1: $150,000 Input

No Times: Input

Flow 2: $173,403 Input

No Times Input

Flow 3: $197,975 Input

No. Times: Input

Flow 4: $223,777 Input

No. Times: Input

Flow 5: $250,868 ENTER $2,401,419 + Input

No. Times: Input

Chart: (G)

Keystrokes

Exit

Gold then hit the arrow pointed up. This will return you to the initial flow.

In order to take the $1,250,000 out of the initial flow, hit:

0 input (this is done in order to test the IRR)

Calc.

26.028801 I (the true IRR is inserted into the "I" key)

NPV

Answer: $1.250.000 (The original investment base)

Chart: (H)

Keystrokes

Exit

Gold Top Arrow

(To return to the initial flow)

$1,771,390 +/- Input

Calc.

IRR = 16%

Chart: (I)

FIN

TVM

Other

1 P/Yr

End Mode

Exit

Gold Clear Data

5 N

$1,250,000 +/- PV

$150,000 PMT

$2,401,419 FV

I 23.546709 (IRR)

To Test:

Zero PV

23.546709 I

PV $1,250,000

(Investment Base)

Measuring investment performance is one such critical business skill for today's real estate managers. Understanding how to accurately calculate net present value (NPV) and the internal rate of return (IRR) is essential to developing effective decision-making criteria. Typically, the management of income-producing properties involves three phases of real estate investment.

Part I: The "Going In" Phase

In this phase, the investor acquires the property for which a price is paid. Although there are some investors who may pay cash for the property; the majority of investors acquire properties with the use of two types of funds--mortgage funds and the investor's cash equity portion. The mortgage portion is typically based on a Loan to Value Ratio (LTV) imposed by the lender. This LTV ratio is applied against the total purchase price or the appraised value, which ever is least, in many cases. (Example: 75% LTV or 80% LTV.) The investor would need to provide the balance in the form of cash equity. This is generally referred to as "Investment Base." (See Chart A.)

In addition to the traditional terms of lending (i.e.; interest rare, LTV ratio, the amortization term, payment periods), the lender most often will use another judgement criteria called the debt coverage ratio (DCR). This is the ratio of net operating income to the annual debt service. It measures the ability of a property to meet its debt service out of net operating income. It is also referred to as the debt service coverage ratio (DSCR). Thus, for a property with a net operating income of $60,000 and annual debt service of $49,275, the debt coverage ratio is calculated as: NOI $60,000 / ADS $49,275 = DCR 1.22 (rounded). The .22 represents the cash flow position as well as the lender's margin of safety.

After considering the mortgage position, the balance of the purchase price must be paid by the borrower in the form of cash equity. In order to place these equity funds (investment base) into an income-producing property, investors want to receive an adequate return on their invested capital. This is called a "cash-on-cash return to equity", an "equity dividend rate", or even a "cash flow" rate. It might also be referred to as a "reinvestment rate", if used in conjunction with a FMRR "Financial Management Rate of Return" calculation.

The selection of the appropriate annual cash-on-cash return may come from various sources. First, the investor either may have owned a similar investment at one time, and received a certain annual return. This may become the benchmark for this new investment.

Second, national economic indicators, such as those from the American Council of Life Insurance Companies, Korpacz Real Estate Investor Survey, Pricewaterhouse-Coopers, LLP, or the Valuation Insight & Perspectives, published by the Appraisal Institute, might indicate that the range of cash-on-cash returns for this property type might, hypothetically, be from 10 percent to 12 percent. Thus, the investor might select a rate that is commensurate with these indicators.

Third, the investor might select a rate based on the "build up" method. Consider, for example, that prior to the acquisition, the $1,250,000, which will be used for the down payment, lies in an interest bearing account, drawing 4.5 percent per annum. This is considered a "safe rate" or return on capital. (See Chart B.)

Whether the owners funds are currently deposited into a 90-day Certificate of Deposit or Corporate Aaa Bond, consideration must be given to the anticipated holding period should the owner acquire this particular property. For example: If the anticipated holding period is five years, the "safe rate" should be commensurate with a return on capital received from a similar holding period. In this case, it might be a five-year Treasury Security of 4.32 percent (for purposes of this example, a safe rate of 4.50 percent).

To withdraw these funds and place them in a real estate venture, further consideration needs to be given to the following issues:

* Lack of Liquidity: An apartment complex, for example, cannot be liquidated overnight. It must first be placed on the open market for a reasonable period of time, before it will (hopefully) sell for the asking price. It cannot be immediately converted into M1 cash (i.e., cash on hand). The investor might consider adding a point or two to the safe rate, in order to build up his or her desired annual return on equity.

* Risk: There is always some risk attached to a real estate venture. The older the property, the greater the risk. The more deferred maintenance and upkeep, the greater the risk. Even tenant mix and lease terms might increase the risk. With an income-producing property, the quantity, quality, and durability of the income stream is extremely important. Therefore, it is essential that these elements be considered prior to the commencement of ownership. If these three factors are favorable, then there is less risk. If the leases are below the indicated market, or the terms are shorter than the terms in the market, then this might add additional risk to the venture. The inverse of this is that the newer the property and the more favorable the lease terms, the less risk.

* Burden of Management: Owners may be involved to some degree with the day-to-day management of the asset. This might consist of periodically visiting the property, spending time conversing with the manager, or consulting on such issues as operational and capital expenditure budgets.

* Profit: Entrepreneurial profit may also be an issue for the investor. (See Chart C.)

Part II: The "Holding Period"

Holding periods will likely vary according to geographic area and property type. In one local apartment market, the typical holding period might be seven years, while the holding period for a suburban office building might range from six to eight years. For purposes of this article, however, let's assume that the typical holding period is five years. During this holding period, the owner wishes to receive a healthy net operating income (NOI) in order to comfortably service the debt. The residual, after servicing the debt, is the pre-tax cash flow position. (See Chart D.)

Part III:

The "Going Out" Phase

In this final phase, the investor will sell the property and pay off the mortgage balance. The remainder is known as the "reversion" to the equity position. Let's assume that the sales price at the end of Year 5 is $6 million. From this amount, a sales commission of 3% was deducted, which left $5.82 million.

Sales Price: $6,000,000

Less Cost of Sale 3% $180,000

Total $5,820,000

From this amount, the loan balance at the end of Year 5 was deducted which resulted in the following:

Sales Price: $6,000,000

Less Cost of Sale 3% $180,000

Less Loan Balance $3,418,581

Reversion

(Sales Proceeds) $2,401,419

(See Chart E)

Net Present Value Calculations

Understanding how to perform a net present value calculation is essential for today's real estate managers. According to the Appraisal of Real Estate, 12th Edition, (the Appraisal Institute), net present value (dollar reward) "is the difference between the present value of all positive cash flows and the present value of all negative cash flows, or capital outlays. When the net present value of the positive cash flows is greater than the net present value of the negative cash flows or capital outlays, an investment is deemed viable. If the reverse relationship exists, the investment is not considered feasible."

As an example, let's assume that the pro-forma indicated earlier has been presented to the owner who desires a pre-tax internal rate of return of 16 percent. When using the HP 19BII to determine the NPV, it should be kept in mind that any time you rake money "out of pocket," you need to change its sign in order to make it a negative number. Thus, the model in the cash flow menu would be set up as follows: (See Chart F.)

In order to test the owner's desired return, the following keystrokes should be utilized:

Calc. 16 I

(The owner's desired return)

NPV $521,390

(will appear on display)

If the number that appears is a positive number, it denotes that the true internal rate of return is higher than the owner's desired return of 16 percent. If the number on display were negative, it would denote that the true internal rate of return is below the owner's desired return of 16 percent, thus falling short of the desired goal. If the number were zero, it would denote that the true internal rate of return was exactly 16 percent. (The IRR key displays: 26.028801).

The internal rate of return is the annualized yield rate or rate of return on capital that is generated or capable of being generated within an investment or portfolio over a period of ownership. This rate is similar to the equity yield rate. According to the Appraisal of Real Estate, the IRR is defined as "the rate of discount that produces a profitability index of one and a net present value of zero. It is often used to measure profitability after income taxes, i.e., the after-tax equity yield rate."

A way to test the internal rate of return is by using the following keystrokes (See Chart G) on the HP19BII (assuming an IRR of 26.028801).

This supports the definition that "it is that rate that will discount all cash flows plus the reversion, back to an amount that is equal to the original investment base."

Returning to the NPV calculation, with a NPV being a positive $521,390, it further denotes that by adding this amount to the original investment base of $1.25 million for a total of $1,771,390, the internal rate of return would be exactly 16 percent. (See Chart H.)

If the previously calculated NPV were a negative number, it would further denote that the investor put that much more down than he or she should have to get a 16 percent IRR.

Returning to the original model, if the cash flows were even, you could use the "financial keys" rather than the cash flow menu. It's only when the cash flows are uneven that you must use the cash flow menu. Thus, the HP19BII would have to be in the "end" mode and at "1 payment per year". The keystrokes would be those indicated in Chart I.

It is also important to keep in mind that when calculating the IRR, multiple answers can be achieved depending upon any changes that occur in the cash flows, the investment base, or the reversion. The only way to obtain an accurate IRR is to sell the property, and be aware of the exact amount of the original investment base, each annual cash flow, and the reversion. Thus, if the seller claims that the property will produce a particular internal rate of return, it must perform exactly as stated. If there are any changes in the projected cash flows or the reversion, the internal rate stated by the seller or agent will change.

In summary, understanding how to perform and analyze both NPV and IRR calculations is essential in order to effectively measure investment performance of today's real estate assets.

Is is only by utilizing such criteria that real estate professionals can make intelligent and sound decisions on behalf of their owners and investors.

Bodie J. Beard, CPM[R], SRA[R], SRPA[R] resides in The Woodlands, Texas where he is Director of the Houston Regional Office of Nationwide Consulting Company. Inc. He is a member of the IREM National Faculty, REM's Academy of Authors, and has served at the local, regional, and national levels within IREM.

Chart (A)

EXAMPLE: Determining Investment Base

Purchase Price: $5,000,000

Mortgage Position (75% LTV): -$3,750,000

Equity Position (Investment Base): $1,250,000

Chart (B)

Return on Capital

According to U.S. Financial Data, published by the Federal Reserve Bank of St. Louis, as of January 25, 2002, the return on capital from selected securities is as follows:

Federal Funds: 1.74

3-Month Treasury Bill: 1.68

2-Year Treasury Securities: 3.02

5-Year Treasury Securities: 4.32

10-Year Treasury Securities: 5.01

30-Year Treasury Securities: 5.44

30-Day Commercial Paper: 1.68

90-Day CDs: 1.74

90-Day Euro Dollars: 1.73

Corporate Aaa Bonds: 6.47

Corporate Baa Bonds: 7.81

Chart (C)

Calculating the Build-Up Method

Safe Rate: 4.5%

Risk: 2.0%

Lack of Liquidity: 2.0%

Burden of Management: 1.0%

Profit: 2.5%

Total: 12%

* In this case, the investor would require an annual "cash on cash" return of $150,000.

(Equity Portion: $1,250,000 x .12 = $150,000).

Chart (D)

Example: Five-Year Cash Flow Projections

Year 1

NOI: $468,051

Debt Service: -$318,051

Cash Flow: $150,000

* $3,750,000 loan financed at 7% interest for 25 years.

The following is based on an annual increase in the Net Operating Income of 5% over the holding period.

Year 2

NOI: $491,454

Debt Service: -$318,051

Cash Flow: $173,403

Year 3

NOI: $516,026

Debt Service: -$318,051

Cash Flow: $197,975

Year 4

NOI: $541,828

Debt Service: -$318,051

Cash Flow: $223,777

Year 5

NOI: $568,919

Debt Service: -$318,051

Cash Flow: $250,868

Chart (E)

Three-Phase Investment Model

"Going In"

Sales Price: $5,000,000

Mortgage: -$3,750,000

Investment

Base: $1,250,000

"Holding Period"

NOI: $468,051

Debt/Yr: -$318,051

Cash Flow: $150,000

"Going Out"

Sales Price: $6,000,000

Sales Cost: -$180,000

Mtg. Bal.: -$3,418,581

Reversion: $2,401,419

Cash Flow Yr. 2: $173,403

Cash Flow Yr. 3: $197,975

Cash Flow Yr. 4: $223,777

Cash Flow Yr. 5: $250,868......Plus...Reversion $2,401,419

Chart: (F)

(To round to six decimals, hit "disp," "grey variable key under fix," 6 input)

CFLO Menu:

Gold Clear Data

Clear the List?

Yes

Initial Flow: $1,250,000 +/- Input

Flow 1: $150,000 Input

No Times: Input

Flow 2: $173,403 Input

No Times Input

Flow 3: $197,975 Input

No. Times: Input

Flow 4: $223,777 Input

No. Times: Input

Flow 5: $250,868 ENTER $2,401,419 + Input

No. Times: Input

Chart: (G)

Keystrokes

Exit

Gold then hit the arrow pointed up. This will return you to the initial flow.

In order to take the $1,250,000 out of the initial flow, hit:

0 input (this is done in order to test the IRR)

Calc.

26.028801 I (the true IRR is inserted into the "I" key)

NPV

Answer: $1.250.000 (The original investment base)

Chart: (H)

Keystrokes

Exit

Gold Top Arrow

(To return to the initial flow)

$1,771,390 +/- Input

Calc.

IRR = 16%

Chart: (I)

FIN

TVM

Other

1 P/Yr

End Mode

Exit

Gold Clear Data

5 N

$1,250,000 +/- PV

$150,000 PMT

$2,401,419 FV

I 23.546709 (IRR)

To Test:

Zero PV

23.546709 I

PV $1,250,000

(Investment Base)

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Author: | Beard, Bodie J. |
---|---|

Publication: | Journal of Property Management |

Date: | Mar 1, 2002 |

Words: | 2555 |

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