Income Approach II

Perpetuity (modern definition)

A finite level income stream with its reversion equal to the present value

Level-equivalent annuity

A level annuity with the same present value and number of periods as a given irregular cashflow for a given discount rate.

Vacancy and Collection Loss (V/C)

An allowance for reductions in potential gross income attributable to vacancies, tenant turnover, and non payment of rent; also called vacancy and credit loss or vacancy and contingency loss. Treatment can differ according to interest being appraised, property type, capitalization method, or whether the property is at stabilized occupancy

Return of Capital

the RECOVERY of invested capital through income or reversion or both

What is the present value of an investment earning $100,000 per year if the reversion is $1,000,000, the holding period is eight years and the discount rate is 10%? - $113,420 - $538,157 -$1,000,000 - $704,096

- $1,000,000

What is the value of an investment that generates $150,000 of net income annually, and has a $1,200,000 expected reversion in 10 years, if the discount rate is 9%? - $506,893 - $1,469.542 - $1,384,337 - $962,648

- $1,469.542 fReg, 150,000PMT, 1,200,000FV, 10n 9i, PV

Based on the following information, what is the indicated reversion in five years? First-year net operating income: $10,000 growing 5% per year Terminal capitalization rate: 8% Sales expenses: 3% Income capitalized: First-year of new ownership - $147,380 - $117,647 - $154,749 - $121,250

- $154,749

What is the net reversion for the following property if the holding period is five years? $160,000 net operating income for the coming year, growing 4% per year compounded $40,000 selling expenses 7% terminal capitalization rate - $2,740,920.92 - $2,750,849.36 - $1,838,690.53 - $1,832,007.09

- $2,740,920.92

What is the net reversion for the following property if the holding period is six years? $200,000 net operating income for the coming year, growing 4% per year compounded $55,000 selling expenses 9% terminal capitalization rate - $2,756,820.041 - $2,768,870.842 - $1,701,254.50 - $1,693,759.73

- $2,756,820.041 Consider this: Calculate what the net income will be in year 7, cap it at the terminal cap rate, and then deduct selling expenses.

If the discount rate is 10%, what is the return-on capital in a first-year income of $200,000 for a $150,000 investment? - $20,000 - $5,000 - $15,000 - $2,000

- $20,000 By definition, return on capital is the additional amount received as compensation for use of an investors capital until it is recaptured.

What is the value of an investment earning $20,000 per year in net income and $150,000 reversion in five years if the discount rate is 5%? - $80,929.61 - $1,176,694.94 - $ 1,167,617.86 - $204,118.46

- $204,118.46 fReg, 20,000 PMT, 150,000 FV, 5n, 5i, PV

If the discount rate is 15%, what is the return on capital in a first year income of $25,000 for a $200,000 investment? - $25,000 -$35,000 - $30,000 - $50,000

- $25,000

What is the value of an investment earning $50,000 per year net income and a $250,000 reversion in five years if the discount rate is 12% - $837,864 - $286,795 - $322,095 - $357,142

- $322,095 fReg, 50,000 PMT, 250,000 FV, 5n, 12i, PV

What is the present value for a property with the following cash flows at 6% and $40,000 reversion? Year 1 -10,000 Year 2 4,000 Year 3 4,000 Year 4 4,000 Year 5 4,000 - $21,840 - $33,532 -$52,400 -$40,708

- $33,532

Given the following information, what is an appropriate replacement allowance expense using the sinking fund method? - All appliances current replacement cost: $25,000 - useful life: 25 years - Carpet age: 15 years - Yield rate: 8% - $26.26 - $920.74 - $341.97 - $72.20

- $341.97 Consider this: This is a sinking fund replacement allowance problem. A sinking fund answers the question, how much do I pay (pmt) each year at a designated rate if i need to end up with a given lump sum in x number of years. In this problem, how much do I need to put aside each year (so looking for level pmt) for 25 years if I want to end up wiith $25,000 at the end of that time period and the interest rate is 8%? The allowance (pmt) is level so solve this in white keys, too: f reg 25 n 8 i 25000 fv solve pmt. Annual pmt (allowance) is your answer.

What is the present value of the following cash flows if the holding period is 5 years and the reversion is based on capitalization of year 6 income. There are no expenses of sale, yield rate is 10.5%, and the terminal capitalization rate (RN) is 9.5%. Year 1: $10,000 Year 2: -$20,000 Year 3: $30,000 Year 4: $40,000 Year 5: -$50,000 Year 6: $60,000 - $394,753 -$397,468 -$297,251 -$395,667

- $394,753 First, let's solve for the reversion. 60,000/.095 = 631,578.95 Now, load all cash flows F reg 10000 g cfj 20000 chs g cfj 30000 g cfj 40000 g cfj 50000 chs enter 631578.95 + g cfj 10.5 i F NPV $394,753

An appraiser values a property's income and reversion at $4,000,000. This figure is based on annual, in arrears discounting using a discount rate reconciled from interviews with investors, who also use end-of-year discounting on similar properties. A reviewer points out that the income occurs monthly and insists that appraiser value the property reflecting that fact. What is the value of this property if the reviewer's demand is met? - $4,000,000 - cannot calculate without knowing the cash flows and discount rates - more than $4,000,000 - less than $4,000,000

- $4,000,000 Consider this: The value is the value. Rate would be different but the answer is the same.

What is the final year's cash flow for the following property held for 10 years if the owner is to yield an 8% return? - $3,500,000 purchase price - $250,000 per year net income for Years 1-10 -$3,634,597 - $3,934,597 - $4,184,596 - $11,177,878

- $4,184,596 Consider this: This is a little tricky, but it's level income so solve for reversion (FV) then (this is the tricky part) add last year's income to it. It also requires you to recognize that the final year's cash flow is equal to final year's income plus the reversion. We know final year's income is 250,000 because income is level. We can solve for reversion by using white keys in 12c: f REG 10 n 8 i 3500000 CHS PV 250000 PMT solve FV So, the reversion is 3,934,596 to which we add 250,000 to get the answer to this problem.

What is the value of an investment earning $50,000 per year in net income and a $350,000 reversion in four years if the discount rate is 8% - $422,866.79 - $2,302,517.85 - $2,336,012.62 - $701,476.74

- $422,866.79 fReg, 50,000PMT, 350,000FV, 8i, 4n, PV

A property recently sold for $450,000 subject to a 8-year net lease, with lease payments of $15,000 per year. The buyer purchased the property based on a yield rate of 7.5%. What is the buyer's anticipated reversion? - $1,146,503.35 - $259,112,236.90 - $959,260.59 - $645,869.45

- $645,869.45

A property recently sold for $625,000 subject to a 10-year net lease, with lease payments of $50,000 per year. The buyer purchased the property based on a yield rate of 9%. What is the buyers anticipated reversion? - $600,000 - $625,000 - $719,956 - $794,743

- $719,956 fReg, 625,000CHS, PV, 10n, 9i, 50,000PMT, FV

What is the value of an investment earning $100,000 per year in net income and $500,000 reversion in ten years if the discount rate is 10% - $1,464,055.34 - $7,751,819.82 - $807,228.36 -$19,130,977.14

- $807,228.36 fReg, 100,000 PMT, 500,000 FV, 10n, 10i, PV

Why does risk usually increase as the holding period increases? - Future forecasts are less risky - Maintenance usually diminishes as a property ages - Markets tend to decline over time. - As a building ages, its maintenance costs increases and its useful life declines.

- As a building ages, its maintenance costs increases and its useful life declines.

In a perpetuity, what is the capitalization rate relative to the yield rate? - Varies - Higher - Equal - Lower

- Equal

Why is the NPV calculator key sometimes used to solve for present value? - In the relationship NPV=PV - Capital Outlay, if there is no capital out lay PV and NPV are the same amount - The calculator does not distinguish between NPV and PV - It signifies a calculator error - There is no explanation why a calculator does with it does

- In the relationship NPV=PV - Capital Outlay, if there is no capital out lay PV and NPV are the same amount

What impact does NPV have on IRR? - Makes a negative IRR become positive IRR - no impact on IRR -Decreases IRR - Increases IRR

- Increases IRR

If the yield rate and the capitalization rate are the same, what is the relationship of the income and value? - There is no identifiable pattern between the two rates, - Neither income nor value are expected to change - Income and value are expected to increase - Income and value are expected to decline

- Neither income nor value are expected to change

Yield rates should apply to the interest being appraised.

- Property yield rates (Yo ) are applied when valuing the cash flow from the entire property. - Equity yield rates (YE ) are applied when valuing the cash flow from the equity. - Mortgage yield rates (YM ) are applied when valuing the cash flow from the mortgage. - The yield rate quoted by an investor who typically buys property financed by mortgages is likely to be the yield rate on the investor's pre-tax equity position, not the property's overall yield rate. (That is, the quoted rate is probably YE, not YO.)

Which of the following is an example of a below-the-line expense? - Replacement Allowance - Management - Vacancy and collection loss - Tenant Improvements and leasing expenses

- Replacement Allowance

Which of the following are periodic expenditures necessary to maintain the real property and continue production of the effective gross income, assuming prudent and competent management. - Effective gross income - Operating expenses - Replacement Allowances - Fixed expenses

- Replacement Allowances

Yield rate on a real estate investment can be thought of as being the sum of the following components:

- Safe rate - Inflation (purchasing power risk—some consider this to be part of the safe rate) Illiquidity premium (marketability risk) - Interest rate changes (capital market risk) - Unanticipated supply and demand changes (market risk) - Environmental, legislative and management risks - Leverage premium for financial risk can be added for a yield rate on an equity position.

Which of the following is not an acceptable method of accounting for replacement allowances? - As a percent of EGI - Sinking fund premise using a property yield rate over useful life - Straight line recapture using current cost over useful life deducted as an operating expense - Straight line recapture using current cost over remaining life deducted as an operating expense.

- Straight line recapture using current cost over remaining life deducted as an operating expense.

In the expression CF0, the 0 represents which of the following? - Period n-1 - The number zero and a time period - Overall rate - End of the first period

- The number zero and a time period

All else being equal, what can be said about an investment with income in advance? - There is no difference in present value - The present value will be higher - The present value will be lower - The reversion will be lower - The reversion moves to beginning of the year too

- The present value will be higher

If income and value are rising, what is the relationship of the capitalization rate and the yield rate? - The capitalization rate is equal to the yield rate. The capitalization rate is higher than the yield rate. - The yield rate is higher than the capitalization rate. There is not identifiable patter between the two rates.

- The yield rate is higher than the capitalization rate

The following investment is a perpetuity over a defined holding period. What additional information do you need, if any, to value the investment? - 8% yield rate - $40,000 level net income per year - holding period only - reversion amount only - no additional information is required - holding period and reversion amount

- holding period and reversion amount

In the classic definition of a perpetuity, what can be said about the income? - It is perpetual and level - It is finite and level - There is no discernable income pattern, it jus infinite income - It is infinite but not necessarily level.

- it is perpetual and level

Given the following information, what is an appropriate replacement allowance expense using the sinking fund method? - Roof current replacement cost: $35,000 - useful life: 15 years - Carpet age: 8 years - Yield rate: 5% -$1,621.98 -$297.26 -$130.94 -$3,665.26

-$1,621.98 This is a sinking fund replacement allowance problem. A sinking fund answers the question, how much do I pay (pmt) each year at a designated rate if i need to end up with a given lump sum in x number of years. In this problem, how much do I need to put aside each year (so looking for level pmt) for 15 years if I want to end up wiith $35,000 at the end of that time period and the interest rate is 5%? The allowance (pmt) is level so solve this in white keys, too: f reg 15 n 5 i 35000 fv solve pmt. Annual pmt (allowance) is your answer.

What is the net reversion for the following property if the holding period is five years? $130,000 net operating income for the coming year, growing 4% per year compounded $45,000 selling expenses 8% terminal capitalization rate -$1,932,060.97 - $1,939,119 - $1,285,880.04 - $1,290,631.55

-$1,932,060.97 Calculate what the income will be in year 6, (the year following the last year of the holding period). Do this on the HP12c by entering the growth rate three times - 1.04 enter, enter, enter 130,000 x = year 2 = 135,200 x = year 3 = 140,608 x= year 4 = 146,232.32 x = year 5 = 152,081.612 x =year 6 = 158,164.8773 enter, divide by cap rate subtract selling expenses

Given the following information, what is an appropriate replacement allowance expense using the sinking fund method? - Roof current replacement cost: $20,000 - Roof useful life: 20 years - Roof age: 10 years - YO: 8.5% -$413.42 -$20,000 -$2,000 -$1,348.15

-$413.42

A property sold for $1,200,000 with a 75% loan to value ratio and an interest rate of 5%, payable monthly and amortized over 30 years. Effective gross income was $100,000 and operating expenses totaled $30,000. What is the indicated debt coverage ratio? -25% -2.10 -1.21 -0.67

-1.21

Based on the following information what is the implied cap rate? Year 1: $12,000 Year 2: $13,000 Year 3: $20,000 Year 4: $20,000 Year 5: $21,000 Reversion: $200,000 Yield rate: 7% -4.8% -7% -6% -5.7%

-5.7% The calculation for the capitalization rate is Ro = Io /Vo, where Io is the first year income and Vo is equal to the present value of the cash flows. 12,000 / 211,723.4642 = 0.056678

Which of the following statements about yield capitalization is NOT true? -Yield capitalization considers all future benefits -In yield capitalization the discount rate provides only for return on -All cash flows are summed then discounted to present value. -Each cash flow and reversion is discounted to present value separately then summed.

-All cash flows are summed then discounted to present value.

Which of the following statements is NOT true? -Direct capitalization explicitly considers only one year -In yield capitalization, the discount rate is a pure rate of return -In yield capitalization, the discount rate must reflect all expected changes in income and value. -Yield capitalization explicitly considers all expected income and reversions

-In yield capitalization, the discount rate must reflect all expected changes in income and value.

A negative NPV signifies which of the following? - Investment surpasses investor yield criteria - Investment will not meet investor yield criteria - Investment is matching investor yield criteria - The investment will not return a positive yield

-Investment will not meet investor yield criteria

Which of the following are NOT used in calculating a built up overall yield rate? -Safe rate -Interest rate changes -Mortgage Capitalization Rate -Inflation

-Mortgage Capitalization Rate

Sellers carry back financing at less-than-market rates for all of the following reasons except - Reduce the sales price - Lack of knowledge -Distress -Tax consequences

-Reduce the sales price

Which of the following is NOT a traditional measure of lender risk? -debt coverage ratio -sales price -DSCR -loan-to-value ratio

-sales price

Steps for calculating a level equivalent annuity -

1. Calculate the PV of the irregular cashflow with a given discount rate 2. Calculate the level payment for that lump sum over the same number periods at the same discount rate. (Note: the calculation is identical to an annual mortgage payment, which is, of course, the level payment to provide the lender with a return on the lender's investment -- the loan -- equal to the interest rate.)

Yield Rate

A rate of return on capital usually expressed as a compound annual percentage rate. Yield rates implicitly reflect only risk (unlike capitalization rates, which implicitly reflect risk as well as change in income and value over the holding period). The cash flows to which the yield rate is applied explicitly reflect change in income and value.

Measures of Lender Risk

Loan to value ratio (M) Debt Coverage Ratio (DCR)

Relationship of NPV, IRR, and PV - If PV of future benefits < CO→

NPV < 0 and IRR < Y If the PV is less than CO, then the NPV will be negative. This investment will not yield the discount rate used to calculate the PV. You would have to spend less (less by an amount exactly equal to the negative NPV) for the property than the CO.

Relationship of NPV, IRR, and PV If PV of future benefits = CO →

NPV = 0 and IRR = Y If PV is equal to CO, NPV will equal zero. This investment just meets investor yield criteria and meets the target. In other words, if you spend an amount equal to CO for the property you will achieve an IRR exactly equal to the discount rate used to calculate the PV.

Relationship of NPV, IRR, and PV -If PV of future benefits > CO →

NPV > 0 and IRR > Y If the PV is greater than the capital outlay (CO), NPV will be positive, and the investment will exceed the investor yield criteria. In other words, the positive NPV is telling you that if you pay an amount equal to the CO you will yield more than the discount rate used to calculate the PV. Stated differently, you can afford to pay more (in fact, an amount exactly equal to the positive NPV) and still yield the discount rate used to calculate the PV.

Now let's see if you can solve the following DCF problem by using the blue cash flow keys on the HP-12C calculating the discounted value of each cash flow and adding them together. What is the PV of the following cash flows at 6%? Period 1 $10,000 Present Value = Period 2 -2,000 Present Value = Period 3 18,000 Present Value = Period 4 18,000 Present Value = Period 5 5,000 Present Value= Reversion 40,000 Present Value = Total Present Value

Period 1 $10,000 Present Value = 9,433.96 Period 2 -2,000 Present Value = -1,779.99 Period 3 18,000 Present Value = 15,113.15 Period 4 18,000 Present Value= 14,257.69 Period 5 5,000 Present Value = 3,736.29 Reversion 40,000 Present Value= 29,890.33 Total Present Value = 70,651.42 f REG, 10,000g CFj, 2,000CHS g CFj, 18,000g CFj, 2g Nj, 5,000 enter 40,000+g CFj, 6i, f NPV

Internal Rate of Return (IRR).

The annualized yield rate or rate of return on capital that is generated within an investment or portfolio over a period of ownership. Alternatively, the indicated return on capital associated with a projected or pro forma income stream. The IRR is the rate of discount that makes the net present value of the investment equal to zero. The IRR discounts all returns from the investment, including returns from its reversion, to equal the original capital outlay.

Net Present Value (NPV).

The difference between the present value of all expected investment benefits (PV), and the present value of capital outlays (CO). For purposes of real property valuation, negative cash flows include the initial cash outlay required to purchase the property. The capital outlays in the definition above refers to what that interest (i.e., property = sale price, equity = down payment, mortgage = loan amount, etc.). The mathematical formula is NPV = PV - Capital Outlay. (Notice that if there is no capital outlay in your problem, NPV would be mathematically equal to PV, which is why we solve for PV in the blue key functions by keying gold key then ) Here is a graph illustrating the NPV concept.

Discounted Cash Flow Analysis (DCF)

The procedure in which a discount rate is applied to a set of projected income streams and a reversion.

Debt Coverage Ratio (DCR)

The ratio of net operating income to annual debt service (DCR = Io/IM); measures the ability of a property to meet its debt service out of net operating income; also called debt service coverage ratio (DSCR)

Potential Gross Income

The total income attributable to property at full occupancy before vacancy and operating expenses are deducted. Year 1 gross income for DCF Analysis purposes is usually the same as for direct capitalization. Subsequent years' gross income can be changed as a lump sum or tenant-by-tenant. If the leased fee is being valued on a tenant-by-tenant basis, the leases control the rate of change. As leases expire, gross income reverts to market.

Present Value (PV).

The value of a future payment or series of future payments discounted to the current date or to time period zero.

Suppose you were buying a property from which you expected the following cash flows: Year 1 income: $10,000 Year 2 income: $12,000 Proceeds from sale at the end of year 2: $140,000 Desired YO: 12% What is the value of the property using the DCF formula?

V = ($10,000 ÷ 1.12)) + ( $12,000 ÷ (1.12 x 1.12)) + ($140,000 ÷ (1.12 x 1.12)) V = $8,928 + $9,566 + $111,607 V = $130,101

Perpetuity (classic definition)

an infinite stream of cash flows that are paid or received with a regular frequency. In general, the word perpetuity is used to refer to a stream where all the cash flows are the same. This kind of stream is also called a level or constant perpetuity.

Return on Capital

the additional amount received as compensation (point or reward) for use of an investor's capital until it is recaptured. The rate of return on capital is the yield rate or the interest rate earned or expected.