Problems - Ted · PDF fileProblems! Amortization of ... Modified Internal Rate of Return ! Value of Office ! Value of Retail ! ... The bold numbers are the solved number

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67"

Problems

!  Amortization of Tenant Finish !  Natural Break Point !  Modified Internal Rate of Return !  Value of Office !  Value of Retail !  Value of Industrial !  Partition the IRR !  Partial Interests !  Calculate Ye !  Wraparound Mortgages !  GIM vs. NIR in graph form

Amortization of Tenant Finish !  A lease is quoted at $20 PSF annually with a $10 PSF

Tenant improvement allowance. What is the equivalent rent on a 7 year lease if the tenant gets a $25 PSF tenant improvement allowance? Compute the monthly rate with a yield requirement of 9%.

!  Add the .24 to 20/12 = $1.91 PSF per month

Step N I PV PMT FV

Calculate the PMT to amortize the excess TI

7 x 12 9/12 25 – 10 = 15 [.24]


68"

Amortization of Tenant Finish !  A lease is quoted at $20 PSF annually with a $10 PSF Tenant

improvement allowance. What is the equivalent rent on a 7 year lease if the tenant gets a $25 PSF tenant improvement allowance? Compute the monthly rate with a yield requirement of 9%. Now assume there is a 20% residual value in the excess tenant improvements at the end of the lease.

Step N I PV PMT FV


Amortization of Tenant Finish !  A lease is quoted at $20 PSF annually with a $10 PSF Tenant

improvement allowance. What is the equivalent rent on a 7 year lease if the tenant gets a $25 PSF tenant improvement allowance? Compute the monthly rate with a yield requirement of 9%. Now assume there is a 20% residual value in the excess tenant improvements at the end of the lease.

!  Add the .22 to 20/12 = $1.87 PSF per month

Step N I PV PMT FV


7 x 12 9/12 25 – 10 = -$15 [.22] 15 x 20% = $3


69"

Natural Break Point !  What is the natural break point (a sales volume where

percentage rents begin) when the percentage rent is 6% and the base rent is $24,000/year?

Natural Break Point

! What is the natural break point (a sales volume where percentage rents begin) when the percentage rent is 6% and the base rent is $24,000/year?

!  24,000/.06 = $400,000

!  Assume sales are $500,000, the rent is $500,000 x .06 = $30,000

!  Proof: Base is $24,000 + Percentage (500,000 – 400,000) x .06 = $30,000


70"

Modified Internal Rate of Return !  What is the Modified Rate of Return given the following

!  Safe rate = 4% !  Reinvestment rate = 8% !  Hurdle rate = 12% !  Investment is $100,000

1 2 3 4 5

10,000 -30,000 0 40,000 160,000

Modified Internal Rate of Return !  What is the Modified Rate of Return given the following

!  Safe rate = 4% !  Reinvestment rate = 8% !  Hurdle rate = 12% !  Investment is $100,000

0 1 2 3 4 5

-100,000 10,000 -30,000 0 40,000 160,000

X 1.084 ÷ 1.042 X 1.082 X 1.081 X 1.080

13,605 -27,737 0 43,200 160,000

N I PV PMT FV

SOLVE I 5 [11.16%] -127,737 216,805

Notes: 1.  All negatives are brought to time zero by discounting

at the safe rate and added to the investment. 2.  All positives are compounded at the reinvestment

rate and added up. 3.  MIRR always solves for I with a lump sum in PV & a

lump sum in FV.


71"

Office !  BOMA (Building Owners & Managers Association)

!  Rentable is measured from inside wall of exterior walls. Use from the dominant surface (glass or sheetrock) !  Take out vertical penetrations of stairs, vents elevators but not

columns

!  Usable is dominant area of interior of exterior wall to outside of hall to middle of adjacent tenant walls.

!  Rentable = Usable x (1 + core, common area, add-on, load

factor) !  Usable = Rentable divided by (1 + load factor) !  Load factor = 1 – Rentable/usable

Retail !  Measured from outside !  CAM is common area maintenance. !  Percentage rents have a higher risk than base rents


72"

Industrial !  Generally measured outside walls. !  Problem: What is the market rent for the subject given

the following terms & a market Yo = 12%? !  3 year level lease !  $10 tenant improvements !  Gross lease

Rent Comp 1 2 3

3 year leases with 2% increases and $15 TI are $10 PSF/year

3 year level leases with $8 TI and $7.50 PSF/year

3 year leases increasing 3% per year and $10 TI at $8 PSF/year

Industrial !  Generally measured outside walls.

!  Problem: What is the market rent for the subject given the following terms & a market Yo = 12%?

!  3 year level lease

!  $10 tenant improvements

!  Gross lease

Rent Comp 1 2 3 3 year leases with 2% increases and $15 TI are $10 PSF/year

3 year level leases with $8 TI and $7.50 PSF/year

3 year leases increasing 3% per year and $10 TI at $8.00 PSF/year

Indicated Rents with Subject Rent Structure

Solve Equivalent Income: 1.02 Enter,Enter, Enter 10 g CFj; x gCFj; x gCFj 12 I f NPV; 3 N, Solve PMT [10.19] Amortize extra TI: 3N; 12 I; 15-10 PV; Solve PMT [2.08] IF 3 year level, $10 TI, then: 10.19 – 2.08 = $8.11 PSF/Year

Amortize extra TI: 3N; 12 I; 10-8 PV; Solve PMT [.83] IF 3 year level, $10 TI, then: 7.50 + .83 = $8.33 PSF/Year

Solve Equivalent Income: 1.03 Enter, Enter, Enter 8 g CFj; x g CFj; x g CFj 12 I f NPV; 3 N, Solve PMT [8.22]


73"

Partition the IRR A property has Io of $100,000 and just sold for $1,200,000. The income is expected to increase 2% per year and the value is expected to increase 3% per year. N = 4. Partition the IRR to (1) the income if level of $100,000, (2) the increases in the income, (3) capital recapture (getting your money back) of $1,200,000 & (4) the increase in the value.

Partition the IRR A property has Io of $100,000 and just sold for $1,200,000. The income is expected to increase 2% per year and the value is expected to increase 3% per year. N = 4. Partition the IRR to (1) the income if level of $100,000, (2) the increases in the income, (3) capital recapture (getting your money back) of $1,200,000 & (4) the increase in the value.

1 2 3 4

Income (2%) 100,000 102,000 104,040 106,121

Reversion (3%)

1,350,611 Reversion: 1,200,000 PV; 4 N; 3 I; Solve FV [1,350,611] Solve Yo: 1,200,000 CHS g Cfo; 100,000 g CFj; 102,000 g CFj; 104,040 g CFj; 106,121 ENTER 1,350,611 + g CFj; Solve IRR [11.22%] Solve PV level Income: 4N; 11.22 I; 100,000 PMT; Solve PV [308,793]. 308,793/1,200,000 = 25.7% Solve PV of recapture: 4N; 11.22 I; 1,200,000 FV; Solve PV [784,241]. 784,241/1,200,000 = 65.3% Solve PV of value increase: 4N; 11.22 I; 150,611 FV; Solve PV [98,429]. 98,429/1,200,000 = 8.2% Solve PV of income increases: 0 g CFj’ 2,000 g CFj; 4,040 g CFj’ 6,121 g CFj; 11.22 I;

Solve f NPV [8,554]. 8,554/1,200,000 = .7% (Note: All pieces add to 99.9%)


74"

Partial Interest !  Owner leases a property to tenant one for $10,000 per

year net for 99 years 49 years ago. !  Tenant built a building and leased to tenant two twenty

years ago for 50 years for $25,000 per year net. !  Tenant two leased to tenant three 10 years ago for 25

years for $55,000 per year net. !  Tenant three leased one year ago for five years to tenant

four for $72,000 but the market softened and market rent is now $60,000.

!  What is the value of all the positions if the Ro = 12%?

Partial Interest Discussion !  If it is a multi-tenant problem, you will be given what

tenants pay in rent & enough information to value the fee simple

!  The combined leasehold (CLH) is the position of all the tenants. Assuming the sum of the parts equal the whole (which they normally do not), fee simple value minus leased fee value is the CLH value. The same is true for fee simple income (market rent) minus rent to the owner (leased fee income) = CLH income.

!  Any tenant paying excess rent has a negative value. That negative value is a positive value to the tenant who receives the rent.


75"

Partial Interest Discussion !  If it is a multi-tenant problem, you will be given what

tenants pay in rent & enough information to value the fee simple

!  The combined leasehold (CLH) is the position of all the tenants. Assuming the sum of the parts equal the whole (which they normally do not), fee simple value minus leased fee value is the CLH value. The same is true for fee simple income (market rent) minus rent to the owner (leased fee income) = CLH income.

!  Any tenant paying excess rent has a negative value. That negative value is a positive value to the tenant who receives the rent.

Ye Calculation

1 2 3 4 5 REV.

Io 25,000 30,000 35,000 40,000 50,000 600,000

Given a loan for $300,000 with an interest rate of 6.5% and an amortization of 25 years, with monthly payments, what is the Ye if the Ro is 5%?


76"

Ye Calculation 1 2 3 4 5 REV.

Io 25,000 30,000 35,000 40,000 50,000 600,000

Im 24,307 24,307 24,307 24,307 24,307 271,686

Ie 693 5,693 10,693 15,693 25,693 328,314

Given a loan for $300,000 with an interest rate of 6.5% and an amortization of 25 years, with monthly payments, what is the Ye if the Ro is 5%?

N I PV PMT FV

Payment 25 X 12 6.5/12 300,000 [2,026] X 12 = 24,307

Balance 5 X 12 [271,686]

The Vo is $25,000/.05 = $500,000 The Ve is $500,000 – 300,000 = $200,000 Ye: 200,000 CHS g Cfo; 693 g CFj; 5,693 g CFj; 10,693 g CFj; 15,693 g CFj; 25,693 Enter 328,314 + g CFj; Solve f IRR [14.63%]

Wraparound !  There is an existing first mortgage with payments of

$5,000 per year at 5% with 15 years remaining. !  A lender will “wrap” the note and provide financing of

$250,000 with an interest rate of 7%, with a 30 year amortization and 10 year call. In addition, the lender will require 3 points. What is the effective yield to the wrap lender.


77"

Wraparound !  There is an existing first mortgage with payments of $5,000 per year at 5% with 15 years remaining.

!  A lender will “wrap” the note and provide financing of $250,000 with an interest rate of 7%, with a 30 year amortization and 10 year call. In addition, the lender will require 3 points. What is the effective yield to the wrap lender.

!  The bold numbers are the solved number. First the payment of the wrap & balance were calculated. The balance of the first was calculated next along with the balloon in ten years. The points were taken care of in the last step by mulitiplying the loan times 1 – the 3 points = .97.

N I PV PMT FV

WRAP 30 7 -250,000 [20,147] Wrap

Balloon 10 [213,433]

First 15 5 [51,898] 5,000

First Balloon

10 [21,647]

Effective Yield

10 [7.98%] - [250,000(.97)– 51,898 = 190,602]

20,147 – 5,000 = 15,147

191,786


78"

NIR & EGIM on a Graph

GIM

!  NIR = 1 – OER & Ro = NIR/EGIM

OER .1 .2 .3 .4 .5 .6

1 2 3 4 5

6 A B

C D

1.  Which is triple-net? 2.  Which one is renovated? 3.  Which one is the oldest?


79"

NIR & EGIM on a Graph

GIM

!  NIR = 1 – OER & Ro = NIR/EGIM

OER .1 .2 .3 .4 .5 .6

1 2 3 4 5

6 A B

C D

1.  Which is triple-net? “A” has the lowest OER. 2.  Which one is renovated? “B” has the lowest cap rate. 3.  Which one is the oldest? “C” has the highest cap rate.

Calculate the Ro for each Point: A: Ro = (1-.1)/5 = 18% B: Ro = (1-.35)/6 =10.8% C: Ro = (1-.35)/3.5 = 18.6% D: Ro = (1-.6)/2.5 = 16%


80"

Additional Income Problems !  The following is expected cash flow for a proposed

property. The Y if stabilized is 11% and is 11.5% based upon actual income.

!  A. What is the value if stable? !  B. What is the value when complete? !  C. What is the discount rate to the short falls? !  D. What would the rent loss adjustment be in the sales &

cost approaches if the discount rate is 5%?

1 2 3 4 Reversion

Is stable 80,000 82,000 85,000 88,000 1,000,000

Actual 15,000 30,000 70,000 88,000 1,000,000


81"

Additional Income Problems !  The following is expected cash flow for a proposed property. The Y if stabilized is 11% and is 11.5% based

upon actual income.

!  A. What is the value if stable?

!  B. What is the value when complete?

!  C. What is the discount rate to the short falls?

!  D. What would the rent loss adjustment be in the sales & cost approaches if the discount rate is 5%?

!  A. 80,000 g CFj; 82,000 g CFj; 85,000 g CFj; 88,000 Enter 1,000,000 + g CFj; 11 I; f NPV [917,476]

!  B. 15,000 g CFj; 30,000 g CFj; 70,000 g CFj; 88,000 Enter 1,000,000 + g CFj; 11.5 I; f NPV [792,012]

!  C. 917,476 – 792,012 CHS g Cfo; 65,000 g CFj; 52,000 g CFj; 15,000 g CFj; f IRR [3.2%]

!  D. 65,000 g CFj; 52,000 g CFj; 15,000 g CFj; 5 I f NPV [122,028]

1 2 3 4 Reversion

Is stable 80,000 82,000 85,000 88,000 1,000,000

Actual 15,000 30,000 70,000 88,000 1,000,000

Shortfall 65,000 52,000 15,000


82"

Nominal to Effective Rate !  The nominal rate is 8%. What is the effective annual yield

for the following frequency of payments? !  1. Annually !  2. Semi-annually !  3. Quarterly !  4. Monthly !  5. Semi-weekly !  6. Daily !  7. Continuous

Nominal to Effective Rate !  The nominal rate is 8%. What is the effective annual yield

for the following frequency of payments? Note: Whatever is calculated in FV, just subtract 1. The effective rate is the result. Note: Bi-weekly is every two weeks.

N I PV PMT FV

Annual 1 8 -1 1.08

Semi-annual

2 8/2 -1 1.0816

Quarterly 4 8/4 -1 1.0824

Monthly 12 8/12 -1 1.083

Semi-weekly

52x2 8/104 -1 1.08325

Daily 365 8/365 -1 1.08328

Continuous

1000 8/1000 -1 1.08328


83"

Leverage !  The Ro in the market is 9-10%. Given I = 8% with 30 year

notes payable monthly, what would happen to Re if M increases?

Leverage !  The Ro in the market is 9-10%. Given I = 8% with 30 year

notes payable monthly, what would happen to Re if M increases?

!  Calculate Rm: 30x12 N; 8/12 I; -1 PV; Solve PMT !  Multiply the PMT by 12 [.088052]

!  Because Rm < Ro, Re is greater and thus positive leverage. When there is positive leverage, the higher the M (LTV) the higher the Re. It will increase.


84"

Profitability Index, NPV & IRR !  Given a profitability index (PI) of .90, what can be said

about the NPV and the IRR?

Profitability Index, NPV & IRR !  Given a profitability index (PI) of .90, what can be said

about the NPV and the IRR?

!  Answer: PI is PV of inflows/Investment, if the PV is less than the investment then it will be less than 1 and the NPV, which is PV of inflows – Investment, will be a negative number. Also, the discount rate will be higher than the IRR because the IRR is the rate that makes the inflows on a present value basis = investment.


85"

Solve for Yo !  Given: Ro = 11.5%; Change in income is zero and the

value is expected to decline 25%, what is Y if N = 5?

Solve for Yo !  Given: Ro = 11.5%; Change in income is zero and the

value is expected to decline 25%, what is Y if N = 5?

!  The income is level so the top financial rows can be used.

!  The .115 PMT is the Ro. The FV reflects the 25% decline to the property.

!  You would know the Y has to be less than the Ro because of the property decline. This may narrow the potential answer to two choices.

N I PV PMT FV

5 [7.17%] -1 .115 .75


86"

Wraparound)

•  Wrap)loan:"$900,000"@"7%,"30"years"amor2za2on"&"5"year"call."Monthly"payments."

•  Underlying)First:"$400,000"@"4.5%,"15"year"amor2za2on"remaining"and"a"4"year"call."Monthly"payments."

•  Market)rates:"8%"for"similar"terms"&"there"was"$200,000"in"down"payment."

What)is)Cash)Equivalent)value?))What)is)effec=ve)yield)rate)to)the)Wrap)Lender?)

Wraparound!N* I* PV* PMT* FV*

Wrap! 30x12! 7/12! 900,000! [5,988]*Wrap!Balance!

5x12! [847,184]*!

First! 15x12! 4.5/12! 400,000! [3,060]*First!Balance!

4x12! [318,127]*

Difference! 500,000! 2,928!


87"

Wraparound!

•  The!problem!creates!an!irregular!Cash!Flow!•  47!payments!of!$2,928!!•  Wrap!lender!gets!2,928,!but!has!to!pay!off!first!balance!of!318,127.!The!net!is!a!F315,199!

•  Then!the!wrap!lender!gets!$5,988!for!11!months.!•  Then!the!wrap!lender!gets!$5,988!+!the!balance!of!$847,184!=!$853,472.!

•  Note:!This!should!add!up!to!60!months.!

Wraparound!Effec&ve!Yield!To!Wrap!Lender!

•  500,000!CHS!g!CFo!•  2,928!f!CFj!•  47!Nj!

•  315,199!CHS!g!CFj!•  5,988!g!CFj!•  11!g!Nj!

•  853,472!g!CFj!•  F*IRR*[.69356]*12*X*!*8.32%*


88"

Wraparound!Cash!Equivalency!

•  The!Wrap!note!will!be!discounted!at!market!terms.!!

The!Cash!Equivalent!Price!is!$1,063,944.!

N* I* PV* PMT* FV*

PAYMENTS* 30x12* 7/12* 900,000* [5,988]*

Balance* 5x12* [847,184]*

Discount*Note*

8/12* [863,944]*

Add*Down* 200,000*


89"

Par$$oning)the)IRR)

!Io!=!$100,000!•  ΔI!=!4%/year!compounded!•  Rn!=!9%!•  Yo!=!10%!•  N!=!4!•  Par<<on!the!IRR!between!(1)!income!if!level,!(2)!increases!in!the!income,!(3)!capital!recapture!of!the!value!when!sold,!(4)!any!increase!in!value!

Par$$oning)the)IRR!

1) 2) 3) 4) 5)for)Reversion)

Io! 100,000! 104,000! 108,160! 112,486! 116,986!

Divided!by!9%!

1,299,843!


90"

Par$$oning)the)IRR!

•  In!this!problem!we!have!Yo,!so!must!solve!for!Vo!

•  100,000!g!CFj!•  104,000!g!CFj!•  108,160!g!CFj!•  112,486!ENTER!1,299,843!+!G!CFj!•  10)I)f)NPV)!)1,222,761)[This)is)the)Vo])

Par$$oning)the)IRR!

•  112,486!ENTER!1,299,843!+!G!CFj!•  10)I)f)NPV)!)1,222,761)[This)is)the)Vo])


91"

Par$$oning)the)IRR!•  Level)Income:))4!N;!10!I;!100,000!PMT;!Solve!PV!316,987![316,987/1,222,761!=!25.9%]!•  Capital)Recapture)at)Reversion:)4!N;!10!I;!1,222,761!FV;!Solve!PV!835,162![835,162/1,222,761!=!68.3%]!•  Value)Increase)at)Reversion:)4!N;!10!I;!1,299,843!@!1,222,761!=!77,082!FV;!Solve!PV!52,648![52,648/1,222,761!=!4.3%]!•  Expected)Increases)in)Io:)0!g!CFj;!4,000!g!CFj;!8,160!g!CFj;!12,486!g!CFj;!10!I;!f!NPV!17,965![17,965/1,222,761!=!1.5%!!CHECK:!25.9%!+!68.3%!+!4.3%!+!1.5%!=!100%!!!!)

Equity'Yield'Calcula/on'•  Yo'='9%'•  Rn'='9.5%'•  ΔI'='4%/year'compounded'•  Io'='$5,000'•  N'='5'•  M'(LTV)'='80%'•  I'='5.5%'•  Amor/za/on'='30'Years,'

Monthly'payments'•  Call'provision'='5'years'

•  What'is'the'equity'yield'rate'given'the'informa/on?'

•  LET’S'GUESS…'[It'has'to'be'higher'than'9%,'because'Yo'is'between'the'Ym'&'Ye]'

•  Yo'='9%'•  Ym'='5.5%'•  (.3'x'Ye)'+'(.7'x'.055)'='.09'•  .3Ye'+'.0385'='.09'•  .3Ye'='.0515'•  Ye'='.0515/.3'='17.2%'•  The'LTV'is'80%,'but'the'loan'is'paid'down'

and'the'average'LTV'over'5'years'is'less'than'80%.'I'used'70%'for'the'guess'and'WACC.'Neither'guessing'an'average'LTV'nor'using'WACC'will'get'an'exact'rate.''

•  Let’s'see'the'exact'Ye…'

'


92"

Equity'Yield'Solu.on''1" 2" 3" 4" 5" 5"

Io' $5,000' $5,200' $5,408' $5,624' $5,849' $6,083'

Rn' .095'

Vn' $64,034'

5,000'g'CFj'5,200'g'CFj'5,408'g'CFj'5,624'g'CFj'5,849'ENTER'64,034'+'g'CFj'9'I''f'NPV'[62,543]'This'is'the'Value'or'Vo'


93"

Equity'Yield'Solu.on'

1" 2" 3" 4" 5" 5"Io' $5,000' $5,200' $5,408' $5,624' $5,849' $64,034'

Im' 3,409' 3,409' 3,409' 3,409' 3,409' 46,263'

Ie' 1,591' 1,791' 1,999' 2,215' 2,440' 17,771'

N" I" PV" PMT" FV"PAYMENT' 30'x12' 5.5/12' 62,543'

x'.80'='50,035'

[284.09]'x'12'='$3,409'

BALANCE' 5'x'12' [46,263]'

Equity'Yield'Solu.on''

1" 2" 3" 4" 5" 5"Io' $5,000' $5,200' $5,408' $5,624' $5,849' $64,034'

Im' 3,409' 3,409' 3,409' 3,409' 3,409' 46,263'

Ie' 1,591' 1,791' 1,999' 2,215' 2,440' 17,771'

Equity:'$62,543'x'20%'='$12,509'12,509'CHS'g'Cfo'1,591'g'CFj'1,791'g'CFj'1,999'g'CFj'2,215'g'CFj'2,440'ENTER'17,771'+'g'CFj'F'IRR'[20.96%]''''''

Note:'My'guess'was'17.2%,'but'the'actual'calcula.on'is'20.96%.'The'Yo'is'between'the'Ym'(5.5%)'and'the'Ye'that'was'unknown.'One'would'know'the'Ye'is'higher'than'9%,'and'with'an'80%'LTV'(M),'probably'considerably'so.'It'is'possible'to'narrow'choices'on'the'test'merely'by'understanding'the'rela.onship'of'Ye,'Ym'and'Yo.'My'guess'could'have'eliminated'two'answers'on'the'test.'


94"

MIRR$

•  Safe$rate$=$3%$•  Reinvestment$rate$=$5%$

0" 1" 2" 3" 4" 5" 6" 7" 8"

440,000$ 425,000$ 43,000$ 0$ 8,000$ 28,000$ 39,000$ 70,000$ 150,000$

MIRR$

•  Safe$rate$=$3%$•  Reinvestment$rate$=$5%$

0" 1" 2" 3" 4" 5" 6" 7" 8"

440,000$ 425,000$ 43,000$ 0$ 8,000$ 28,000$ 39,000$ 70,000$ 150,000$

PV"of"Ou1lows"40,000$g$Cfo$25,000$g$CFj$3,000$g$CFj$3$I$$F$NPV$[67,100]$

FV"of"Inflows"0$g$CH$3$g$Nj$8,000$g$CFj$28,000$g$CFj$39,000$g$CFj$70,000$g$CFj$150,000$g$CFj$5$I$F$NPV$[208,896]$8$N$$FV$[308,635]$

N" I" PV" PMT" FV"

8$ [21.02%]"SOLVED"

467,100$ 308,635$


95"

MIRR$$$

3$


96"

Some%Rela)onship%Ques)ons%%•  When%does%Re%=%Ye?%

–  When%there%is%no%loan,%no%increase%in%rents%or%value.%–  When%there%is%a%loan,%no%increase%in%rents%or%value%&%interest%only%loan.%

%•  Why%would%a%terminal%cap%rate%be%lower%than%a%going%in%cap%rate?%

–  When%the%perceived%risk%is%higher%in%the%current%market%than%expected%in%the%future.%–  When%the%current%income%is%higher%because%of%a%high%risk%tenant%in%the%property%&%an%

expectaAon%of%renAng%at%a%lower%risk%tenant%in%the%future.%%•  Why%would%you%use%a%land%residual%technique?%

–  When%I%have%a%known%building%value,%NOI,%and%rates%to%land%&%building.%

•  Why%can’t%you%blend%yield%rates?%–  You%cannot%blend%rates%using%WACC%unless%you%have%level%income,%no%change%in%value,%interest%

only%loan%and%no%closing%costs.%This%does%not%happen,%therefore%you%cannot%blend%rates%–  You%can%blend%rates%when%you%don’t%expect%the%loan%and%equity%raAos%to%change%over%Ame.%In%

other%words%you%expect%an%interest%only%loan,%no%change%in%income%or%value%and%no%closing%costs.%In%other%words,%NEVER%blend%yield%rates%for%real%estate.%

8"


97"

Income'Ques+on'

'•  The'mortgage'constant'(Rm)'is'0.136476(?)'with'a'current'loan'balance'of'$139,729(?).''What'was'the'mortgage'constant'(Rm)'when'the'loan'balance'was'$147,624(?)?'–  Increased'– No'change'– Decreased'– Can’t'answer'

The'Rm'increases'over'the'life'of'a'loan'because'it'is'the'PMT'that'stays'constant'divided'by'the'loan'balance'that'decreases'on'a'normally'amor+zing'loan.'Therefore,'the'same'payment'divided'by'a'higher'balance'would'be'a'lower'Rm.'

Rela%onship,of,Ro,,Rn,&,Yo,

•  What,can,be,expected,of,the,Discount,Rate,if,the,Going,In,cap,rate,and,the,Terminal,cap,rates,are,equal?,Assume,income,and,values,are,increasing.,– Lower,– Same,as,cap,rates,– Higher,– Can’t,answer,

Assuming,that,R,=,Y,–,CR,,this,assumes,a,“frozen”,cap,rate,as,described,in,this,problem.,The,difference,between,the,Ro,and,Yo,is,the,expected,increase,or,decrease,in,income,&,value.,We,would,expect,the,Yo,to,be,the,same,as,the,Ro,if,there,is,no,expecta%on,of,growth,and,less,than,Ro,if,a,decline,is,forecast.,


98"

Lease%Op(on%to%Purchase%•  A%tenant%is%4%years%into%a%15%year%lease%of%a%2500sf%building%at%$18/sf.%%The%building%is%currently%valued%at%$130,000.%%He%has%an%op(on%to%purchase%the%property%for%$55/SF%any%(me%aJer%the%5th%year.%%Property%values%and%rents%are%both%expected%to%increase%3%%per%year.%%When%should%you%expect%the%reversion%to%occur?%–  1%year%–  3%years%–  5%years%%–  9%years%

The%current%Ro%is%18/55%=%33%.%I%would%expect%the%owner%to%op(on%the%property%as%soon%as%it%is%legally%possible.%(1%Year)%

Lease%Op(on%to%Purchase%•  A%tenant%is%4%years%into%a%15%year%lease%of%a%2500sf%building%at%$18/sf.%%The%building%is%currently%valued%at%$130,000.%%He%has%an%op(on%to%purchase%the%property%for%$55/SF%any%(me%aJer%the%5th%year.%%Property%values%and%rents%are%both%expected%to%increase%3%%per%year.%%When%should%you%expect%the%reversion%to%occur?%–  1%year%–  3%years%–  5%years%%–  9%years%

The%current%Ro%is%18/55%=%33%.%I%would%expect%the%owner%to%op(on%the%property%as%soon%as%it%is%legally%possible.%(1%Year)%


99"

Income$Problem$–$Solve$for$Ve,$Vm$&$Vo$$

Given:"Loan:"Total"of"18"years,"6"have"gone"by,"it"balloons"in"2"years."Interest"for"the"first"8"years"of"the"loan"is"8%"and"14%"for"the"last"10"years."N"="5"years"Ye"="17%"DCR"="1.10"Io"="$50,000"and"the"change"in"income"is"4%/year"Rn"="10%"What"are"the"Ve,"Vm"and"Vo?""Solution:$Debt"service"is"$50,000/1.10"="$45,455/year""" Year"1" Year"2" Year"3" Year"4" Year"5" Year"6"Io" $50,000" $52,000" $54,080" $56,243" $58,493" $60,833"Im" 45,455" 45,455" 58,170" 58,170" 58,170" "Ie" $4,545" $6,545" V$4,090" V$1,927" $323""Reversion"in"year"5:""$60,833/.10"="""""$608,330"Loan"balance"in"year"5:" " $258,669""See"mortgage"calculations,"below"Equity"reversion"in"year"5:" " $349,661""Ve:"" 4545"g"CFj"" 6545"g"CFj"" 4090"CHS"g"CFj"" 1927"CHS"g"CFj"" 323"Enter"349,661"+"g"CFj"" 17"i"" F"NPV"[164,715]""Vo:" $349,935"+"164,715"="$514,650"(value"of"the"mortgage"+"value"of"the"equity)""Mortgage$calculations:$[Brackets$indicate$number$solved$for]$" N$ I$ PV$ PMT$ FV$1."Balance" 12x12" 8/12" [349,935]" 45,455/12"2."Balance"in"2"yrs" 24" " " " [312,203]""3.New"payment"beginning"in"2"years"and"extending"for"a"total"of"10"years"with"a"balloon"in"3:"CLEAR"REG"" 10x12" 14/12" 312,203" [4,847.46]"" " " "(Multiply"by"12"="$58,170)"4."Balance"in"3"yrs" 3x12" " " " [258,669]" ""

ProblemsIncome ApproachIncome Approach

Direct capitalizationDirect capitalizationYield capitalizationRate relationships

i l iPartial interestsMixed problem set oneMixed problem set twopMixed problem set threeAdditional problemsA Nasty hard problemA Nasty hard problem

100

Direct Capitalization Problems 1. A buyer reportedly purchased a property based upon a 9% overall rate with a net income of $40,000, which

included $5,000 of capital improvements and $3,000 of corporation franchise tax fees (included in expenses that were used to calculate NOI). What is the indicated overall rate from this sale?

2. A property sold on an 11% overall rate with financing being provided with an 80% loan-to-value ratio and a debt

coverage ratio of 1.2. What is the implied mortgage capitalization rate? 3. A property sold with an NOI of $25,000. The land value is estimated at $50,000 and the current rate to the land is

10%. What is the property value given building capitalization rates being generally 50 to 100 basis points higher than land capitalization rates?

4. A property sold with an overall rate of 10.5% and a gross income multiplier of 6. What was the operating expense

ratio of this sale? 5. Given market overall rates of from 10% to 11% and the current financing terms of prime plus 1% (prime currently

being 9.5%) and typical loan terms being for 80% LTV-ratio, and 25 years with monthly payments. What is the range of equity capitalization rates in the marketplace?

6. Overall rates in an area for the subject's property type are approximately 8%. Current taxes are $2.50 per $100

value based on 100% of market value. Given a proposed project, with no estimate of property taxes and gross income projected to be $100,000 and expenses of $40,000, excluding property taxes, what is the value of the property?

7. What would property taxes be for a property that sold for $1,000,000 based upon a market overall rate of 10%

applied to NOI, if net income before taxes (NIBT) is $120,000? 8. A property was purchased with a $200,000 down payment and an equity capitalization rate of 8%. The NOI on

the property is projected to be $40,000 and mortgage terms are currently at 10% with monthly payments over 25 years. What was the value of the property?

9. A property recently sold for $500,000 with an NOI of $48,000. Given an overall rate to the land of 8% ... a. What is the indicated overall rate to the buildings? b. Given a 16.67% land-to-value ratio, what is the indicated building capitalization rate? c. What is the value of the land? d. What is the value of the building?

101

10. Given the following data:

Tenant 1 Tenant 2 Tenant 3 Base Rent-Monthly $10,000 $5,500 $3,200 Sales-Average (Year) $1,000,000 $500,000 $400,000 %* 12% 10% 8% Market Rent (Year) 10% 12% 6% (Based on % of sales) ----------- ----------- ----------- Gross Rental Income: $120,000 $66,000 $38,400 = $224,400 Expenses: 30% of Gross Income Ancillary Income: $10,000 per year Vo: $1,400,000

*Lease payments are based on the % or base rent, whichever is higher. a. What is the net operating income of the subject? b. Given a remaining term of 10 years on the leases, and a discount rate of 10%, as applied to the net operating

income, what is the indicated value of the NOI, assuming the income stream is level? c. What is the indicated reversionary value of the subject if the reversion was discounted at 10%? d. What is the contract rent for the subject, excluding ancillary income? e. What is the market rent for the subject? f. What is the overage rent, if any, for the subject? g. What is the excess rent for the subject? h. What is the gross income multiplier? i. What is the gross rent multiplier?

102

PROBLEM SOLUTIONS - DIRECT CAPITALIZATION

1. A buyer reportedly purchased a property based upon a 9% overall rate with a net income of $40,000, which included $5,000 of capital improvements and $3,000 of corporation franchise tax fees (included in expenses that were used to calculate NOI). What is the indicated overall rate from this sale?

$40,000 ÷ .09 = $444,444

(40,000 + 5,000 + 3,000) ÷ 444,444 = 10.8% [Comment: The expenses are inappropriate and so should be added back to the income stated.] 2. A property sold on an 11% overall rate with financing being provided with an 80% loan-to-value ratio and a debt

coverage ratio of 1.2. What is the implied mortgage capitalization rate? Solution with formula: Solution with numbers: Loan = $1,000 (Made up) Ro = DCR x M x RM or Vo = $1,000 ÷ .80 = $1,250 .11 = 1.2 x .80 x RM NOI = $1,250 x .11 = $137.50 .11 = .96 RM D.S. = $137.50 ÷ 1.2 = $114.58 RM = .11458 Rm = $114.58 ÷ $1,000 = .11458 [Comment: It is better practice to use the second solution and no rely on the formula.] 3. A property sold with an NOI of $25,000. The land value is estimated at $50,000 and the current rate to the land is

10%. What is the property value given building capitalization rates being generally 50 to 100 basis points higher than land capitalization rates?

VL = $50,000 NOI = 25,000 NOIL = 5,000 (50,000 x .10) NOIB = 20,000 VB = 20,000 ÷ .105 = $190,476 to 20,000 ÷.110 = $181,818 Vo = $231,818 to $240,476 4. A property sold with an overall rate of 10.5% and a gross income multiplier of 6. What was the operating expense

ratio of this sale? Solution with formula: Solution with numbers: Ro = 1-OER or NIR EGI = $10,000 (made up) GIM GIM Vo = $10,000 x 6 = $60,000 NOI = $60,000 x .105 = $6,300 .105 = 1-OER Exps = $10,000 - 6,300 = $3,700 6 OER = $3,700 ÷ 10,000 = .37 .63 = 1 - OER OER = .37 5. Given market overall rates of from 10% to 11% and the current financing terms of prime plus 1% (prime currently

being 9.5%) and typical loan terms being for 80% LTV-ratio, and 25 years with monthly payments. What is the range of equity capitalization rates in the marketplace?

Rm: N i PV PMT FV 25g 10.5g -1 [.0094418] 12 x [.1133] .80 X .1133 = .0906 .80 X .1133 = .0906 .20 X RE = .0094 .20 X RE = .0194 .10 .11 RE = 4.68% to 9.68% [Comment: The Re is the weighted portion / the ratio. Eg. .0094/.20 = .0468, or 4.68%]

103

6. Overall rates in an area for the subject’s property type are approximately 8%. Current taxes are $2.50 per $100 value based on 100% of market value. Given a proposed project, with no estimate of property taxes and gross income projected to be $100,000 and expenses of $40,000, excluding property taxes, what is the value of the property?

Vo = 100,000 – 40,000 .08 + .025 = 60,000 .105 = $571,429 7. What would property taxes be for a property that sold for $1,000,000 based upon a market overall rate of 10%

applied to NOI, if net income before taxes (NIBT) is $120,000? NIBT - NOI = TAXES 120,000 – 100,000 = $20,000 8. A property was purchased with a $200,000 down payment and an equity capitalization rate of 8%. The NOI on

the property is projected to be $40,000 and mortgage terms are currently at 10% with monthly payments over 25 years. What was the value of the property?

Rm: N i PV PMT FV 25g 10g -1 [.009087] 12 x [.10904] VE = $200,000 NOI = $40,000 NOIE = (16,000) [200,000 X .08] NOIM = $24,000 VM = $24,000 ÷ .10904 = $220,095 Vo $420,095 9. A property recently sold for $500,000 with an NOI of $48,000. Given an overall rate to the land of 8% … Ro = 9.6% RL = 8% a. What is the indicated overall rate to the buildings? Cannot be determined.

b. Given a 16.67% land-to-value ratio, what is the indicated building capitalization rate? Ratio x Rate = Weighted Average .1667 x .08 = .01334 .8333 x RB = .08266 So: RB = .08266/.8333 = .0992 .096 c. What is the value of the land? $500,000 X .1667 = $83,350

d. What is the value of the building? $500,000 X .8333 = $416,650

104

10. Given the following data: Tenant 1 Tenant 2 Tenant 3 Base Rent-Monthly $10,000 $5,500 $3,200 Sales-Average (Year) $1,000,000 $500,000 $400,000 %* 12% 10% 8% Market Rent (Year) 10% 12% 6% (Based on % of sales) ----------- ----------- ----------- Gross Rental Income: $120,000 $66,000 $38,400 = $224,400 Expenses: 30% of Gross Income Ancillary Income: $10,000 per year Vo: $1,400,000 *Lease payments are based on the % or base rent, whichever is higher. [Comment: Most of this problem set is understanding and applying definitions with numbers.]

a. What is the net operating income of the subject? Income: $224,400 + 10,000 = $234,400 Less Expenses: (30%) = (70,320) NOI = $164,080 b. Given a remaining term of 10 years on the leases, and a discount rate of 10%, as applied to the net operating

income, what is the indicated value of the NOI, assuming the income stream is level? N i PV PMT FV 10 10 -164,080 $1,008,201 (PV of Income) c. What is the indicated reversionary value of the subject if the reversion is discounted at 10%? $1,400,000 – 1,008,201 = $391,799 (PV of Reversion) N i PV PMT FV 10 10 -391,799 (PV of Reversion) $1,016,226 d. What is the contract rent for the subject, excluding ancillary income? $224,400, with a potential for overage rents

e. What is the market rent for the subject? $1,000,000 x .10 = $100,000 $500,000 x .12 = $60,000 $400,000 x .06 = $24,000 $184,000 f. What is the overage rent, if any, for the subject? There are no overage rents. g. What is the excess rent for the subject? $224,400 – 184,000 = $40,400 h. What is the gross income multiplier? $1,400,000 ÷ 234,400 = 5.97

i. What is the gross rent multiplier? $1,400,000 ÷ 224,400 = 6.24

105

PROBLEMS – YIELD CAPITALIZATION

1. Given NOI of $25,000 in year 1, a projection period of 10 years, and a yield rate of 10% … a. What is the present value (PV) of the income if the income stream is expected to continue into perpetuity? b. What is the PV of the income if the income stream is capitalized assuming the Inwood premise? c. What is the PV of the income stream assuming the Hoskold premise, and a safe rate of 5%? d. What is the PV of the income stream if expected to change in a straight-line pattern of $2,500 per year?

e. What is the PV of the income stream if expected to change at a constant ratio pattern of 5% per year?

2. Given NOI of $25,000, a projection period of 10 years and a yield of 10% … a. What is the present value of the property assuming a level income stream and no change in value over the holding

period? b. What is the present value of the property assuming a straight-line change in value of +25%, and level income? c. What is the indicated present value of the property assuming a straight-line change in value of 50% over the

holding period, and a corresponding change in income over the projection period? d. What is the income expected to be in year 3 given the above assumptions in part c.? e. What is the PV of the property assuming a change in property value of 50%, with a corresponding constant

ratio change in income and value to achieve the 50% increase over the projection period? f. What is the PV of the property assuming no change in income for the first 2 years, a 3% per year increase in

income for the next 4 years, a 5% increase per year in income over the remaining projection period and a property value change of +40% over the holding period?

3. Given an equity yield requirement of 13%, a projection period of 10 years, and an NOI of $40,000, value the

property given the following criteria … a. There is no loan, no change in property value or income expected over the projection period. b. A mortgage is available with a LTV-ratio of 70% at 10% interest for 25 years with monthly payments. c. In addition to the above mortgage, property value is expected to increase 10% over the projection period. d. In addition to the mortgage above and property increase, income is expected to increase at a rate of 5% per

year. (K-factor = 1.1982)

e. In addition to the above mortgage terms and increase in property value, income is expected to increase 40% over the projection period assuming a J-factor pattern of income. (J-factor = .352)

106

4. Identify, from the following information, which models and equations would be appropriate … a. The present value of 5 years of level lease payments given a yield rate of 12%. b. The present value of NOI in the following pattern: Year NOI 1 $10,000 2 $12,000 3 $14,000 4 $16,500 5 $19,000 c. Income and property value are expected to remain stable over the projection period. d. Income is expected to increase $500 per year, property value is expected to increase at a compound rate of

2% per year. e. Income is expected to remain level, however, the property is expected to decline in value by 10%. f. The investment rate is 12% and recapture of the investment is to be computed at 5%. 5. What do the following account for in the Ellwood Formula? a. M x P x SFF b. ∆o x SFF c. ∆IJ 6. Assuming an equity yield requirement of 15%, no mortgage, income expected to increase at a rate of 5%

per year, compounded, property value expected to increase 30% over the projection period (5 years), what is the indicated overall rate? (K-factor = 1.0902)

7. A property has a net operating income of $50,000 and a current building value of $250,000. Given a

projection period of 7 years, an expected change in building value of -50%, and a change in land value of +50%, what is the estimated value of the property assuming a yield rate of 11%?

8. A property with a long-term level lease sold on an overall capitalization rate of 10% and was financed with

an 80% loan with an interest rate of 8% and a 30 year amortization with monthly payments. The property is expected to increase in value by 20% over the next 10 years. What was the yield to equity? What is the overall yield rate?

9. In the Akerson format, do you add or subtract depreciation x SFF in the formula?

107

10. Given the following, and assuming level income: Ro = 11.5% M = 75% ∆I = 0% N = 5 years ∆o = -20% P = .10 RM = 10.5% a. What is the indicated ∆e?

b. What is the indicated Ye? 11. The following are the terms of a lease. The sales are $2,500,000. $20,000 base + sales in excess of percentage rent $1,000,000 2% $2,000,000 3% $3,000,000 4% a. What is the income for the above lease that is owed to the lessor? b. Assuming sales will increase at 5%/year, what is the overall property yield with overall rates ranging from

8% to 9% for sales of similar properties? What would the yield to equity be if the property were purchased for all cash?

12. Given a 10 year lease that was negotiated with $15 tenant finish, $15 psf rents and increasing 3%/year.

What would the equivalent rental rate be for a similar property, but the owner offers $20 tenant finish and a 10 year level lease? Assume Yo = 13%.

13. A property with NOI of $20,000 is expected to have a stable income for 2 years, a 5% increase in NOI

compounded each year throughout the next 3 years, and a 4% increase in NOI up through year 8. A 7 year discounted cash flow was utilized to derive a value estimate for this property. The current capitalization rate for similar properties is 12% and the terminal capitalization rate is 25 basis points higher than the current capitalization rate. Additionally, 6% expenses of sale are expected in the terminal year.

a. What is the indicated value of the subject given a discount rate of 12%?

b. What is the before tax yield to equity assuming a loan being available for 70% of value, with terms being 10.5%, for 30 years with annual payments?

c. Assuming straight-line depreciation for 31.5 years (tax depreciation), and land being 20% of total value what is the indicated after tax yield to equity if the marginal tax bracket is 28% and average taxes paid by an investor are 20%? Treat reserves for replacement as an expense.

d. Compare the value derived from the DCF, and from direct capitalization. Are they consistent?

108

14. A property with an NOI of $25,000 per year was sold based upon a 10 year projection and a discount rate applied to the NOI at 10% and the discount rate to the reversion at 12%. NOI is expected to remain level throughout the projection period.

a. What is the expected reversionary value if the value of the property is $275,000?

b. What would be the compound rate of property increase or decrease per year to indicate the future value of the property?

c. When would property increase in value over a projection period, even though NOI remains level?

d. When would it be appropriate to have a higher reversionary yield rate than the yield rate applied to NOI?

e. When would it be appropriate to have a higher yield rate to NOI than applied to the reversionary value? 15. Stock was recently purchased at $100 per share. Dividends begin at $5.00 per share and are expected to

increase by $1.00 per share per year over the next 8 years. Given an investor requirement of 14% (yield), what is the expected sales price of the stock in 8 years?

109

PROBLEM SOLUTIONS – YIELD CAPITALIZATION 1. Given NOI of $25,000 in year 1, a projection period of 10 years, and a yield rate of 10% … [Comment: All of the following in problem 1 are income models, with no reversion.]

a. What is the present value (PV) of the income if the income stream is expected to continue into perpetuity?

Ro = .10 $25,000 ÷ .10 = $250,000

b. What is the PV of the income if the income stream is capitalized assuming the Inwood premise? Ro = .10 + .06275 (SFF at 10%, 10 years) = .16275 $25,000 ÷ .16275 = $153,614 c. What is the PV of the income stream assuming the Hoskold premise, and a safe rate of 5%? Ro = .10 + .0795 (SFF at 5%, 10 years) = .1795 25,000 ÷ .1795 = $139,272

d. What is the PV of the income stream if expected to change in a straight-line pattern of $2,500 per year?

PV = (25,000 + 2,500 (10) ) 6.1446 – 2,500 (10-6.1446) .10 = (50,000) 6.1446 – 96,385 = $210,835 or, 2,500 Enter Enter Enter [Flood the registers of the HP-12c] 25,000 g CFj + g CFj … [Until a total of 10 cash flows are entered into the cash flow keys] 10 i f NPV [Display: $210,835]

e. What is the PV of the income stream if expected to change at a constant ratio pattern of 5% per year?

PV = 1 – (1 + .05)10 ÷ (1 + .10)10 x 25,000 .10 - .05 = 1 – 1.62889 ÷ 2.59374 x 25,000 .05 = 7.43984 x 25,000 = $185,996 or, 1.05 Enter Enter Enter [Flood the registers of the HP-12c] 25,000 g CFj x g CFj … [Until a total of 10 cash flows are entered into the cash flow keys] 10 i f NPV [Display: $185,996] 2. Given NOI of $25,000, a projection period of 10 years and a yield of 10% … [Comment: All of the following in problem 2 are property models, including a reversion.]

a. What is the present value of the property assuming a level income stream and no change in value over the holding period?

Ro = .10 $25,000 ÷ .10 = $250,000 b. What is the present value of the property assuming a straight-line change in value of +25%, and level

income? Formula needed: Ro = Yo - ∆o x SFF Ro = .10 – (.25)(.06275) = .08431 $25,000 ÷ .08431 = $296,512

110

c. What is the indicated present value of the property assuming a straight-line change in value of 50% over the holding period, and a corresponding change in income over the projection period? Formula needed: Ro = Yo - ∆o x 1/n

Ro = .10 – (.50) (1/10) = .05 $25,000 ÷ .05 = $500,000

d. What is the income expected to be in year 3 given the above assumptions? ∆I Per Year = (Vo x ∆o ÷ N) x Yo 1. ∆I Per Year = (500,000 x .5 ÷ 10) x .10 = $2,500 2. Year NOI 1 $25,000 2 $27,500

3 $30,000 4

e. What is the PV of the property assuming a change in property value of 50%, with a corresponding constant ratio change in income and value to achieve the 50% increase over the projection period? Formula needed: Ro = Yo – CR

N i PV PMT FV 10 -1 1.50

4.14% Ro = .10 - .0414 = .0586 Vo = 25,000 ÷ .0586 = $426,621 f. What is the PV of the property assuming no change in income for the first 2 years, a 3% per year increase in

income for the next 4 years, a 5% increase per year in income over the remaining projection period and a property value change of +40% over the holding period?

Time Cash Flow 1 25,000 2 25,000 3 25,750 PV of Income = $170,330 4 26,523 5 27,318 6 28,138 Reversion Factor at 10%, 7 29,545 10 years = .38554 8 31,022 9 32,573 10 34,202 10 Vo x 1.40 Formula Needed: Vo = PVIncome + PVReversion Vo = 170,330 + (Vo x 1.40) .38554 Vo = 170,330 + .53976 Vo 1Vo - .53976Vo = 170,330 .46024Vo = 170,330 Vo = $370,090 or, 1. Calculate equivalent level income stream. N i PV PMT FV 10 10 170,330 [27,720]

111

2. Formula needed: Ro = Yo - ∆o x SFF. Derive level income capitalization rate. First calculate SFF at 10%, 10 years.

N i PV PMT FV 10 10 -1 [.0627454] Use the yield rate (10%), change in value (40%), and SFF (.0627454) and plug into equation. Ro = .10 - (.40 x .0627454) = .0749018

d. Capitalize the equivalent income stream with the level capitalization rate. Vo = $27,720 ÷ .0749018 = $370,085 3. Given an equity yield requirement of 13%, a projection period of 10 years, and an NOI of $40,000, value the

property given the following criteria … a. There is no loan, no change in property value or income expected over the projection period. Ro = .13 Vo = 40,000 ÷ .13 = $307,692 b. A mortgage is available with a LTV-ratio of 70% at 10% interest for 25 years with monthly payments. RM, P, SFF Routine: Always do first in an Ellwood problem. N i PV PMT FV 25 10 -1 g g .00909

12 x [Display: .10904 = RM] 10 g .84561 1 -

[Display: .15439 = P] f CLR REG

N i PV PMT FV 10 13 -1 .05429 [Display = SFF] Ro = .13 - .70 (.13 + .15439 (.05429) - .10904) = .13 - .02054 = .10949 Vo = 40,000 ÷ .10949 = $365,428

c. In addition to the above mortgage, property value is expected to increase 10% over the projection period. Ro = .10949 - .10 (.05429) = .10406 Vo = 40,000 ÷ .10406 = $384,390 d. In addition to the mortgage above and property increase, income is expected to increase at a rate of 5% per

year. (K-factor = 1.1982) Ro = .10406 = .0868 1.1982 Vo = 40,000 ÷ .0868 = $460,802

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e. In addition to the above mortgage terms and increase in property value, income is expected to increase 40% over the projection period assuming a J-factor pattern of income. (J-factor = .352)

Ro = .10406 = .09122 1 + .40(.352) Vo = 40,000 ÷ .09122 = $438,516 4. Identify, from the following information, which models and equations would be appropriate … a. The present value of 5 years of level lease payments given a yield rate of 12%. Ro = Yo + SFF at Yo b. The present value of NOI in the following pattern: Year NOI 1 $10,000 2 $12,000 DCF (No Pattern) 3 $14,000 4 $16,500 5 $19,000 c. Income and property value are expected to remain stable over the projection period. Ro = Yo d. Income is expected to increase $500 per year, property value is expected to increase at a compound rate of 2%

per year. 1. Income model for straight-line change. + 2. Reversion present value (calculated separately).

e. Income is expected to remain level, however, the property is expected to decline in value by 10%. Ro = Yo - ∆o SFF (at Yo) f. The investment rate is 12% and recapture of the investment is to be computed at 5%.

Ro = Yo - ∆o SFF at safe rate 5. What do the following account for in the Ellwood Formula? a. M x P x SFF Mortgage Reduction b. ∆o x SFF Appreciation or Depreciation c. ∆IJ Income Change over Projection Period 6. Assuming an equity yield requirement of 15%, no mortgage, income expected to increase at a rate of 5%

per year, compounded, property value expected to increase 30% over the projection period (5 years), what is the indicated overall rate? (K-factor = 1.0902)

Ro = .15 - .30 (.14832)

1.0902 = .09678 Note: Ro = Yo – CR, will not work because ∆I ≠ ∆o.

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7. A property has a net operating income of $50,000 and a current building value of $250,000. Given a projection period of 7 years, an expected change in building value of -50%, and a change in land value of +50%, what is the estimated value of the property assuming a yield rate of 11%?

RL = .11 – (.50)(.10222) = .05889 RB = .11 – (-.50)(.10222) = .16111 VB = $250,000 NOI = 50,000 NOIB = (40,278) [250,000 x .16111] NOIL = 9,722 ÷ .05889 = $165,087 Vo = $415,087 8. A property with a long-term level lease sold on an overall capitalization rate of 10% and was financed with

an 80% loan with an interest rate of 8% and a 30 year amortization with monthly payments. The property is expected to increase in value by 20% over the next 10 years. What was the yield to equity? What is the overall yield rate?

Start by making up a value: I will use $100,000 If the value is $100,000, then the NOI would be $10,000 ($100,000 x 10%) The future sale price would be $120,000 ($100,000 x (1 + 20%)) The loan would be $80,000 ($100,000 x 80%). The payment of 7,044 & balance of 70,180 are calculated. The yield to the property (Yo) is calculated by using the top line [11.2%] The yield to the equity position is calculated by using the bottom line [20.4%]

N I PV PMT FV R Property 10 11.2% -100,000 10,000 120,000 10.0% Loan 360

120 8/12 -80,000 587 x 12 = 7,044

70,180 8.8%

Equity 10 20.4% -20,000 2,956 49,820 14.8%

9. In the Akerson format, do you add or subtract depreciation x SFF in the formula? -∆o SFF is the portion of the formula that accounts for property change So if there is a loss in value: -(-∆o) SFF or + ∆o SFF 10. Given the following, and assuming level income: Ro = 11.5% M = 75% .75 x .105 = .07875 ∆I = 0% .25 x RE = .03625 N = 5 years Ro = .11500 ∆o = -20% P = .10 So: RE = .1450 RM = 10.5% a. What is the indicated ∆e? ∆E = (∆o + M x P) ÷ (1-M) ∆E = (-.20 + .75 x .10) ÷ (1 - .75) = -.50

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b. What is the indicated Ye? N i PV PMT FV 5 -1 .145 .50 5.6% Alternate solution: Make up an NOI and solve using dollars instead of rates. For example, if NOI =

$10,000, then value is 10,000/.115 = $86,957, and the loan is equal to $86,957 x 75% = $65,217. The debt service would be $65,217 x .105 = $6,848, and the cash flow to equity would be $10,000 – 6,848 = $3,152. The original equity is the value minus the loan ($86,957 – 65,217 = 21,740). The change in the equity position is the future sale price ($86,957 x (1 – 20%) = $69,565) minus the loan balance (65,217 x (1 – 10%) = $58,695), divided by the original equity ($21,740), minus 1. The equity cash flow at the reversion is the sale price minus the loan balance ($69,565 – 58,695 = $10,870). The yield to equity is as follows:

N i PV PMT FV 5 -21,740 3,152 10,870 5.6% 11. The following are the terms of a lease. The sales are $2,500,000. $20,000 base + sales in excess of percentage rent $1,000,000 2% $2,000,000 3% $3,000,000 4% a. What is the income for the above lease that is owed to the lessor? $20,000 + 1,000,000 x 2% + 500,000 x 3% = $55,000

b. Assuming sales will increase at 5%/year, what is the overall property yield with overall rates ranging from 8% to 9% for sales of similar properties? What would the yield to equity be if the property were purchased for all cash?

The overall yield would be approximated by Yo = Ro + CR. Yo = 8.5% + 5% = 13.5%. An exact yield could not be calculated because of the range of Ro and because the holding period and expected reversion are not given. The increase in sales would result in income at some point increasing at a greater rate than 5%, because the sales in excess of $3,000,000 would receive higher percentage rents.

Without a loan, the yield to equity would equal the overall yield. 12. Given a 10 year lease that was negotiated with $15 tenant finish, $15 psf rents and increasing 3%/year.

What would the equivalent rental rate be for a similar property, but the owner offers $20 tenant finish and a 10 year level lease? Assume Yo = 13%.

The equivalent level income for the $15 rent increasing at 3% per year at a yield of 13% is calculated as

follows: 1.03 Enter Enter Enter 15 g CFj x g CFj x g CFj …[After loading the 15 CFj, hit the times (x) gCFj nine times for a total of 10 cash flows]

13 i f NPV [90.61] This is the present value of the lease payments at 13% 10 N PMT [16.69] This is the equivalent level lease payment at 13% The extra $5 in tenant finish can be amortized as follows: 10 N; 13 i; 5 PV; solve PMT [.92] Therefore, the equivalent level lease with an extra $5 tenant finish would be: $16.69 + .92 = $17.61 psf

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13. A property with NOI of $20,000 is expected to have a stable income for 2 years, a 5% increase in NOI throughout the next 3 years, and a 4% increase in NOI up through year 8. A 7 year discounted cash flow was utilized to derive a value estimate for this property. The current capitalization rate for similar properties is 12% and the terminal capitalization rate is 25 basis points higher than the current capitalization rate. Additionally, 6% expenses of sale are expected in the terminal year.

a. What is the indicated value of the subject given a discount rate of 12%? 20,000 CFj 2 Nj 21,000 CFj Note: Reversion 22,050 CFj 26,043 ÷ .1225 = $212,596 23,153 CFj x .94 24,079 CFj $199,840 25,042 ENTER 199,840 + CFj 12 i f NPV ------Æ $189,824

b. What is the before tax yield to equity assuming a loan being available for 70% of value, with terms being 10.5%, for 30 years with annual payments?

Loan Amount: $132,877 [189,824 x 70%] Debt Service: $14,687 per year Down Payment: $189,824 – 132,877 = $56,947 Loan Balance in 7 Years: $125,800 Year NOI - Debt Service= BTCF 1 20,000 - 14,687 = 5,313 USE: IRR 2 20,000 - 14,687 = 5,313 ROUTINE 3 21,000 - 14,687 = 6,313 4 22,050 - 14,687 = 7,363 15.02% 5 23,153 - 14,687 = 8,466 6 24,079 - 14,687 = 9,392 7 25,042 - 14,687 = 10,355 [BTCF Reversion: $199,840 – 125,800 = $74,040]

c. Assuming straight-line depreciation for 31.5 years (tax depreciation), and land being 20% of total value what is the indicated after tax yield to equity if the marginal tax bracket is 28% and average taxes paid by an investor are 20%? Treat reserves for replacement as an expense.

Depreciation: 189,824 x 80% ÷ 31.5 = $4,821 Book Value: 189,824 – (4,821 x 7) = $156,077 Gain: 199,840 – 156,077 = $43,763 Taxable ATCF Time BTCF + Principal - Depreciation = Income Taxes (BTCF – Taxes) 1 $5,313 + $735 - $4,821 = $1,227 $344 $4,969 2 $5,313 + $812 - $4,821 = $1,304 $365 $4,948 3 $6,313 + $897 - $4,821 = $2,389 $669 $5,644 4 $7,363 + $992 - $4,821 = $3,534 $990 $6,373 5 $8,466 + $1,096 - $4,821 = $4,741 $1,327 $7,139 6 $9,392 + $1,211 - $4,821 = $5,782 $1,619 $7,773 7 $10,355 + $1,338 - $4,821 = $6,872 $1,924 $8,431 Taxes at Sale: $43,763 x 28% = $12,254 ATCF (Reversion) = $74,040 (BTCF) – 12,254 (Taxes) = $61,786 IRR = 11.7%

d. Compare the value derived from the DCF, and from direct capitalization. Are they consistent? $20,000 ÷ .12 = $166,667 (Direct) $189,824 (DCF)

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14. A property with NOI of $25,000 per year was sold based upon a 10 year projection and a discount rate applied to the NOI at 10% and the discount rate to the reversion at 12%. NOI is expected to remain level throughout the projection period.

a. What is the expected reversionary value if the value of the property is $275,000? 1. PV of NOI = $153,614 [25,000 PMT ; 10 N ; 10 i PV ] 2. PV of Reversion = 275,000 – 153,614 = $121,386 3. N i PV PMT FV 10 12 -121,386 377,006 b. What would be the compound rate of property increase or decrease per year to indicate the future value of the

property? N i PV PMT FV 10 -275,000 377,006 3.21% c. When would property increase in value over a projection period, even though NOI remains level? 1. Lease with level payments. 2. Land value at reversion is large. d. When would it be appropriate to have a higher reversionary yield rate than the yield rate applied to NOI? The Risk in the reversion is higher than the risk in the NOI.

e. When would it be appropriate to have a higher yield rate to NOI than applied to the reversionary value? The Risk in the NOI is higher than the risk in the reversion. 15. Stock was recently purchased at $100 per share. Dividends begin at $5.00 per share and are expected to

increase by $1.00 per share per year over the next 8 years. Given an investor requirement of 14% (yield), what is the expected sales price of the stock in 8 years?

Step 1: Step 2: 1. Time Payment 2. PV of Reversion: $100 – 36.30 = $63.70 1 5 2 6 N i PV PMT FV 3 7 8 14 -63.70 4 8 5 9 $181.72 6 10 7 11 8 12 PV of payments = $36.30 [Use NPV routine.]

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PROBLEMS – RATE RELATIONSHIPS

1. Refer to the DCF problems from Yield Capitalization, problem 13.

a. Was the leverage positive or negative based upon before tax cash flows?

b. Was the leverage positive or negative, considering before tax yield rates?

c. Was the leverage positive or negative considering the after tax yield rates?

2. The present value of an ordinary annuity discounted at 12% is $50,000. What is the present value of the

lease payments if paid in advance?

3. Given two properties with income characteristics being identical except Property 1 is within an area of

higher tax rates, and very little chance of change in tax structure between the two properties… a. Would you expect the overall rates to be higher, lower or the same, when comparing property 1 to property 2? b. Would you expect the gross income multiplier to be higher, lower or the same when comparing property 1 to

property 2? 4. Given an increase in long-term interest rates, how would overall rates change? 5. Given no change in value or NOI, can the debt coverage ratio be increased? If so, how? 6. What is the indicated interest rate on a second mortgage if terms are for 20 years (annual payment), Ro =

.105, a first mortgage on the property is for 9% interest, with M = 80%, 20 years (annual payments), and RE is .06, with 10% down?

7. Given expected increases of income and value of 4% per year (to follow expected inflationary trends), and a

yield requirement of 12%, what is the indicated overall rate? 8. Given NOI of $10,500, a DCR of 1.25 and a mortgage capitalization rate of 12%, what is the indicated loan

amount?

9. Given a $50,000 loan, an NOI of $10,000 and a DCR of 1.15, what is the mortgage capitalization rate? 10. Given: M = 80% Rm = .1234 OER = 40% GIM = 6 NOI = $10,000 What is the debt service?

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11. Given: OER = 35% DCR = 1.18 Rm = .115 M = .80 What is the GIM? 12. Given: Value = $1,000,000 Ro = .09 DCR = 1.15 Rm = .12 What is the debt service and loan amount? 13. Given: NOI = $10,000 OER = 40% (of EGI) Vacancy & collection loss = 5% What is the potential gross income?

14. What is the PGIM given an EGIM of 6 and a vacancy & collection loss of 7%?

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PROBLEM SOLUTIONS – RATE RELATIONSHIPS 1. Refer to the DCF problems from Yield Capitalization, problem 13. a. Was the leverage positive or negative based upon before tax cash flows? RM = .1105 RM > Ro Ro = .1054 Therefore, Negative RE = .0933 [Comment: To determine the effect of leverage focus on the mortgage rate, if it is the lowest that is positive leverage. The overall rate (including yield) has to be between the equity and mortgage rates.] b. Was the leverage positive or negative, considering before tax yield rates? YM = .105 YM < Yo Yo = .120 Therefore, Positive

YE = .150 c. Was the leverage positive or negative considering the after tax yield rates? YM = .076 (.105 x (1-28%)) YM < Yo YE = .117 Therefore, Positive 2. The present value of an ordinary annuity discounted at 12% is $50,000. What is the present value of the

lease payments if paid in advance? $50,000 x 1.12 = $56,000 Please note that the “lease payments” language is a distractor. The present value of an ordinary annuity by

definition is level payments made in arrears. 3. Given two properties with income characteristics being identical except Property 1 is within an area of

higher tax rates, and very little chance of change in tax structure between the two properties... a. Would you expect the overall rates to be higher, lower or the same, when comparing property 1 to property 2? The overall rates should be equal. b. Would you expect the gross income multiplier to be higher, lower or the same when comparing property 1 to

property 2? The GIM should be lower for Property 1. 4. Given an increase in long-term interest rates, how would overall rates change? Ro = Rm x M x DCR, Rm increases so Ro increases. However, the overall rates often do not change if the reason the interest rates are higher is due

to expected inflation. Real estate is looked upon as an inflation hedge. 5. Given no change in value or NOI, can the debt coverage ratio be increased? If so, how? (1) Lower the loan-to-value ratio. (2) Lower the interest rate. (3) Extend the term of the loan.

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6. What is the indicated interest rate on a second mortgage if terms are for 20 years, Ro = .105, a first mortgage on the property is for 9% interest, with an 80% LTV, for 20 years (annual payments), and RE is .06, with 10% down?

Rm: 20 N, 9 i, -1 PV PMT [Display: .1095465] .80 x .1095465 = .087637 .10 x Rm2 = .011363 Rm2 = 11.36% .10 x .06 = .006000 .105 N i PV PMT FV 20 -1 .1136 9.5% 7. Given expected increases of income and value of 4% per year (to follow expected inflationary trends), and a

yield requirement of 12%, what is the indicated overall rate? Ro = Yo - CR Ro = .12 - .04 = .08 8. Given NOI of $10,500, a DCR of 1.25 and a mortgage capitalization rate of 12%, what is the indicated loan

amount? ($10,500 ÷ 1.25) ÷ .12 = $70,000 Note: NOI ÷ DCR = Debt Service 9. Given a $50,000 loan, an NOI of $10,000 and a DCR of 1.15, what is the mortgage capitalization rate? (10,000 ÷ 1.15) ÷ 50,000 = .1739 10. Given: M = 80% Rm = .1234 OER = 40% GIM = 6 NOI = $10,000 What is the debt service? Ro = 1-OER 1 - .40 GIM, so 6 = .10 NOI ÷ Ro = Vo: 10,000 ÷ .10 = $100,000 Vo x M x Rm = Debt Service: $100,000 x 80% x .1234 = $9,872 or, EGI = $10,000 ÷ (1 - 40%) = $16,667 Vo = $16,667 x 6 (GIM) = $100,000 Loan = $100,000 x 80% = $80,000 Debt Service = $80,000 x .1234 = $9,872

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11. Given: OER = 35% DCR = 1.18 Rm = .115 M = .80 What is the GIM? Solution with formulas: Solution with cash flows: Ro = DCR x Rm x M: Vo = $1,000 (made up) So, Ro = 1.18 x .115 x .80 = .10856 Loan = $1,000 x 80% = $800 Ro = NIR 1 - .35 D.S.= $800 x .115 = $92 GIM: So, .10856 = GIM NOI = $92 x 1.18 = $108.56 EGI=$108.56 ÷ (1 - 35%) = $167.02 .10856 = .65 EGIM = $1,000 ÷ $167.02 = 5.99 GIM .10856 GIM = .65 GIM = 5.99 12. Given: Value = $1,000,000 Ro = .09 DCR = 1.15 Rm = .12 What is the debt service and loan amount? Debt Service:Value x Ro ÷ DCR = 1,000,000 x .09 ÷ 1.15 = $78,261 Loan Amount:Debt Service ÷ Rm = 78,261 ÷ .12 = $652,174 13. Given: NOI = $10,000 OER = 40% (of EGI) Vacancy & collection loss = 5% What is the potential gross income? $10,000 ÷ .60 = $16,667 (EGI) $16,667 ÷ .95 = $17,544 (PGI) 14. What is the PGIM given an EGIM of 6 and a vacancy & collection loss of 7%? Solution with formula: Solution with cash flows: PGIM = EGIM x (1 - vac.) Vo = $10,000 PGIM = 6 x (1 - .07) = 5.58 EGI = $10,000 ÷ 6 = $1,666.67 PGI = $1,666.67 ÷ (1 - .07) = $1,792.11 PGIM = $10,000 ÷ $1,792.11 = 5.58

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PROBLEM - PARTIAL INTERESTS

1. A 90 year lease was originated 55 years ago for $500 per year. Current market rent is $20,000 per year for

long-term leases, on a level basis. Tenant #1 leased to Tenant #2 for $5,000, Tenant #2 leased to Tenant #3 for $8,000, Tenant #3 leased to Tenant #4 for $12,000, Tenant #4 leased to Tenant #5 for $19,000, and Tenant #5 leased to Tenant #6 for $22,000. The market value of the property is currently $150,000 and is expected to be $500,000 at the termination of the lease.

a. What is the applicable yield rate to the fee simple?

b. What is the applicable yield rate to the reversion?

c. What is the indicated value to each of the tenant's positions? d. What is the present value of the leased fee?

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PROBLEM SOLUTIONS - PARTIAL INTERESTS

A 90 year lease was originated 55 years ago for $500 per year. Current market rent is $20,000 per year for long-term leases, on a level basis. Tenant #1 leased to Tenant #2 for $5,000, Tenant #2 leased to Tenant #3 for $8,000, Tenant #3 leased to Tenant #4 for $12,000, Tenant #4 leased to Tenant #5 for $19,000, and Tenant #5 leased to Tenant #6 for $22,000. The market value of the property is currently $150,000 and is expected to be $500,000 at the termination of the lease.

The following principles apply to the partial interest analysis: 1. The sum of the leased fee and combined leasehold estate = value of fee simple. [Note that this is not generally true, but is used to analyze partial interests created by a lease. If a test question asks if the parts equal to fee simple, the answer is NO!!!] 2. The fee simple yield rate is the average risk rate to all cash flows and is applicable to the "middle dollar" of the fee simple income & reversion. All dollars with more risk should be discounted at a higher rate and all dollars with less risk than the "middle dollar" should be discounted at a lower rate. 3. The leased fee income is generally the safest cash flow because it is received first (vertical risk). The

reversion, because it is the last cash flow in time (horizontal risk), has a higher rate than the fee simple yield rate. The middle layer of cash flow is approximately at the middle of risk (fee simple risk rate) and should be discounted at approximately the fee simple rate. All cash flows above the middle should be discounted at a higher than fee simple rate, and all cash flows lower than the middle at a lower than fee simple yield rate.

T6 $22,000 $2,000 Market Rent = $20,000 $1,000 T5 $19,000 $7,000 T4 $12,000 13.6% is the average risk to the combined leasehold (calculated) $4,000 T3 $8,000 $3,000 T2 $5,000 $4,500 T1 $500 $500

Position N I PV PMT FV R Fee Simple 35 13.7 150,000 20,000 500,000 Leased Fee 35 8,600 500 500,000

Combined leasehold 35 13.6 141,400 19500 0 T1 35 10 J 43,400 4,500 0 T2 35 12 J 24,500 3,000 0 T3 35 14 J 28,300 4,000 0 T4 35 17 J 41,000 7,000 0

T4 & T5 35 19 J 5,300 -5,300

2,000 -2,000

0

Note: The bold numbers in each row are calculated. The rates marked with a “J” are selected with judgment. The selection of rates is based upon the principle that the risk increases vertically as one moves from T1 to T5. The rate to T1 has to be greater than at least the rate to the leased fee income. The rate to T2 has to be higher than T1 rate, etc. Furthermore, there is a reasonableness to the selection process because the weighted average of the rates has to be the rate to the combined leasehold which is always calculated after estimating the fee simple and leased fee values. An 8% (safe rate) is selected for the leased fee income (judgment). The lower the leased fee income relative to the fee simple income, the less impact the selection has on the calculated value as a percent of the fee simple value. Since market rent is $20,000 and the leased fee income is $500, it would not make much difference what rate is chosen to value the income stream. However, the rate has to be consistent with the risk of that position. The leased fee income is the safest income position and the reversion (to the leased fee and fee simple) is one of the highest risks in the cash flows. That is why the rate is often split when calculating the value of each position. The present value of the leased fee income is $5,827. The present value of the reversion (using the market rate of 13.7% + 2.3% = 16%) is $2,773. Therefore, the

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present value of the leased fee estate is $8,600, and the present value of the combined leasehold is the difference between the fee simple value of $150,000 and the leased fee value of $8,600, or $141,400. The applicable yield rate to the combined leasehold is solved by the following (the $19,500 is market rent minus leased fee income): 35 N -141,400 PV 19,500 PMT, and solve for i [Display: 13.6%] This is the applicable yield rate to the combined leasehold position. The rate to the leasehold position is almost always a calculation, and not a judgment call. This is because the leasehold is the residual between the fee simple and leased fee positions with both the values and the income positions. (Fee simple – leased fee = combined leasehold). Once the rate is calculated this is the average of the combined leasehold position. Although not a linear relationship, the rate increases as the position increases. However, the middle cash flow position should be discounted at or near the combined leasehold rate calculated for the leasehold. .Because it is the weighted average risk in the combined leasehold, the rate is applicable at the midpoint of the combined leasehold cash flow, or $10,250 ($20,000 market rent + $500 leased fee income, divided by 2). All income below is at a lower rate, and all income above $10,250 is at a higher rate. The T1 position should be discounted at a lower rate than the combined leasehold, but when applicable, at a higher rate than the leased fee income. The combined leasehold represents all the tenants positions. Since T1 is at the lower end of the risk of that position, the rate should be lower than the combined leasehold rate. The tenant in the middle cash flow position should be discounted at approximately the combined leasehold rate since the combined leasehold is the average risk to all the tenants’ positions. However, this should be adjusted depending upon how much of the income layer is above the middle income or below the middle income. For example, the combined leasehold rate is calculated at 13.6%. The combined leasehold extends from $500 to $20,000, and the middle dollar is ($20,000 + 500) / 2 = $10,250. At $10,250 there is $9,750 below the middle to the leased fee income and $9,750 to the market rent line. T3 has the income layer that the middle falls into. The income to T3 is from $8,000 to $12,000, and there is more income above $10,250 than below $10,250. Therefore, a reasonable discount rate would be 14% which is the combined leasehold rate rounded upward. The positions below T3 should be discounted lower and the positions above T3 should be discounted higher than 14%. There is always a check to the reasonableness of the judgment calls made in the rate selection. Since the combined leasehold is all the tenants’ positions added up, the values of all tenants’ positions should add up to approximately the combined leasehold value. (However, note that the value of the excess rent always nets to zero because the tenant who pays the excess rent is in a negative value position and the tenant who receives the excess rent gets the value the tenant who pays loses.) The combined leasehold is always from contract rent to the leased fee to market rent. The excess rent nets to zero in the problems. The value of each of the positions is the present value of the cash flow to the position at the applicable rate previously derived. The cash flow to the position is represented by the money within the bar and is the difference between what is received by the position and what is paid by the position. The values are as follows. Tenant 1: 35 N 10 i 4,500 PMT , solve for PV [Display: 43,398] Tenant 2: 35 N 12 i 3,000 PMT , solve for PV [Display: 24,527] Tenant 3: 35 N 14 i 4,000 PMT , solve for PV [Display: 28,280] Tenant 4: 35 N 17 i 7,000 PMT , solve for PV [Display: 41,007] Tenant 5: 35 N 19 i 1,000 PMT , solve for PV [Display: 5,251] Note: Tenant 5's position is the difference between market rent and rent paid plus Tenant 5 receives excess rent. Only the difference between market rent and what tenant 5 pays was discounted to test the reasonableness of the methodology used. The indicated value of the combined leasehold is the sum of the positions or $142,463. The combined leasehold value was previously derived at $141,400. Therefore, the allocation of value is reasonable because the total derived is only 3% higher than the combined leasehold value derived by subtracting fee simple value minus leased fee value. Tenant 5 also receives excess rent of $2,000 which may be discounted at 22% to indicate a value for the excess rent of $9,082. Therefore, Tenant 5's position is worth the present value of the excess rent ($9,082) plus the present value of the rent received from the market level ($4,992), or $14,333. Tenant 6 loses what Tenant 5 gains because of the assumption that the sum of the parts equals the whole. Therefore, Tenant 6's position is worth a minus or negative $9,082. The positions can be approximated without a lot of thought by calculating the leased fee position at a low rate, the top position at a credit card rate and the positions in between relative to those rates.

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Mixed Problem Set One

1. A property sold with an operating expense ratio of 43% (on effective gross income) and loan terms included a debt coverage ratio of 1.15, 9% interest rate with 25% down and a 30 year term with monthly payments. What was the potential gross income multiplier if vacancy and collection loss is 7%?

a). 6.36 b). 5.16 c). 5.54 d). 6.84 2. The market indicates a yield rate of 14% with annual year end accounting. You are appraising a subdivision that

will have a 3 year sell-out with the values and absorption expected to remain stable throughout the projection. Lender instructions require a quarterly discounting of cash flows. What quarterly yield rate (annualized) would result in the same present value?

a). 14.0% b). 4.18% c). 16.7% d). Cannot be determined from information given. 3. A property sold for $325,000 based on a 14% yield rate. The projections included the following: Year 1 - 23,000 Year 2 - 50,000 Year 3 - 42,000 Year 4 - ?????? Year 5 - 20,000 Year 6 - 400,000 [Reversion] What is the fourth year’s NOI? a). 45,380 b). 76,646 c). 19,868 d). 33,555 Questions 4 - 8 are based on the following: A tract was leased 30 years ago to a manufacturing company for 90 years at $100 per year. The original tenant

built a facility for $50,000 that subsequently burned down. Tenant One died five years ago. Tenant One leased to Tenant Two 20 years ago for 60 years at $5,000 per year. Tenant Two subsequently leased to Tenant Three for $10,000 per year (35 years remaining on lease). Tenant Three leased to Tenant Four for $15,000 per year (30 years remaining). Tenant Four leased to Tenant Five for $17,500 (35 years remaining). Tenant Five leased to Tenant Six for $19,000 (30 years remaining). The market rent (absolute net) for long-term leases (with level payments) is currently $18,500 for similar properties with 60 years with an appropriate discount rate being 13%. The property is expected to be worth $40,000,000 at the end of the lease and the applicable rate to the reversion is 16%.

4. What is the applicable yield rate to fee simple? a). 13% b). 16% c). 14% d). Cannot be determined from the information given.

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5. What is the value of the combined leasehold position? a). $6,665 b). $148,000 c). $141,000 d). Cannot be determined from the information given. 6. What is the value of Tenant 1's position? a). $35,000 to $45,000 b). $45,001 to $55,000 c). $55,001 to $65,000 d). Cannot be determined from the information given. 7. What is the value of Tenant 3's position? a). $30,000 to $35,000 b). $35,001 to $45,000 c). $45,001 to $55,000 d). Cannot be determined from the information given. 8. What is the value of Tenant 5's position? a). $5,000 to $10,000 b). $10,001 to $15,000 c). $15,001 to $20,000 d). Cannot be determined from the information given. Questions 9 - 10 are based on the following: Land was purchased for $2.00 psf with terms of 25% down at 11%, 20 years, with monthly payments. Inflation

is expected to be 6% over the next 5 years. Assume taxes are $1.50 psf per 100 valuation based on 100% of value and the current assessed value is $1.75 psf. Furthermore, the taxes are expected to remain stable over 5 years. Assume annual year end accounting.

9. What are the taxes per square foot in Year 1? a). $.02534 b). $.01500 c). $.01313 d). $.02625 10. Assuming the taxes begin at $.02534 per square foot, what is the indicated price in 5 years given an expected

equity yield rate of 20% at the time of purchase and expenses of sale of 5%. a). $2.55 psf b). $4.13 psf c). $4.17 psf d). $4.40 psf Questions 11 - 13 are based on the following: A property with NOI of $20,000 and an operating expense ratio of 42% on effective gross income, sold with a

PGIM of 5 and was 10% vacant at the time of sale. Financing was for 75% of value with terms being at 10%, 30 years with monthly payments.

11. What is the overall rate? a). 10.4% b). 12.6% c). 11.6% d). Need an equity cap rate to determine

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12. What is the implied DCR? a). 1.20 b). 1.30 c). 1.45 d. 1.60 13. What is the effect of leverage on this property? a). Positive based upon cash flows and yield. b). Negative based upon cash flows and yield. c). Positive based upon cash flows d). Negative based upon cash flows. 14. What was the change in the equity position if property value increases 25%, with an original loan to value ratio

of 70% and an interest only loan? Assume level income and 5% expenses of sale. a). 62.5% b). 85% c). 80% d). 67% 15. Given NOI of $20,000, a DCR of 1.15 and a mortgage cap rate of 11%, what is the indicated loan amount if the

loan is for 20 years, annual payments? a). $138,500 b). $158,100 c). $209,000 d). $183,200 Use the following for questions 16 & 17: Ro = 11.5% Ym = 10.5% Term = 30 years, monthly payments M = 80% 16. Given a change in equity of + 30%, level income, and a 5 year projection period, what is the equity yield rate? a). -0.6% b). 7.8% c). 18.0% d). 16.9% 17. Given a change in equity of +30%, a 5 year projection, but the equity cash flows increased 5% per year, what is

the equity yield rate? a). 1.4% b). 22% c). 18% d). 19% 18. Given a $50,000 loan, NOI of $15,000 and a DCR of 1.15, what is the mortgage capitalization rate? a). .26 b). .35 c). .30 d). Cannot be determined without knowing the remaining term of the loan.

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19. The present value of a reversion is $50,000 and the property is worth $250,000. Given an overall discount rate of 13%, what is the indicated level income equivalent if the property was held 10 years? [What would the income be if it were level?]

a). 200,000 b). 20,000 c). 46,070 d). 36,860 20. Although no changes have occurred in property or income tax law changes, building capitalization rates have

increased. If land capitalization rates decrease, what can be said about overall rates. a). They will remain the same. b). Given higher building to value ratios, overall rates will increase. c). Increased risk will cause overall rates to increase. d). Cannot be determined. 21. Given land value = $50,000 the total property is worth $150,000. What is the RL if the Ro is 10%, and RB =

11%? a). 9% b). 8% c). 2.7% d). Cannot be determined

22. A property sold with an operating expense ratio of 40% (on Effective Gross Income) and loan terms included a

debt coverage ratio of 1.15, 9% interest rate with 25% down and a 30 year term with monthly payments. What was the potential gross income multiplier if vacancy and collection loss is 5%?

a). 7.20 b). 7.72 c). 7.34 d). 6.84 23. Given NOI beginning (paid in advance) for $5,000 per year and increasing at CPI each year, for 21 years, what

is the present value of the cash flows if CPI is expected to increase 4% for the first 10 years, then 6% for the remaining term of the lease? Assume annual accounting, and a discount rate of 11%.

a). $57,500 b). $60,000 c). $62,500 d). $65,000 24. What must a property sell for to yield 13% if there are sales commissions of 6% at time of resale and other

closing costs of $2,500, the original purchase price was $500,000 and NOI in year 1 was $40,000 and increased $2,000 per year for 9 years? Assume annual year-end accounting and the reversion to be at the end of the 10th year.

a). $244,791 b). $830,959 c). $833,459 d). $886,659 Questions 25 - 29 are based on the following: Property value in fee simple = $600,000, and market rent is $72,000 for level leases of a long-term structure.

The reversion is expected to be $3,000,000. Inflation is expected to be 4% per year over the next 20 years. The owner leased to tenant one 35 years ago for 80 years for $100 per year Tenant 1 leased to tenant two 20 years ago for the remaining term for $25,000 per year Tenant 2 leased to tenant three 10 years ago for 30 years for $70,000 per year Tenant 3 leased to tenant four 5 years ago for 10 years for $80,000 per year

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25. What is the applicable yield rate to fee simple? a). 12.3% b). 12.5% c). 13.25% d). 13.5% 26. What is the value of the combined leasehold position? a). $500,000 b). $650000 c). $590,000 d). $483,356 27. What is the value of Tenant 1's position? a). $200,000 to $240,000 b). $240,001 to $280,000 c). $280,001 to $305,000 d). $305,001 to $335,000 28. What is the value of Tenant 3's position? a). $5,000 to $30,000 b). $30,001 to $45,000 c). $45,001 to $55,000 d). Greater than $55,000 29. What is the value of Tenant 3's rent received below market rent? a). $5,000 to $30,000 b). $30,001 to $45,000 c). $45,001 to $55,000 d). Greater than $55,000 Questions 30 & 31 are based upon the following: Land was purchased with terms of 20% down at 11%, 30 years, with monthly payments. Inflation is expected to

be 5% over the next 5 years. Assume taxes are $1.50 per 100 valuation based on 100% of value and the current assessed value is $1.75 per sf. Furthermore, the taxes are expected to remain stable over 5 years. Assume annual year end accounting, and taxes on the subject of $25,000 per year.

30. What is the value of the land assuming the assessed value is approximately 85% of actual value? a). $1,250,000 or less b). $1,500,000 c). $1,750,000 d). $1,950,000 or more 31. Assuming the value is $1,500,000, what is the indicated price in 5 years given an expected equity yield rate of

20% at the time of purchase and expenses of sale of 5%. a). $2,500,000 or less b). $3,000,000 c). $3,500,000 d). $4,000,000 or more

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Questions 32 - 34 are based on the following: Apartments recently sold in four different neighborhoods all subject to short-term leases. Neighborhood 1 Ro=7.0% Yo required by the market =14.5% Neighborhood 2 Ro=10.0% Yo required by the market =14.0% Neighborhood 3 Ro=14.0% Yo required by the market =13.5% Neighborhood 4 Ro=18.0% Yo required by the market =13.0% 32. Which neighborhood appears to be the most stable? a). Neighborhood 1 b). Neighborhood 2 c). Neighborhood 3 d). Neighborhood 4 33. Which neighborhood appears to be experiencing rising rents? a). Neighborhood 1 b). Neighborhood 2 c). Neighborhood 3 d). Neighborhood 4 34. Which neighborhood appears to offer the least risk for $1 invested? a). Neighborhood 1 b). Neighborhood 4 c). They are all of equal risk d). Cannot be determined 35 - 38 are based upon the following: A loan was originated 3 years ago with a 30 year amortization, monthly payments of $2,000, and has a current balance of $223,689. 35. What is the amount of the original loan? a). $227,900 b). $230,000 c). $231,465 d). $235,000 36. What is the interest rate on the loan? a). 9% b). 9.5% c). 10% d). 10.5% 37. What is the loan worth (current balance) if discounted at 14%? a). $167,000 b). $175,354 c). $182,987 d). $176,090 38. What is the loan worth (current balance) if it balloons in 3 years and is discounted at 14%? a). $189,012 b). $201,000 c). $218,010 d). $254,767

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39. Given a $1,000,500 loan, NOI of $45,000 and a DCR of 1.2, what is the mortgage capitalization rate? a). 4.5% b). 3.75% c). 5.4% d). Cannot be determined without knowing the remaining term of the loan. 40. The present value of a reversion is $150,000 and the property is worth $250,000. Given an overall discount rate

of 15%, what is the indicated level income equivalent if the property was held 5 years? [What would the income be if it were level?]

a). $20,000 b). $74,579 c). $29,832 d). $44,663 41. "Air rights" are an example of a(n): a). Financial partial interest. b). Economic partial interest. c). Legal division partial interest. d). Vertical interest. 42. Before tax cash flow (equity cash flow) is $10,000. Loan terms include a first loan with a RM = 10.5% (M =

75%). The lender requires a 1.20 debt-coverage-ratio. What is the value of the subject? a). $600,000 or less b). $615,000 c). $635,000 d). $675,000 or greater 43. Given land value of $100,000 and the total property is worth $450,000. What is the RL if the Ro is 10%, RB =

11%, gross income is $50,000, vacancy is 5%, and rents and occupancy are expected to remain stable throughout the projection period?

a). 8.5% b). 7.5% c). 6.5% d). Cannot be determined without knowing expenses or an expense ratio.

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Questions 44 through 49 are based upon the following: Sale 1 sold for $392,700 in 6/90 and was rented for $5,100 per month at the time of sale with the owner paying 23% of gross income in expenses. The land area is 45,000 sf and the licensed child capacity is 200 per day. Typical financing at the date of sale was 11%. Sale 1 is 10,300 sf. Sale 2 sold for $170,000 on 4/90 and was rented for $2,588 per month at the time of sale with the owner paying 35% of gross income in expenses. The land area is 21,780 sf and the licensed child capacity is 90 per day. Typical financing at the date of sale was 11%. Sale 2 is 5,000 sf. Sale 3 sold for $175,000 on 3/89 and was rented for $2,025 per month at the time of sale with the owner paying 19% of gross income in expenses. The land area is 21,800 sf and the licensed child capacity is 90 per day. Typical financing at the date of sale was 10%. Sale 3 is 4,558 sf. Sale 4 sold for $230,000 on 8/89 and was rented for $2,850 per month at the time of sale with the owner paying 26% of gross income in expenses. The land area is 20,000 sf and the licensed child capacity is 120 per day. Typical financing at the date of sale was 10%. Sale 4 is 5,100 sf. Sale 5 sold for $220,000 on 7/88 and was rented for $2,558 per month at the time of sale with the owner paying 29% of gross income in expenses. The land area is 18,350 sf and the licensed child capacity is 110 per day. Typical financing at the date of sale was 9%. Sale 5 is 3,842 sf. Sale 6 sold for $260,000 on 6/88 and was rented for $2,532 per month at the time of sale with the owner paying 15% of gross income in expenses. The land area is 18,800 sf and the licensed child capacity is 125 per day. Typical financing at the date of sale was 9%. Sale 6 is 4,860 sf. The subject daycare center has a gross building area of 6,000 sf and land area of 26,000 sf. The licensed child capacity is 125 per day. Assume the expense ratio differences in the comparables are due, not to different actual expense structures between the comparables, but are solely the result of different lease negotiations. Therefore, assume that the differences in expenses paid by the owner are expressed in the lease rate. The more expenses the owner passed through, the lower the rental rate for the tenant. Assume a 25% expense ratio for the subject. The appraisal date is 10/90. 44. What is a reasonable conclusion of market rent for the subject? a). $3,250 per month b). $3,000 per month c). $2,750 per month d). $2,500 per month 45. What is a reasonable conclusion for a capitalization rate for the subject? a). 10% b). 11% c). 12% d). 13% 46. What is a reasonable gross income multiplier for the subject? a). 8.25 b). 7.25 c). 6.25 d). 5.25 47. What is the pattern of rent change over time? a). Rents increased b). Rents declined c). Rents were stable d). There is no established pattern

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48. What is a reasonable value conclusion for the subject? a). $350,000 b). $300,000 c). $250,000 d). $200,000 49. What is the pattern of value change over time? a). Values increased greater than 3% per year b). Values declined greater than 3% per year c). Values were stable d). Values declined by greater than 3%, then increased at a greater rate than 3% per year. Use the following information to answer questions 50 - 53: An investor has the following alternative investments for a 5 year holding period. Property Overall Rate Income Growth Value Growth Mortgage Constant Debt Coverage Ratio Office 11.5% 4% 3.5% 10.250% 1.25 Retail 12.5% 3% 2.5% 10.500% 1.20 Apartment 8.0% 6% 5.5% 10.125% 1.15 Industrial 13.5% 2.5% 2.5% 10.875% 1.30 50. Which property would have the highest total property yield if the expected overall rates, growth rates, and financing all

occur as anticipated? a). Office b). Apartment c). Industrial d). Cannot be determined from the information given 51. Which property would require the least down payment as a percentage of value? a). Office b). Retail c). Industrial d). Cannot be determined from the information given 52. Which property has the lowest Re (equity capitalization rate)? a). Office b). Retail c). Industrial d). Cannot be determined from the information given 53. Which property has positive leverage on the basis of yield? a). Apartments only b). All of the properties c). None of the properties d). Cannot be determined from the information given 54. An apartment sold for $36.50 psf with current rents at 60¢ psf, 85% occupancy, and $3.00 psf expenses. The average

rents for the preceding year were 55¢ psf per month, occupancy averaged 90%, and expenses were $3.00 psf. The proforma statement of the comparable indicates expected rents of 65¢ psf, occupancy to average 92% (the market is 95%), and expenses of $3.25 (similar properties have expenses of $3.30 psf). What capitalization rate would you use if the market rental level is 65¢ psf, and the subject property has expected NOI of $4.11 psf one year from the date of appraisal?

a). 8.50% b). 10.00% c). 11.00% d). 11.25%

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55. What can you conclude about a market if inflation is 5% per year, improvements are physically depreciating 1.5% per year, capitalization rates are 11% and mortgage interest rates are 10.5%?

a). Values are increasing greater than 2% per year b). Values are declining greater than 2% per year c). Values are stable d). Cannot be determined from the information given 56. Given taxes of $1.75 per 100 valuation and valuation is based on 100% of market value, what is the capitalization rate if

net income before taxes is $35,500, the property sold for $350,000, and is assessed for $350,000? a). 8.40% b). 10.14% c). 11.89% d). 12.23% 57. What is the value of a loan with payments of $5,000 per month for 300 months if expected inflation is 5% per year and

an investor requires a real rate of return of 6% per year, compounded? a). $450,000 b). $500,000 c). $776,000 d). $855,000 58. A property has a loan for $400,000 with terms of 11.5% interest, and monthly payments for 25 years, and a balloon after

the fifth year. Net income is $52,500 and the required equity capitalization rate range is 9% to 10%. What is the value of the property?

a). $400,000 or lower b). $450,000 c). $500,000 or higher d). Cannot be determined from the information given. 59. A property sold with a potential gross income multiplier of 6.25, net operating income of $125,000, expenses of 40% of

effective gross income and vacancy and collection loss of 7%. What was the sale price? a). $1,300,000 b). $1,400,000 c). $1,500,000 d). $1,950,000 60. A debt coverage ratio is... a). the number of times debt service covers net income b). the number of times net income covers debt service c). always greater than one d). equal to loan-to-value ratio times loan constant divided by overall capitalization rate 61. Given net income of $10,000, an expense ratio of 38%, and a potential gross income multiplier of 6, what is the vacancy

and collection loss if the property sold for $100,000? a). 3% b). 4% c). 5% d). 6% 62. Net operating income is $40,000, and the rate to the land is 11% with rates to buildings being typically 50 basis points

lower. If improvements are worth $300,000, what is the indicated value of the property? a). $300,000 b). $77,272 c). $375,000 d). $395,000

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63. What is the indicated overall rate if typical first loans are 75% loan-to-value at 9.875% interest, second loans are typically 15% loan-to-value at 12% interest and equity yields are typically 17%? Assume all loans to be monthly for 30 years.

a). 10.9% b). 11.47% c). Greater than 11.47% d). Cannot be determined from the information given 64. What is the loan-to-value ratio for a sale that sold on the basis of an 11.5% overall rate, 1.15 debt coverage ratio, and

10.5% loan constant. a). 65% b). 75% c). 85% d). 95% 65. A property sold with a net income multiplier of 12 and an expense ratio of 40%, what was the effective gross income

multiplier? a). 4.80 b). 5.70 c). 6.60 d). 7.20 66. Given net income of $23,000, a debt coverage ratio of 1.25, and market terms of 10% interest for 15 years with monthly

payments, what is the loan if the expense ratio is 40%? a). $142,700 b). $250,450 c). $654,890 d). $1,712,300 Use the following to answer questions 67 - 72: The following is information concerning sales of 4 retail centers. Rents and values have increased 5% per year over the

past 3 years within the city, while expenses have remained unchanged. The subject is a non-anchored retail center of 42,500 sf with average collected rents of $8.00 psf per year, average occupancy of 95%, and the owner paying taxes of 90¢ psf, a CAM (common area maintenance) of $1.75 psf, and insurance of 40¢ psf. The owner is able to pass 40% of the above expenses to the tenant and individually manages the center. Assume pass-throughs are treated as income and are not "grossed up". ("Grossed up" means that the tenant pays expenses on the total income regardless of occupancy level. Assume the tenant pays a proportionate share of expenses as a ratio of occupied to total space.)

(1) Sale 1 is 40,000 sf and sold 1 year ago for $70 psf, with typical institutional terms except the seller paid $30,000 in points. The center was 90% occupied, with $9.00 rents. The terms of the lease were net except the owner paid taxes of $1.00 psf, and the center individually. Insurance is 30¢ psf and the CAM (common area maintenance) is $1.68 psf. Shortly after the sale, the new owner contracted with a leasing company to manage the center for 4% of collected rent and occupancy increased to 95%, and rents 2%. This center is located 15 miles from the subject.

(2) Sale 2 is a 100,000 sf anchored center that sold 1.5 years ago for $55 psf. Collected rents were $8.00 and lease terms were absolutely net. Rents increased 2% after the sale but were anticipated to increase 5%. Expenses on the center were 50¢ below typical (expenses were $3.00 psf) because of energy efficiency and state of the art construction. The anchor tenant pays $5.00 psf, absolute net (pays all expenses), and occupies 40,000 of the center. This center is adjacent to the subject.

(3) Sale 3 sold recently for $80 psf and is a strip center with 30,000 sf. Gross rents are $12 psf and the owner pays taxes of $1.25 psf, insurance of 40¢ psf, CAM of $1.44, and management of 4% of collections. This property is located 10 miles from the subject on a heavily traveled road leading to an affluent neighborhood. Occupancy averaged 92% after the sale.

(4) Sale 4 is a 35,000 sf strip center that sold 2.5 years ago for $65 psf, with gross rents at the time of sale of $7.25 psf. The tenants paid a CAM of $1.38 psf, taxes of 90¢ psf and the owner paid insurance of 30¢ psf and management of 5% of collections. The center had deferred maintenance of $30,000 at the time of sale. The purchaser renovated and was able to increase rents by 25¢ psf in the year following the sale, and occupancy increased to 95%. This property is located approximately 2 miles the subject.

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67. What is the subject's net operating income? a). $225,000 b). $250,000 c). $275,000 d). $300,000 68. What is an appropriate expense ratio for the subject? a). 37% b). 42% c). 48% d). 54% 69. What is an appropriate capitalization rate for the subject? a). 9.0% b). 9.5% c). 10.0% d). 10.5% 70. What would a lender loan per square foot for sale 1 if lender requirements were a loan-to-value ratio of 80%, a debt

coverage ratio of 1.25 on calculated net operating income, and a constant of 9.875%? Assume the loan is based upon the $70 sale price and calculated NOI.

a). $55.00 psf b). $60.00 psf c). $65.00 psf d). $67.50 psf 71. What is the appropriate EGIM (effective gross income multiplier) for the subject? a). 6.00 b). 6.50 c). 7.00 d). 7.50 72. What is the value of the subject? a). $2,225,000 b). $2,500,000 c). $2,750,000 d). $3,000,000 73. A reversion is... a). the total property resale price b). the property resale price less commissions c). a future value d). the present worth of the resale price less commissions 74. A net income multiplier is... a). the number of times net income covers debt service b). net income divided by gross income c). net income divided by effective gross income d). price divided by net income 75. What is the mortgage interest rate on a loan if financing was for 20 years, with monthly payments, the loan-to-

value ratio was 65%, the property sold on a 10.25% overall capitalization rate, and an 8% equity capitalization rate?

a). 9.85% b). 11.46% c). 12.13% d). 13.28%

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Use the following information to answer questions 76 - 79: A property is worth $100 psf in fee simple and has current long-term, level, gross market rents of $16.45 psf and

typical expenses of $5.00 psf. (1) The owner leased the property to T1 for 50¢ psf 20 years ago for 70 years. (2) T1 leased to T2 for $3.75 psf 15 years ago for 50 years. (3) T2 leased to T3 for $6.90 psf 8 years ago for 40 years. (4) T3 leased to T4 for $9.75 psf 5 years ago for 30 years. (5) T4 leased to T5 for $12.00 psf recently for 25 years. The above leases are all absolutely net and the market is rising. 76. What is the value of the leased fee estate? a). $0 to $5.00 psf b). $5.01 to $15 psf c). $15.01 to $22.50 psf d). $22.51 to $30.00 psf 77. What is the value of T2's position? a). $0 to $10 psf b). $10.01 to $20 psf c). $20.01 to $30.00 psf d). $30.01 to $40.00 psf 78. What is the value of T4's position? a). $0 to $10 psf b). $10.01 to $20 psf c). $20.01 to $30.00 psf d). $30.01 to $40.00 psf 79. What is the value of T5's position? a). $0 to $10 psf b). $10.01 to $20 psf c). $20.01 to $30.00 psf d). $30.01 to $40.00 psf

End of Mixed Problem Set One

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Solutions – Mixed Problems Set One

1. a). 6.36 Ro = (1 - .43) , and Ro = .75 x 1.15 x .096555 = .08328 EGIM .08328 = .57 Therefore, EGIM = 6.844 EGIM EGIM x (1 - vacancy & collection loss) = PGIM, [6.844 x (1 - .07) = 6.36] Note: An alternative method to answer the question would be to make up a hypothetical NOI and solve for the

debt service, loan, value and gross income. For example, suppose NOI = $10,000. Annual debt service would be $10,000 divided by 1.15 = $8695.65. The loan would be derived by: 30 g N, 9 g i, 8695.65 divided by 12 CHS PMT, solve for PV [Display: $90,059.32]. Value would be $90,059.32 divided by 75% (loan-to-value ratio, or 1 minus 25%) = $120,079. Effective gross income is $10,000 divided by .57 (1 minus expense ratio) = $17,543.86. Potential gross income is $17,543.86 divided by .93 (1 minus vacancy and collection loss) = $18,864.37. The potential gross income multiplier is therefore $120,079 divided by $18,864.37, or 6.36.

2. c). 16.7% N i PV PMT FV Step 1: 3 14 1 2.321632 Step 2: 12 2.321632 .25 4.182397 x 4 = 16.72% 3. b). 76,646 f CLR REG Year 1 - 23,000 23,000 g CFj Year 2 - 50,000 50,000 g CFj Year 3 - 42,000 42,000 g CFj Year 4 - ?????? 0 g CFj Year 5 - 20,000 20,000 g CFj Year 6 - 400,000 [Reversion] 400,000 g CFj 14 i f NPV [Display: 279,620] PV of 4th Year: 325,000 - 279,620 = 45,380 N I PV PMT FV 4 14 -45,380 $76,646

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Questions 4 - 8: T6 $19,000 (30 Yrs)

500(20%) Market $18,500

1000(18%) T5 $17,500 (35 Yrs)

2500(17%) T4 $15,000 (30 Yrs)

5000(15%) T3 $10,000 (35Yrs)

5000(12.25%) T2 $5,000 (40 Yrs)

4900(9.5%) T1 $100 (60Yrs)

100(8%)

Note: Bold designates the number solved for. Position N I PV PMT FV Fee income 60 13 $142,215 $18,500 Fee reversion 60 16 $5,427 $40,000,000 Total fee 60 14 $147,642 $18,500 $40,000,000 Leased fee inc. 60 8 $1,238 $100 Plus:PV rever. $5,427 Total leased

fee $6,665

Combined LH 60 13 $140,977 $18,400 Note: The combined leasehold is fee simple value minus leased fee value. T1 60 9.50 $51,356 $4,900 T2 40 12.25 $40,415 $5,000 T3 35 15.00 $33,083 $5,000 T4 30 17.00 $14,573 $2,500 T5 35 18.00 $5,539* $1,000 See note below $144,966

The fee income and reversion rates were given. Therefore, the value in fee was calculated and there was no judgment in rate selection. The leased fee income rate was based upon the income being safe and the reversion was given based upon the 16% yield rate to discount the reversion to present value. At any selected rate the leased fee value would be low compared to the fee simple value. Therefore, the rate selection for the leased fee income was not critical. However, the rate should be significantly lower than the 13% rate given for the fee simple (market rent) income. The combined leasehold rate was calculated based upon the fee simple - leased fee value = combined leasehold value, and the market rent - contract rent = combined leasehold income. The T1 rate is higher than the 8% leased fee income rate, but lower than the combined leasehold rate. The other tenants were discounted relative to their risk position so that the rates would average the 13% calculated combined leasehold rate (roughly). The T5 income paid is a negative value to T5, but a positive value to T4 because it is excess rent. The $5,539 value is a negative value to T5, but a positive value to T4. 4. c). 14% 5. c). $141,000

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6. b). $45,001 to $55,000 7. a). $30,000 to $35,000 8. a). $5,000 to $10,000 Questions 9 - 10 are based on the following: Loan: $2.00 psf x 75% = $1.50 [ Down payment = $.50 psf] Payments: $.1858 [20 g N, 11 g i, 1.50 PV, solve for PMT ,times 12 to get annual debt service] Taxes (Year 1) = $.026250 [ 1.50 ÷ 100 x 1.75 = .02625] Loan Balance: (Year 5) = $1.362209 [After calculating the payment, leave all calculations in the financial

registers, 5 g N, solve for FV] 9. d). $.02625 [$1.75 psf valuation ÷ 100 times $1.50 = $.02625 psf] 10. d). $4.40 psf Step 1: N I PV PMT FV 5 20 -.50 -.21114 2.8154 [Equity Reversion] Step 2: Expected Sales price: 2.8154 [Equity Reversion] +1.362209 [ Mortgage Balance] 4.177588 Divided by (1-5%) ÷ .95 [Expenses of Sale] 4.397461 The problem assumes that the 20% is an equity yield rate that applies to equity cash flows. Furthermore, the

mortgage balance is calculated from the information provided above. The -.50 is the initial equity investment. The -.21114 is the taxes of .02534 plus the debt service of .1858, calculated previously. The purchaser of land generally has a down payment as a negative cash flow plus negative cash flows of debt service and property taxes. The equity reversion is a part of the future sales price. The other elements of the sales price includes the mortgage balance and expenses of sale.

11. a). 10.4% [ (1 - .42) ÷ (5 ÷ ( 1 - 10%)] Note: This may also be derived with cash flows. 12. b). 1.30 [Ro = DCR x M x Rm; .104 = DCR x .75 x .105309] 13. d). Negative based upon cash flows. [Cannot determine yields, but can capitalization rates.]

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14. a). 62.5% Equity in: $1.00 - 70¢ loan = $.30 Equity out: [($1.00 x 1.25) x (1 - 5%)] - 70¢ = $.4875 Change in equity: .30 Enter .4875 ∆% [Display: 62.5] 15. b). $158,100 Loan = NOI ÷ DCR ÷ Rm 16. c). 18% .80 x .109769 = .087815 .20 x Re = .027185, Re = .027185/.2 = .135925 .115 N I PV PMT FV 5 17.8% -1 .135925 1.30 17. d). 19% 0 - -1 1 - .135925 IRR = 18.9% 2 - .142721 3 - .149857 4 - .157350 5 - .165218 + 1.30 = 1.465218 18. a). .26 [ 15,000 ÷ 1.15 ÷ 50,000] 19. d). 36,860 250,000 - 50,000 = 200,000 PV of Income N I PV PMT FV 10 13 200,000 -36,858 20. d). Cannot be determined. (The ratios of land-to-value and building-to-value are unknown). 21. b). 8% .3333 x RL = .026663, RL = .026663/.3333 = 8% .6667 x .11 = .073337 .10 22. d). 6.84 Solution: Constant (Rm): N i PV PMT FV 30g 9g -1 x 12 [ .0966] [Ro = 1.15 x .75 x .0966 = .0833] .0833 = (1 -40%), EGIM = 7.2 EGIM PGIM = 7.2 x (1 - .05) = 6.84

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Solution with cash flows: Make up an NOI, e.g. $1,000. Therefore, effective gross income is 1,000 ÷ (1-40%) = $1,666.67. Therefore, potential gross income is 1666.67 ÷ (1 - 5%) = $1,754.39. Debt service is 1000 ÷ 1.15 = $869.57; and 869.57 ÷ 12 = $72.46 [monthly payments] The loan is 30 g N, 9 g i, -72.46 PMT, calculate PV [Display:$9005.93] Value is $9005.93 ÷ (1 - 25%) = $12,008. The PGIM is $12,008 ÷ 1,754.39 = 6.84. 23. b). $60,000 [Note: This is the best answer.] Solution: 1.04 Enter, Enter, Enter [Note: This is "flooding the registers".] 5,000 g CFO X g CFj [Display: 5,200] X g CFj [Display: 9,344] X g CFj [Display: 5,408] X g CFj [Display: 9,904] X g CFj [Display: 5,624] X g CFj [Display: 10,498] X g CFj [Display: 5,849] X g CFj [Display: 11,128] X g CFj [Display: 6,083] X g CFj [Display: 11,796] X g CFj [Display: 6,327] X g CFj [Display: 12,504] X g CFj [Display: 6,580] X g CFj [Display: 13,254] X g CFj [Display: 6,843] 11 i X g CFj [Display: 7,117] f NPV [60,966] X g CFj [Display: 7,401] 1.06 Enter, Enter, Enter Flooding the registers allows for a 7.401 X g CFj [Display: 7,845] chain operation. If you have a X g CFj [Display: 8,316] program in storage you will not have X g CFj [Display: 8,815] enough memory to solve this problem. 24. d). $886,659 Solution: Value and enough information is given to determine the PV of income. The PV of the reversion is the

difference between the two because value is the sum of the present value of income and reversion. The reversion may be calculated by compounding the PV of reversion to future value. The gross sales price is determined by adding costs, and dividing by one minus sales commissions (and any other percentages).

PV of Income: 2,000 Enter, Enter, Enter + g CFj [Display: 50,000] 40,000 g CFj + g CFj [Display: 52,000] + g CFj [Display: 42,000] + g CFj [Display: 54,000] + g CFj [Display: 44,000] + g CFj [Display: 56,000] + g CFj [Display: 46,000] + g CFj [Display: 58,000] + g CFj [Display: 48,000] 13 i f NPV [255,209] PV of Reversion: [Value = PV of income + PV or reversion] 500,000 [Value] -255,209 [PV of Income] 244,791 [PV of Reversion] Reversion: N i PV Pmt FV 10 13 244,791 830,959 + 2,500 [Expenses of sale] 833,459

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÷ (1- .06) [Commissions] 886,659 [Gross sales price] Solution for 25 - 29: T4 $80,000 (5 Yrs) (17.3%)

8,000 (18%) Market $72,000 (16.4%)

2,000 (16.5%) T3 $70,000 (20 Yrs) (17.5%)

45,000 (14%) T2 $25,000 (45 Yrs) (10.9%)

24,900 (9.5%) T1 $100 (45Yrs) (8%)

100 (8%)

Note: Bold designates the number solved for. Position N I PV PMT FV Fee simple 45 12.3 $600,000 ($72,000) ($3,000,000) Leased fee inc. 45 8 $1,211 ($100) Reversion 45 14 $8,249 ($3,000,000) Total leased fee $9,460 Combined LH 45 12.2 $590,540 $71,900 Note: The combined leasehold is fee simple value minus leased fee

value.

T1 45 9.50 $253,552 $24,900 T2 45 14.00 $320,545 $45,000 T3 (below mkt.) 20 16.50 $11,550 $2,000 T3 (above mkt.) 5 18.00 $25,017 $8,000 T4 [T4's loses what T3 gains from excess rent] ($25,017) See below. Add all positions to check-------------------> $585,647

The fee simple yield rate is calculated based upon the fee simple value, the fee simple income (market rent) and reversion values being given. The leased fee income was discounted lower and the reversion higher (judgment) to value the leased fee position. The judgment was not important because the value is so low compared to the fee simple value that the combined leasehold value is almost equal to the fee simple value. The 12.2% rate to the combined leasehold was calculated based upon the value to the combined leasehold being $600,000 - 9,460, and the income to the combined leasehold being $72,000 - 100. The average yield to all tenant positions is 12.2% (the combined leasehold rate). Therefore, T1’s position was discounted higher than the leased fee income (8%), but lower than the 12.2% combined leasehold rate. The rates increased (judgment) as the risk in the positions increased. The value of T4’s position is negative because T4 pays excess (above market) rent. What T4 loses in value is picked up by T3 who receives the excess rent. The values therefore wash to zero. 25. a). 12.3% 26. c). $590,000 27. b). $240,001 to $280,000

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28. b). $30,001 to $45,000 29. a). $5,000 to $30,000 30. d). $1,950,000 or more Solution: Assessed value = taxes ÷ effective tax rate Assessed value = 25,000 ÷ (1.50 ÷ 100 x 100%) = $1,666,667 Value = $1,666,667 ÷ .85 = $1,960,784 31. c). $3,500,000 (Note: This is the best answer among alternative answers.) Solution: Equity Yield Rate: N i PV Pmt FV 5 20 -300,000 -162,136(1) 1,953,040(Equity Reversion) (1) Taxes (25,000) + debt service (11,428 x 12) = 162,136 Loan: N i PV Pmt FV Payments 30g 11g 1,200,000 -11,428 Balance 5g -1,165,976 Property Reversion: 1,953,040 (Equity) + 1,165,976 (Loan) = $3,119,016 [net sales price] 3,119,016 ÷ (1 -.05) = $3,283,175 [gross sales price] 32. c). Neighborhood 3 (if Ro = Yo, then no growth. Ro is closest to Yo) Stable may be thought of as little or no change. The relationship presented that likely has this

condition is from neighborhood 3 because the yield and overall rates are closest to being equal. 33. a). Neighborhood 1 (if Ro < Yo, then rising rents. Neighborhood 1 is best choice) When the spread between the overall capitalization rate and yield rate is significant, with the

overall rate being lower, the perception is rising income and/or values. 34. b). Neighborhood 4 The market is requiring a lower yield in neighborhood 4. Therefore, the market is indicating less risk

in this neighborhood. This is somewhat counter-logical when considering the higher capitalization rate in this neighborhood, compared to the others. However, the higher the capitalization rate, the more income is expected in early years, and therefore there is less risk as opposed to a property that has a significant amount of return in later years. Generally, however, the higher the capitalization rate the higher the risk.

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35. a). $227,900 Solution: N i PV PMT FV 27g 223,689 -2,000 Step 1: .83333 [x 12 = 10%] Step 2: 30g .83333 -2,000 Solve for PV [Display: 227,901], 36. c). 10% 37. a). $167,000 Solution: N i PV PMT FV 27g 14g -2,000 Solve for PV [Display: 167,430] 38. b). $201,000 Solution: N i PV PMT FV 3g .83333 223,689 -2,000 Step 1: Solve for balloon: [Display: -218,010] Step 2: 3g 14g -2,000 -218,010 Solve for PV [Display: 202,109] 39. b). 3.75% Solution: Debt Service = 45,000 ÷ 1.2 = $37,500 Rm = 37,500 ÷ 1,000,500 = .037481 40. c). $29,832 Solution: Value: $250,000 PV of Reversion: 150,000 100,000 (PV of Income) N i PV Pmt FV 5 15 -100,000 [29,832] 41. d). Vertical interest

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42. c). $635,000 Solution: Debt Service = BTCF ÷ (DCR -1) Debt Service = 10,000 ÷ .20 = $ 50,000 Loan = 50,000 ÷ .105 = $476,190 Vo = $476,190 ÷ .75(M) = $634,920 43. c). 6.5% Solution: .2222 x RL = .0144, RL = .065 .7778 x .11 = .0856

Sales Analysis Chart Net Net Sale Date Price SP/SF SP/Child Rent/PSF Rent/Child Ro GIM OER 1 6/90 $392,700 $38.13 $1964 $.3813 $19.64 .1200 6.42 23% 2 4/90 $170,000 $34.00 $1889 $.3364 $18.69 .1190 5.47 35% 3 8/89 $230,000 $45.10 $1917 $.4135 $17.58 .1100 6.73 26% 4 3/89 $175,000 $38.39 $1944 $.3599 $18.23 .1125 7.20 19% 5 7/88 $220,000 $57.26 $2000 $.4727 $16.51 .0990 7.17 29% 6 6/88 $260,000 $53.50 $2080 $.4428 $17.22 .0990 8.56 15% Subject Rent: $20/Child x 125 = $2,500 (net) This is the net rent per child. The best unit of comparison is price and rent per child capacity. The rental rate of $20 is a projection based upon increasing rents as evidenced by sales on through three. The rental rate per child capacity is typically the best unit of comparison for daycare facilities because income is generated per child and not per square foot. Gross Rent: $2,500 net rent divided by 1 minus the expense ratio (25%) = $3,333 per month $3,333 x 12 = $40,000 per year. Net Income: $40,000 minus $10,000 expenses (25% expense ratio) = $30,000 Value: $30,000 divided by .12 = $250,000. A 12% capitalization rate was chosen because the latest sales indicate rates of 12%. Furthermore, this is consistent with rising interest rates (mortgage rates) that are expressed in the sales. As you can see, averaging rates would not be appropriate. GIM: $250,000 divided by $40,000 = 6.25 44. a). $3,250 per month. This is the best answer among alternatives. 45. c). 12% 46. c). 6.25 47. a). Rents increased, as evidenced by rent per child. 48. c). $250,000 49. c). Values were stable [Increased rents were off-set by higher capitalization rates] 50. c). Industrial Yo = .135 + .0250 = .1600 Formula Needed: Yo = Ro + CR Note: The CR used for office, apartment, and retail is the average growth of income and value.

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51. b). Retail M = .125/(1.20 x .105) M = 99.2% Formula Needed: Ro = DCR x M x Rm; Ro DCR x Rm 52. a). Office RE = (.115 - .1025 x .898) ÷ (1 - .898) = 22.5% Formula Needed: Band of Investment [Ro = RM x M + RE x (1 - M)] RE= (Ro - Rm x M) ÷ (1 - M) 53. b). All of the properties d). Cannot be determined from the information given Although the lowest overall yield was determined in Question 1 to be 13.75%, no equity yield or mortgage yield (interest

rate) is given. It appears that the yield to the mortgage is the lowest yield because all of the constants (Rm) are below the overall yields. However, the constants could be for negatively amortizing loans. Correct answer is b) or d).

54. c). 11.00% Reconstruct Statement of Sale: 65¢ x 12 = $7.80 Vacancy (8%) = (62.4) EGI 7.176 Expenses (3.25) NOI $3.926 Ro = 3.926 ÷ 36.50 = .1076 55. d). Cannot be determined from the information given Neither inflation nor physical depreciation provide evidence of a particular market direction. The capitalization rate and

mortgage interest rate levels, alone, also will not help. 56. a). 8.40% Taxes = [350,000 ÷ 100] x 1.75 = $6,125 NOI = 35,500 - 6,125 = $29,375 Ro = 29,375 ÷ 350,000 = .08393 57. b). $500,000 N i PV PMT FV 300 11g $510,145 -5,000 Note: 1 + Real = (1 + Nominal)/(1 + Inflation) 1.06 = (1 + Nominal)/(1 + 5%) Nominal = 11.3%, which is approximately 11%. 58. b). $450,000 Vm = $400,000 NOI = $52,500 NOIm = 48,792 [400,000 x .12198] NOIE= 3,708 VE = 3,708 ÷ .095 39,032 Vo = $439,032 Rm: N i PV PMT FV 25g 11.5g -1 12 x [.12198] 59. b). $1,400,000 EGI = 125,000 ÷ (1 - 40%) = $208,333 PGI = 208,333 ÷ (1 - 7%) = $224,014 Vo = $224,014 x 6.25 = $1,400,090

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60. b). the number of times net income covers debt service d) is incorrect because the DCR = Ro ÷ (M x Rm) 61. a). 3% PGI = 100,000 ÷ 6 = $16,667 EGI = 10,000 ÷ (1-38%) = 16,129 Vacancy = 538 538 ÷ 16,667 = 3.2% 62. c).$375, 000 VB $300,000 NOI = 40,000 NOIB= 31,500 [300,000 x .105] NOIL= 8,500 VL= 8,500 ÷ .11 = 77,273 Vo = $377,273 63. d). Cannot be determined from the information given An equity yield rate cannot be used in a band-of-investment. 64. d). 95% Ro = M x DCR x Rm .115 = M x 1.15 x .105, M = 95.2% 65. d). 7.20 Ro = 1 ÷ 12 = .08333 Ro = (1 - OER) (1 - 40%) EGIM .0833 = EGIM EGIM = 7.20 66. a). $142,700 D.S. = $23,000 ÷ 1.25 = $18,400 ÷ 12 = $1,533.33 N i PV PMT FV 15g 10g $142,700 $1,533.33 Use the following to answer questions 67 - 72: Sale------------------> 1 2 3 4 Potential Gross Income $9.18(1) $??? $12.60(3) $7.50(4) Vacancy .46 ??? 1.01 .38 EGI-Before Passthrough 8.72 7.14(2) 11.59 7.13 Passthroughs 1.88 ??? 0.00 2.17 EGI 10.60 7.14 11.59 9.30 EXPENSES: Taxes 1.00 ??? 1.25 .90 CAM 1.68 ??? 1.44 1.38 Insurance .30 ??? .40 .30 Management .35 ??? .46 .36 TOTAL EXPENSES 3.33 ??? 3.55 2.94 NOI 7.27 7.14 8.04 6.36 Ro 10.5% 13.0% 10.1% 9.8% (1) 2% increase (2) The average of anchor and non-anchor leases (3) 5% increase (4) 25¢ increase

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67. b). $250,000 $8.00 x 1.05 = $8.40 Vacancy (.42) EGI before pass-throughs 7.98 Pass-throughs 1.22 EGI 9.20 Expenses (CAM, Insur,Tax) 3.05 Management .32 NOI $5.83 psf 68. a). 37% 3.37 ÷ 9.20 = 36.6% 69. c). 10.0% The most recent sale is Sale 3 that indicates a 10.1%, this is in line with Sale 4 (9.8%). 70. a). $55.00 psf (1) $70 x 80% = $56 psf (based upon LTV ratio) NOI DCR D.S. Rm Loan (2) 7.27 ÷ 1.25 = 5.82 ÷ .09875 = $59 psf (Based upon DCR) 71. b). 6.50 Vo = 5.83 ÷ .10 = $58.30 EGIM = 58.30 ÷ 9.20 = 6.34 72. b). $2,500,000 $58.30 psf x 42,500 = $2,477,750 73. c). a future value 74. d). price divided by net income 75. a). 9.85% Rm: .65 x Rm = .0745 .35 x .08 = .028 .1025 Rm = .11462 (.0745 / .65) Ym: N i PV PMT FV 20g -1 .11462 ÷ 12 = .0095517 12 x [9.85]

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Solution for 76 through 79: T5 $12.00(25Yrs)

.55 (18%) Market $11.45 (16.45 - $5.00)

1.70 (16%)

T4 $9.75 (25 Yrs)

Ro=11.45% 2.85 (13%)

T3 $6.90 (32 Yrs)

3.15 (11.5%)

T2 $3.75 (35 Yrs)

3.25 (9%)

T1 $.50 (50Yrs)

.50 (8%)

Note: Bold designates the number solved for.

Position N I PV PMT FV Fee simple 50 12 $100.00 $11.45 $1,420.00 LF income 50 8 $6.12 $0.50 LF reversion 50 14 $2.03 $1,420.00 Total leased fee $8.15 Combined LH 50 11.9 $91.85 $10.95 Note: The combined leasehold is fee simple value minus leased fee value. T1 50 9.00 $35.63 $3.25 T2 50 11.50 $27.27 $3.15 T3 35 13.00 $21.87 $2.85 T4 (below mkt.) 32 16.00 $10.62 $1.70 T4 (above mkt.) 25 18.00 $3.05 $0.55 T5 [T5's loses what T3 gains from excess rent] ($3.05) Add all positions to check-------------------> $95.39 compared to 91.85 76. b). $5.00 to $15 psf 77. c). $20.01 to $30.00 psf 78. b). $10.01 to $20 psf 79. a). $0 to $10 psf The fee simple capitalization rate of $11.45 divided by $100 is 11.45%. The yield to the fee simple would have to be approximately the same because the income is level for 50 years. The formula R = Y - ∆ x SFF would indicate that the R and Y would almost be equal regardless of the ∆ because a SFF at any rate near 11.45% would be small. The reversion of $1,420 was calculated based upon a fee simple value of $100 and market rent of $16.45 - 5.00 = $11.45 (all given). The leased fee income of $.50 was discounted at a low, safe rate of 8% and the reversion of $1,420 was discounted at a higher rate of 14%. The 14% is higher than the overall yield to fee simple of 12% because the reversion has more risk than the rental payments to the fee simple interest (horizontal risk). The leased fee is the present value of the income plus reversion to the leased fee. The combined leasehold estate is the difference between the fee simple and leased fee or $91.85. The yield to the combined leasehold estate is calculated with leasehold income of $10.85 ($11.45 - .50) and the value of $91.45 for 50 years. The various tenants were discounted based upon the average rate being the combined leasehold rate of almost 12% (11.8%). The T1 position was discounted below this rate, but above the safer leased fee income rate of 8% and then the various other tenants discounted higher than 9% based upon their risk position. The excess rent was discounted at 18% (a high rate) and is a negative value to T5 who pays above market, but is a positive value to T4 who receives the excess rent. The values offset to zero (T5 loses what T4 gains).

End of Mixed Problem Set One

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