REAL ESTATE INVESTMENTS

Transcription

1 RAL STAT ISTMTS PROBLM ST 6. o deb ad o Taxes OI SP ( y) ( y) 2. Deb ad o Taxes BTCF BTR ( L / )( ) ( y) ( y) 3. o Deb ad Taxes ATCF ATR ( k) ( k) 4. Deb ad Taxes ATCF ( L / )( ) ATR ( k) ( k) alue of ivesme. OI e operaig icome i period. SP e sale price a ed of period. L/ Loa-o-value raio. BTCF Before-ax cash flow i period. BTR Before-ax equiy revisio a ed of period. ATCF Afer-ax cash flow i period. ATR Afer-ax equiy revisio a ed of period. y Before-ax required rae of reur. k Afer-ax required rae of reur. Holdig period.

2 PROBLM :. Basic quaios: M OI DS BTCF SP ( g) ( S) ) xample A: o deb Suppose a ivesme has he followig assumpios:. OI $ 48, g 0% S 0% 3. years 4. y % The projec will be fiaced wih 0% equiy. BTCF ( y) 48,000 (.) (.) 8, (.6209( ) 8,98 8,98/.3708 $480,000 T ( y) ) ) BTR Proof: Year OI SP 0-480,000 48, , , ,000 48, ,000 y IRR % I his example wih cash flow cosa ad sale price equal o he curre value, he: OI R BTCF y 48,000. $480,000 2

3 xample B: Wih deb Suppose he ivesor borrows $300,000 a a ieres rae of 9% wih ieres-oly paymes for years wih a balloo payme a ed of year. Give he use of deb he ivesor s required yield o equiy icreases o.67%. 48,000 27, , ,000 (.67) (.67) 300,000 76, ( ) 72,78 203,6/ $479,90 (rouded, $480,000) Proof: Year T OI SP 0 $80,000 2, , , ,000 2,000 $80,000 Wih he BTCF cosa ad he BTR equal o he iiial ouflow he: DR 2,000 80,000.67% Aleraive 2, $80,000 xample C: Wih amorized deb M $300,000 i 9.00% Mauriy 20 years, mohly paymes Morgage Cosa (mohly) or.7967 (aual) DS 300,000 (.7967) $32,390 Upaid Balace afer years $266,22 48,000 32, ,22 300,000 (.67) (.67) 300,000 6, ( ) 3, ( ) 203,48 203,48/ $479,760 3

4 xample D: Wih loa-o-value raio M M L / ( ) where: BTCF ( ) BTR ( y) y M BTCF BTR y L/ alue of Morgage alue of quiy Holdig Period Before-ax cash flow i year Before-ax equiy reversio i year Required before-ax yield Loa-o-value raio oe ha he deb service ad upaid morgage balace mus be expressed i relaioship o he origial deb. OI L/()(mor. cos.) (prop. ou)(l/)() L / ( ) ( y) ( y) Suppose L/ 62.%, oher facs as i xample 3 48,000.62( )(.7967).88707(.62)( ). 62( ) (.67) (.67) $480,000 4

5 PROBLM 2: 2. A aparme ivesme has he followig assumpios: OI Reversio $,000 per year (cosa) years Sellig price equal o oday s value (o chage i propery values) Wha is he value of his ivesme? o deb If he projec is fiaced wih 0% equiy a a required rae of reur of 9.7%, he value of he ivesme is:,000 (.097) 6.2,000 $2,6 (97) [ ].3944[ ] Wih deb If he projec is fiaced as follows: 7% loa-o-value 9% ieres rae (ieres oly) Balloo payme is years 2% equiy yield The value of he ivesme is: M L ().7().09 6,02 $2,6 BTCF ( y) BTR ( y),000.09(.7)().7() (.2) (.2).7()..602(,000).602(.09)(.7)().322[.7]

6 PROBLM 3: 3. A appraiser is aalyzig a real esae projec wih he followig assumpios: OI $4,000 per year L/ Raio 7% Morgage Ieres Rae 2% Mauriy 20 years wih mohly paymes BTCF OI DS BTR SP UM Holdig Period years xpeced Appreciaio i Propery alue 4% per year Sellig xpeses 6% Ivesor s required rae of reur o equiy (before-ax) % Wha is he value of his projec? SUGGSTD SOLUTIO: BTCF alue (L/) ( y) L/() PAF DS (Morgage Cosa)(Am. Borrowed) DS MC(L/)() SP ( g) UM (Prop. Ou)(Am.Borrowed) (Prop. Ou)(L/)().7() PAF ()( S).36() 0,849 y, (OI %, yrs. $424,4(say, $424,000) BTR ( y) - DS) PF (SP - UM) [ 4,000.7(.322)()] PF [(.04) (.94)() - (.9744)(.7)()].7() 3.322(4,000) (.7)(.322)().4972(.2663)(.94)() (.9744)(.7)() -.7().3327() ().342() 0,849 y, %, yrs. Proof: $424,000 alue x.7 Loa-o-alue $38,000 Deb $6,000 quiy $3,0.4 Mohly Morgage Payme x 2 $42,07.00 Aual Deb Service 6

7 Year OI DS BTCF BTR $4,000 $42,07 $2, ,000 42,07 2, ,000 42,07 2, ,000 42,07 2,983 4,000 42,07 2,983 $93,6 Sellig Price $,860 Mius Sellig xpeses - 30,92 quals e Sellig Price 484,908 Mius Upaid Morgage -29,747 BTR $93,6 P of BTCF Prese alue of $2,983 per year for years a % $,000 P % BTR Prese alue of $93,6 i year a % 96,000 Toal P % quiy $6,000 P of quiy a % 6,000 6,000 $0 COMMT: The value of his propery is derived from he cash flows ha is produces. These cash flows come from wo sources; ) operaig cash flows, ad 2) equiy reversio. Before ax operaig cash flows are esseial o he OI mius deb service. If OI ad deb service are boh cosa, he hey may be reaed as a auiy. Before ax equiy reversio mus ake io accou sellig expeses, growh raes, ad he upaid morgage balace. I is impora o oe ha zero axes are cosidered i his problem. Oe migh hik ha zero axes are o realisic, however, here are several isaces, such as o-profi orgaizaios or pesio fuds, whe his is i fac he case. 7

8 PROBLM 4: 4. A real esae ivesor is cosiderig he purchase of a aparme propery. The followig assumpios are made: OI quiy Ivesme Required Afer-Tax Rae of Reur o quiy Holdig Period $47,600 per year 0% (o morgage) 2% years e sellig price a ed of holdig period is expeced o be 20% higher ha oday sellig price. Margial Tax Rae Capial Gais Tax Rae Depreciaio Recapure Tax Rae Buildig-o-alue Raio Depreciable Life Depreciable Mehod 28% 20% 2% 80% 27. years Sraigh-lie Wha is he maximum price ha he ivesor could pay for his ivesme? SUGGSTD SOLUTIO: alue alue ATCF ATR ( k ) ( k ) OI- TO ( k ) SP- TDS ( k ) MTR Ivesors margial ax rae i year CGTR Capial gais ax rae DRTR Depreciaio recapure ax rae L Useful life (depreciaio) B/ Buildig-o-value raio k Ivesors afer ax required rae of reur DP Depreciaio deducio i year B/ ()(/L) Taxes from Operaio: TO MTR [TI ] TO MTR [OI -DP ] TO MTR [OI - (B/)()(/L)] Taxes from Sale: TDS CGTR (SP -) DRTR[(B/)()(/L)()] 8

9 If OI is a Auiy, he: PAF k, [OI-TD]PF k, [SP-TDS] PAF k, [OI-(MTR(OI-DP))]PF k, [SP-CGTR (SP-)-DRTR((B/)()(/L)())] PAF k, [OI-MTR(OI)MTR(DP)]PF k, [SP-CGTR(SP)CGTR()-DRTR(B/)() (/L)()] [47, (47,600).28(.8)(/27.)()].67427[.2()-.20(.2)().20()-.2(.8)()(/27.)()] 7,87-48, ().6809()-.368().348() () 23, () () 23, () 23,43 $37,000 (rouded) Proof: Afer-ax equiy reversio: Dep. Ded. $37,000 [(37,000).8]/27. $,793 SP Mius CGT Mius DRT ATR $44,200 (37,000)(.2) - 4,840-3,49 $46,869 Afer-ax cash flow per year: Taxes due o sale: OI Mius Taxes ATCF $47,600 -,306 $37,294 SP Mius Basis Taxable Gai Times Tax Rae CGT $44,200-37,000 $ 74,200 x.20 $ 4,840 Taxes per year: OI Mius Dep Ded TI Times Tax Rae Taxes $47,600 -,793 $36,807 x.28 $,306 Depreciaio Recapure Times Tax Rae Recapure Tax Prese alue of ATCFs: (37,294)( ) Prese alue of ATR: (46,869)(.674) Toal Prese alue $ 3,96 x.2 $ 3,49 $34, ,3 $37,000 9

10 PROBLM : A ivesor is cosiderig he purchase of a small aparme real propery. The propery has wo real uis. The followig iformaio has bee obaied: OI y Reversio Margial Tax Rae Buildig o Toal alue Raio Depreciable Life Capial Gai Tax Rae Dep. Recapure Tax Rae $,000 per year (cosa) years 9.7% (before-ax rae) Sellig price equal o oday s value (o chage i propery values) ( 0 ) 28% 8% 27. years 20% 2% Wha is he value ( 0 ) of he propery? If here were o axes, he value of he propery would be:,000 (.097 ) (.097 ) 0 0 $2,6 B. Wih axes, he value of he propery is:, , (.097 ) ( ) - CGTR [ - 0 ] DRTR (.097 ) 0 0 B 0 ( 0) (,000) (2,800) 6.2 (.0086) ( 0 ).3944 [ - (.2 ( - 0 )) -.2 () (.8) () ( )] 0 $76,793 Proof: $76,793 Dep. Ded. 76,793 (.8) (/27.) $2,374 ATCF, (, ) $7,86 ATR 76,793 - (.2) (23740) ATR $70, ,88 ( y ) ( y ) y 9.7%

11 C. If he required afer-ax discou rae is 7.33%, he value of he propery is:, , (.0733 ) ( ) 27. [ - ] () (.8) (0 ) ( ) (.0733) (,000) (2,800) (.0086) ( 0 ).4966 [ ] 0 $2,6 Rob Grovesei pse_6_as