Discounted Cash Flow:
Ratio Analysis
by
James R. DeLisle, Ph.D.
March 20, 2014
© JR DeLisle, Ph.D.
Lecture Preview
DCF Prelude
• The Value Proposition
• Frontdoor/Backdoor Models
Introduction to Discounted Cash Flow
• DCF: A Visual Overview
• One Word: GiNiTiBtAtNR
• Basic Inputs
DCF Schedules
• Schedule 1: Pro Forma Cash Flow
• Schedules II-III: Depreciation and Loan Amortization
• Schedules IV-V: Capital Gain Taxes and Net Reversion
• Schedules VI: Financial Ratios
© JR DeLisle, Ph.D.
DCF MODELS:
A VISUAL PERSPECTIVE
PV CF
+
Equity Justified: PV of CF + PV Net Reversion
NIr
© JR DeLisle, Ph.D.
GIr
Net Reversion
Sales Price
TRCm
Net Sales Price
- Sales Exp
Appreciation
CG Appr
x 15%
Land Value
Depreciation
Mortgage
CG Depr
x 25%
Amortization
Net Reversion
Pb
Stabilized
NOI
NIr
© JR DeLisle, Ph.D.
GIr
= Ej
Equity Justified: PV of CF + PV Net Reversion
Sales Price
- Sales Exp
- Tax on Sale
- Mtg. Bal.
PV CF
+
PV NR
Net Reversion
NIr
© JR DeLisle, Ph.D.
GIr
Cash Flow: The One Key Word
GI NI TI BT AT NR
Gross Income
Net Income
Taxable Income
Before Tax Cash Flow
After Tax Cash Flow
Net Reversion
© JR DeLisle, Ph.D.
DCF CASE STUDY:
INPUTS AND SCHEDULES
Cash Flow Variables and TRC/FD/BD Inputs
Total Replacement Costs
Income & Expenses
Debt Assumptions
Income Taxes
Terminal Value
Equity Assumptions
Land Value
Building Value
Total Replacement Cost
LandV
BldgV
TRC
Gross Income
Vacancy Loss
Expenses
Property Taxes
GI, GIC
VacR
ExpR, ExpC
PTXr, PTxC
Loan-to-Value
Mortgage Interest Rate
Periodicity (Payments/Year
Loan term (years)
$ 435,600
$ 3,436,567
$ 3,872,167
$468,557
10.00%
10.00%
8.00%
LV
Mr
Ppy
Term
DeprLife
Depreciable Life (R=27.5; C=39)
Capital Gain Tax Rate on Appreciation CGTxR
CGTxV
Capital Gain Tax Rate on Value
80.00%
7.50%
12
30
39
15.00%
25.00%
Selling Expense
Exit Cap Rate
SellExp
Ce
2.00%
10.00%
Marginal Tax Rate
Equity discount rate
Reinvestment rate
MTxR
Ec
RIr
36.00%
10.00%
6.00%
Value Assumptions
© JR DeLisle, Ph. D.
4.00%
4.00%
3.00%
Terminal Value Method (1=App, 2=Cap)
2
Real Estate Fundamentals
Appreciation Rate
2%
Exit Cap Rate
10.00%
Discounted Cash Flow and Financial Ratios
• Schedule I: Cash Flow
• Schedule II: Depreciation
• Schedule III: Loan Amortization
• Schedule IV: Net Reversion
• Schedule V: Capital Gain Tax
• Schedule VI: Financial Ratios
© JR DeLisle, Ph.D.
Schedule I: Cash Flow Overview
Cash Flow Component
Gross Income
Less: Vacancy
Effective Gross Income
Less: Expenses
Less: Property Taxes
Net Operating Income
Less: Depreciation
Less: Interest
Taxable Income
Plus: Depreciation
Less: Principal Reduction
Before Tax Cash Flow
Less: Income Tax Due
Plus: Tax Savings
After Tax Cash Flow
Plus: Net Equity Reversion
After Tax CF + Net Reversion
© JR DeLisle, Ph.D.
Code
GI
Vac
EGI
Exp
Ptx
NI
Depr
Int
TI
Depr
Prin
BTCF
Itax
TSOI
ATCF
NR
ATCF+NR
Year 1
468,557
(46,856)
421,701
(46,856)
(37,485)
337,361
(88,117)
(231,362)
17,882
88,117
(28,556)
77,443
(6,438)
0
71,006
372,880
443,885
Year 2
487,299
(48,730)
438,569
(48,730)
(38,609)
351,230
(88,117)
(229,145)
33,968
88,117
(30,773)
91,313
(12,229)
0
79,084
545,118
624,202
Year 3
506,791
(50,679)
456,112
(50,679)
(39,767)
365,666
(88,117)
(226,756)
50,793
88,117
(33,162)
105,748
(18,285)
0
87,463
687,712
775,174
Year 4
527,063
(52,706)
474,357
(52,706)
(40,960)
380,690
(88,117)
(224,181)
68,391
88,117
(35,736)
120,772
(24,621)
0
96,151
824,014
920,166
Year 5
548,145
(54,815)
493,331
(54,815)
(42,189)
396,327
(88,117)
(221,407)
86,803
88,117
(38,511)
136,409
(31,249)
0
105,160
968,091
1,073,252
Schedule II: Depreciation
Schedule II: Depreciation
Component
Total Replacement Cost
Less: Land
Beginning of Year Tax Basis
Less: Depreciation
Plus: Capital Improvements
End of Year Tax Basis
Plus Land
Adjusted Basis
Accumulated Depreciation
$3,436,567*(1/39) = $88,117
Year 2
Year 1
3,872,167
(435,600)
3,436,567
(88,117)
3,348,450
(88,117)
3,348,450
435,600
3,784,050
88,117
3,260,333
435,600
3,695,933
176,234
Schedule II: Depreciation
Total Replacement Cost
Less: Land
Beginning of Year Tax Basis
Less: Depreciation
Plus: Capital Improvements
End of Year Tax Basis
Plus Land
Adjusted Basis
Accumulated Depreciation
© JR DeLisle, Ph.D.
Year 1
3,872,167
(435,600)
3,436,567
(88,117)
Year 2
Year 3
Year 4
Year 5
3,348,450
(88,117)
3,260,333
(88,117)
3,172,216
(88,117)
3,084,099
(88,117)
3,348,450
435,600
3,784,050
88,117
3,260,333
435,600
3,695,933
176,234
3,172,216
435,600
3,607,816
264,351
3,084,099
435,600
3,519,699
352,468
2,995,981
435,600
3,431,581
440,586
Schedule III: Loan Amortization
Calculate Payment
Factor
Compounding/Period
Term
Present Value
Payment
Future Value
Interest Rate
Amortization
Beginning of Year Balance
Mortgage Payment
Interest
Principal Reduction
End of year balance
Code
m
t
PV
PMT
FV
I
Initial
12
30
3,097,734
Payment
$21,660
$0
7.50%
#/yr
12
Annual
$259,918
Year 1
3,097,734
259,918
(231,362)
28,556
3,069,178
Code
m
t
PV
PMT
FV
I
3,097,734 Pb1
(3,069,178) - Pb2
28,556 Pr
259,918 Pmt
(28,556) -Pr
231,362 Int
© JR DeLisle, Ph.D.
Calc. Principal Balance
Calc. Interest
Initial
12
29
Prin Bal.
3,069,178
21,660
$0
7.50%
Calc. Prin.
Reduction
Schedule III(b): Loan Amortization
Amortization
Beginning of Year Balance
Mortgage Payment
Interest
Principal Reduction
End of year balance
Year 1
3,097,734
259,918
(231,362)
28,556
3,069,178
Year 2
3,069,178
259,918
(229,145)
30,773
3,038,405
Schedule III: Loan Amortization
Beginning of Year Balance
Mortgage Payment
Interest
Principal Reduction
End of year balance
© JR DeLisle, Ph.D.
Year 1
3,097,734
259,918
(231,362)
28,556
3,069,178
Year 2
3,069,178
259,918
(229,145)
30,773
3,038,405
Year 3
3,038,405
259,918
(226,756)
33,162
3,005,243
Year 4
3,005,243
259,918
(224,181)
35,736
2,969,507
Year 5
2,969,507
259,918
(221,407)
38,511
2,930,996
Schedule IV-V: CGTaxes on Sale & AT Proceeds
Schedule IV: AT Proceeds
Schedule IV: After Tax After Sale Proceeds
Cash Flow Component
Year 1
Gross Sales Price
3,512,303
Less: Sales costs
(70,246)
Net Sales Price
3,442,057
Less: Capital Gain Tax
0
After Tax Sale Proceeds
3,442,057
Less: Mortgage Balance
(3,069,178)
After Tax Net Equity Reversion
372,880
Year 2
3,656,656
(73,133)
3,583,523
0
3,583,523
(3,038,405)
545,118
Schedule V: Capital Gain Tax On Sale
If, CapGain * 15%
Schedule V: Capital Gain on Sale
Year 1
Capital Gain Tax on Value
Gross Sales Price
Less: Sales costs
Net Sales Price
Less: Original Cost Basis
Capital Gain on Appreciation
CGTax on Appreciation
Capital Gain on Accumulated Depreciation
CGTax on Accumulated Depreciation
Total Capital Gain (Tax) or Saving
Capital Gain Tax
©
JR DeLisle,
Capital
Gain Ph.D.
Saving to other Cap Gains *
3,512,303
(70,246)
3,442,057
3,872,167
(430,110)
86,022
88,117
(22,029)
63,993
0
63,993
Schedule III: Loan Amortization
Year 1
Year 2
Beginning of Year Balance
3,097,734 3,069,178
Mortgage Payment
259,918
259,918
Interest
(231,362) (229,145)
Principal Reduction
28,556
30,773
End of year balance
3,069,178 3,038,405
Year 2
3,656,656
(73,133)
3,583,523
3,872,167
(288,644)
57,729
176,234
(44,059)
13,670
0
13,670
AccDepr * 25%
* If value is positive (Saving) this can be used against outside gains from other assets in current year. If savings exceed outside gains, they will be carried over future
Schedule I: Cash Flow 1- 10
Cash Flow Component
Gross Income
Less: Vacancy
Effective Gross Income
Less: Expenses
Less: Property Taxes
Net Operating Income
Less: Depreciation
Less: Interest
Taxable Income
Plus: Depreciation
Less: Principal Reduction
Before Tax Cash Flow
Less: Income Tax Due
Plus: Tax Savings
After Tax Cash Flow
Plus: Net Reversion
After Tax CF + Net Reversion
© JR DeLisle, Ph.D.
Year 1
468,557
(46,856)
421,701
(46,856)
(37,485)
337,361
(88,117)
(231,362)
17,882
88,117
(28,556)
77,443
(6,438)
0
71,006
436,872
507,878
Year 2
487,299
(48,730)
438,569
(48,730)
(38,609)
351,230
(88,117)
(229,145)
33,968
88,117
(30,773)
91,313
(12,229)
0
79,084
558,789
637,873
Year 3
506,791
(50,679)
456,112
(50,679)
(39,767)
365,666
(88,117)
(226,756)
50,793
88,117
(33,162)
105,748
(18,285)
0
87,463
687,712
775,174
Year 4
527,063
(52,706)
474,357
(52,706)
(40,960)
380,690
(88,117)
(224,181)
68,391
88,117
(35,736)
120,772
(24,621)
0
96,151
824,014
920,166
Year 5
548,145
(54,815)
493,331
(54,815)
(42,189)
396,327
(88,117)
(221,407)
86,803
88,117
(38,511)
136,409
(31,249)
0
105,160
968,091
1,073,252
Year 10
666,903
(66,690)
600,212
(66,690)
(48,909)
484,613
(88,117)
(203,950)
192,546
88,117
(55,967)
224,696
(69,316)
0
155,379
1,820,641
1,976,020
Teams
© JR DeLisle, Ph.D.
INTRODUCTION TO DCF RATIOS:
KEY FINANCIAL INDICATORS
Schedule VI: Financial Ratios
Schedule VI: Ratio Analysis
Debt Coverage Ratio
Default Ratio
Profitability Index
Before Tax Cash on Cash
After Tax Cash on Cash
Implicit Cap Rate
Gross Income Multiplier
Net Income Multiplier (P/E)
Payback Ratio (w/o sale)
Modified Payback (w/o sale)
NPV Equity (sold/year)
IRR if Sold/Year
Modified IRR if Sold/Year
Marginal Rate of Return
© JR DeLisle, Ph.D.
Code
DCR
DR
PI
BTCF
ATCF
ICr
GIM
NIM
PB
MPB
NPV
IRR
MIRR
MRR
Year 1
1.30
0.73
0.52
10.00%
9.17%
10.00%
7.50
10.41
9.17%
9.17%
($370,901)
-42.68%
-42.68%
Year 2
1.35
0.71
0.75
11.79%
10.21%
10.00%
7.50
10.41
19.38%
19.93%
($194,013)
-5.52%
-4.96%
40.62%
Year 3
1.41
0.69
0.92
13.65%
11.29%
10.00%
7.51
10.41
30.67%
32.42%
($62,124)
6.69%
6.63%
24.19%
Year 4
Year 5
1.46
1.52
0.67
0.65
1.06
1.20
15.59%
17.61%
12.42%
13.58%
10.00%
10.00%
7.52
7.53
10.41
10.41
43.09%
56.67%
46.78%
63.17%
$49,674 $153,266
11.96%
14.76%
11.25%
13.48%
18.70%
16.64%
Schedule VI: Financial Ratios
Debt Coverage Ratio
Default Ratio
Profitability Index
Before Tax Cash on Cash
After Tax Cash on Cash
Implicit Cap Rate
Gross Income Multiplier
Net Income Multiplier (P/E)
Payback Ratio (w/o sale)
Modified Payback (w/o sale)
NPV Equity
IRR if Sold/Year
Modified IRR if Sold/Year
Marginal Rate of Return
© JR DeLisle, Ph.D.
NIn
E1
ATCFn
BTCFn
NRn
MVn
GIn
NIn
IRR
MIRR
PV
RR
FV
NIn / MtgPayment
Sum (Exp +Property Tax + Mtg Payments)n / GIn
[(PV ((ATCF)1-n + PV (NRn))] / E1
BTCFn / E1
ATCFn / E1
NIn+1 / MVn
MVn / GIn
MVn / NIn
Sum(ATCF/E1)1 ->n
Sum ATCF1-> n + Reinvested/E1
[PV (ATCF 1->n) + PV (NRn)] - E1
[PV (ATCF 1->n) + PV (NRn)]IRR = PV(E1)IRR
[(FV (ATCF 1->n)RR ) + (FV (NRn)RR)]IRR = PV(E1)IRR
[(ATCFn + NRn) - (ATCFn-1 + NRn-1)] / (ATCFn-1 + NRn-1)
Net Income in nth Year
Initial Equity Investment
After Tax Cash Flow in nth Year
Before Tax Cash Flow in nth Year
Net Reversion in nth Year = After Tax Sales Proceeds
Market Value in nth Year = Gross Sales Price
Gross Income in nth Year
Net Income in nth Year
Internal Rate of Return
Modified Internal Rate of Return
Present Value
Reinvestment Rate
Future Value
© JR DeLisle, Ph. D.
Debt Coverage Ratio
•
•
Interpretation
– DCR provides a measure of the safety of the mortgage position, indicates the
cushion between required payments and NOI.
– DCR’s should normally be 1.2 or more
Equation
NIn / MtgPayment
Thousands
MtgPay
NI
DCR
$700
2
1.8
$600
1.6
$500
1.4
DCR: 1.3 Target
1.2
$400
1
$300
0.8
0.6
$200
0.4
$100
0.2
$0
0
1
Debt Coverage Ratio
2
3
4
Year 1
1.30
5
6
7
Year 2
1.35
8
9
Year 3
1.41
10
Year 4
1.46
Year 5
1.52
Real Estate Fundamentals
© JR DeLisle, Ph. D.
Default Ratio
What
DR is a measure of financial risk of real estate investments
In essence it is the ratio of Fixed Costs to Gross Income
How Used:
Establish maximum variation expectations vs. realizations
Sum (Exp +Property Tax + Mtg Payments)n / GIn
Thousands
Fixed Payments
GI
DR
$700
1
0.9
$600
0.8
$500
DR: .85 Target
0.7
0.6
$400
0.5
$300
0.4
0.3
$200
0.2
$100
0.1
$0
0
1
Default Ratio
2
3
Year 1
0.73
4
5
Year 2
0.71
6
7
Year 3
0.69
8
9
10
Year 4
0.67
Year 5
0.65
Real Estate Fundamentals
Profitability Index
What
Ratio of PV Receipts to PV Outlays
Variation of NPV; shows when hit breakeven point
How Used:
Determine economic viability; insights to minimum Holding Period
[(PV ((ATCF)1->n + PV (NRn))] / E1
Thousands
Equity PV
PVATCF + PVNR
PI
$1,600
2
$1,400
1.8
1.6
$1,200
1.4
$1,000
1.2
$800
1
$600
0.8
0.6
$400
0.4
$200
0.2
$0
0
1
Profitability
Index
© JR DeLisle, Ph.D.
2
3
4
5
6
7
Year 1
0.52
8
9
10
Year 2
0.75
Year 3
0.92
Year 4
1.06
Year 5
1.20
© JR DeLisle, Ph. D.
Before Tax Cash on Cash Return
What
Measure of Nominal Return using Initial Investment as base
Ratio of pretax distributable cash to initial investment
How Used:
Determine economic viability and optimal Holding Period
Compare alternative investments
BTCFn / E1
Thousands
BTCF
Equity PV
BTCC
$2,000
35%
$1,800
30%
$1,600
$1,400
25%
$1,200
20%
$1,000
15%
$800
$600
10%
$400
5%
$200
0%
$0
1
2
Before Tax Cash on Cash
3
4
5
6
Year 1
10.00%
7
8
Year 2
11.79%
9
10
Year 3
13.65%
1
Year 4
Year 5
15.59% 17.61%
2
3
4
5
6
7
8
9
Real Estate Fundamentals
10
After Tax Cash on Cash Return
What
Measure of Nominal Return using Initial Investment as base
Ratio of After Tax distributable cash to initial investment
How Used:
Determine economic viability and optimal Holding Period
Compare alternative investments
ATCFn / E1
Thousands
ATCF
BTCF
Equity PV
BTCC
$2,000
ATCC
35%
$1,800
30%
$1,600
25%
$1,400
$1,200
20%
$1,000
$800
15%
$600
10%
$400
5%
$200
$0
0%
1
2
3
© JR DeLisle, Ph.D.
After Tax Cash on Cash
4
5
6
Year 1
9.17%
7
8
9
Year 2
10.21%
10
Year 3
11.29%
1
Year 4
12.42%
2
3
Year 5
13.58%
4
5
6
7
8
9
10
Implicit Cap Rate
What
Ratio of NI in current period divided by end of year Value
Measure corresponds with “cap rate” rule of thumb
How Used:
Indication of relative pricing level; establish reasonableness of exit pricing
Fixed in this case due to application of Exit Cap to NOIn+1
NOIn+1 / MVn
Thousands
NI
MV
35%
30%
$5,000
25%
$4,500
$4,000
20%
$3,500
15%
$3,000
$2,500
Implicit Cap Rate
10%
$2,000
$1,500
5%
$1,000
0%
$500
1
2
3
$0
1
2
© JR DeLisle,
Ph.D.
Implicit
Cap Rate
3
4
5
6
Year 1
10.00%
7
8
9
Year 2
10.00%
10
Year 3
10.00%
Year 4
10.00%
Year 5
10.00%
4
5
6
7
8
9
10
Gross Income Multiplier
What
Ratio of current period Market Value to Gross Income
How Used:
Rule of thumb comparison of alternative projects
Relatively stable in this case due to use of Exit Cap in estimating Sales Price
MVn / GIn
GIM
35.0
30.0
GI
MV
Thousands
25.0
$5,000
20.0
$4,500
$4,000
15.0
$3,500
$3,000
10.0
$2,500
5.0
$2,000
0.0
$1,500
1
2
3
4
$1,000
$500
$0
1
2
3
©
JR DeLisle,
Gross
Income Ph.D.
Multiplier
4
5
6
Year 1
7.50
7
8
9
Year 2
7.50
10
Year 3
7.51
Year 4
7.52
Year 5
7.53
5
6
7
8
9
10
Net Income Multiplier
What
Ratio of current period Market Value to Net Income
Analogous to the PE ratio in finance
How Used:
An industry rule of thumb sometimes used to compare projects
Relatively fixed in this case due to Exit Cap on NOI
MVn / NIn
Thousands
NI
NIM
MV
GIM
35.0
$5,000
$4,500
30.0
$4,000
$3,500
25.0
$3,000
20.0
$2,500
$2,000
15.0
$1,500
10.0
$1,000
5.0
$500
0.0
$0
1
2
3
4
©Net
JR DeLisle,
Ph.D.
Income Multiplier
(P/E)
5
6
7
Year 1
10.41
8
9
1
10
Year 2
10.41
Year 3
10.41
Year 4
10.41
2
3
Year 5
10.41
4
5
6
7
8
9
10
Payback Ratio (w/o Sale)
What
Cumulative sum of After Tax Cash Flow/Equity Ratio
Multiperiod look at return of initial equity
How Used:
Ratio that determines speed of return of equity
Used to compare risk vs. other investments
PB
Sum(ATCF/E1)1 ->n
200%
180%
Thousands
ATCF1-n
160%
140%
Equity PV
120%
100%
80%
$5,000
$4,500
$4,000
60%
40%
$3,500
$3,000
20%
0%
$2,500
$2,000
1
2
3
4
$1,500
$1,000
$500
$0
1
2
3
©
JR DeLisle,
Payback
RatioPh.D.
(w/o sale)
4
5
6
7
Year 1
9.17%
8
9
10
Year 2
19.38%
Year 3
30.67%
Year 4
43.09%
Year 5
56.67%
5
6
7
8
9
10
Modified Payback Ratio (w/o Sale)
What
Cumulative sum of FV of After Tax Cash Flow/Equity Ratio
How Used:
Compare timing of returns against other alternatives
Understand exposure period with reinvestment
Modified PB
PB
Sum ATCF1-> n Reinvested/E1
200%
180%
Thousands
FV ATCF
ATCF
160%
140%
Equity PV
120%
100%
80%
$5,000
$4,500
$4,000
60%
40%
$3,500
$3,000
20%
0%
$2,500
$2,000
1
2
$1,500
$1,000
$500
$0
1
2
3
4
© JR
DeLisle,
Ph.D.(w/o sale)
Modified
Payback
5
6
Year 1
9.17%
7
8
9
Year 2
19.93%
10
Year 3
32.42%
Year 4
46.78%
Year 5
63.17%
3
4
5
6
7
8
9
10
NPV Equity
What
Cumulative sum of PV of Benefits less PV of Equity
How Used:
Determines whether discount rate is exceeded at specified cost of capital
If NPV is Positive (>1), indicates return exceeds required yield
[PV (ATCF 1->n) + PV (NRn)] - E1
ATCF
NR
ATCF + NR
Thousands
Thousands
$2,000
$1,800
$1,600
$1,400
$1,200
$1,000
$800
$600
$400
$200
$0
PVATCF + PVNR
PV Equity
2,500
2,000
1,500
1,000
500
1
2
3
4
5
6
7
8
9 10
0
1
© JR DeLisle, Ph.D.
NPV Equity (sold/year)
Year 1
NPV ($370,901)
Year 2
($194,013)
Year 3
($62,124)
Year 4
$49,674
2
3
Year 5
$153,266
4
5
6
7
8
9
10
Marginal Rate of Return
What
The net increase/decrease in total return relative to prior year
The additional return from owning from period to period
How Used:
Determining optimal holding period
Project has peaked when it drops off
[(ATCFn + NRn)- (ATCFn-1 + NRn-1)] / (ATCFn-1 + NRn-1)
$637,873
$507,878
= $129,995
$637,873
= 25.6%
$507,878
$507,878
1
© JR DeLisle, Ph.D.
2
3
4
5
6
7
8
9
10
Marginal Rate of Return
[(ATCFn + NRn)- (ATCFn-1 + NRn-1)] / (ATCFn-1 + NRn-1)
Thousands
ATCF
NR
ATCF + NR
MRR
$2,500
30%
25%
$2,000
20%
15%
MRR
$1,500
$1,000
10%
$500
5%
$0
0%
1
© JR DeLisle, Ph.D.
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
Internal Rate of Return: Overview
Interpretation
Rate that balances PV Outlays against PV Benefits; NPV=0
It assumes reinvestment at the IRR
Equation [PV (ATCF
) + PV (NRn)] = PV(E )
1->n
IRR
PV NR
PV NR + PV CF
PV CF
PV EQUITY $
IRR
© JR DeLisle, Ph.D.
PV EQUITY $
1 IRR
Net Reversion
Internal Rate of Return: Overview
Interpretation
Rate that balances PV Outlays against PV Benefits; NPV=0
It assumes reinvestment at the IRR
Equation [PV (ATCF
) + PV (NRn)] = PV(E )
1->n
IRR
PV NR
PV NR + PV CF
PV CF
PV EQUITY $
IRR
© JR DeLisle, Ph.D.
PV EQUITY $
1 IRR
Net Reversion
Internal Rate of Return
• Interpretation
– Rate that balances PV Outlays against PV Benefits; NPV=0
– It assumes reinvestment at the IRR
• Equation
[PV (ATCF 1->n) + PV (NRn)]IRR = PV(E1)IRR
ATCF
NR
ATCF+NR
Year 1
71,006
372,880
443,885
Year 2
79,084
545,118
624,202
Year 3
87,463
687,712
775,174
Year 4
96,151
824,014
920,166
Year 5
105,160
968,091
1,073,252
14.76%
© JR DeLisle, Ph.D.
IRR if Sold/Year
IRR
Year 1
-42.68%
Year 2
-5.52%
Year 3
6.69%
Year 4
11.96%
Year 5
14.76%
Modified Internal Rate of Return
• Interpretation
– Rate that balances PV Outlays vs. PV of the FV of Benefits
– FV is ATCF reinvested at a specified rate and NPV=0
– It may have multiple solutions, or may not converge
• Equation
[(FV (ATCF 1->n)RR ) + (FV (NRn)RR)]IRR = PV(E1)IRR
© JR DeLisle, Ph.D.
Modified Internal Rate of Return
PV NR
PV CF
PV EQUITY $
© JR DeLisle, Ph.D.
Net Reversion
Modified Internal Rate of Return
[(FV (ATCF 1->n)RR ) + (FV (NRn)RR)]IRR = PV(E1)IRR
ATCF
NR
Year 1
Year 2
Year 1
71,006
372,880
71,006
75,266
Year 2
79,084
545,118
Year 3
87,463
687,712
Year 4
96,151
824,014
Year 5
105,160
968,091
$71,006 * (1 + 6%) = $75,266
Reinvestment rate
154,350
13.48%
© JR DeLisle, Ph.D.
Modified IRR if Sold/Year
Year 1
-42.68%
Year 2
-4.96%
Year 3
6.63%
Year 4
11.25%
Year 5
13.48%
GIGO Caveats in DCF Analysis
• Forecasted Cash Flows
– Must Be REALISTIC Expectations
– Neither Optimistic, Nor Pessimistic
• Discount Rate should be Opportunity Cost of Capital
– Based on Ex Ante Total Returns in Capital Market
– REALISTIC Property Market Expectations
– Target Most Probable Buyer
© JR DeLisle, Ph.D.
Equity Justified: PV of CF + PV Net Reversion
= Ej
Most Common Mistakes in DCF
Sales Price
© JR DeLisle, Ph. D.
- Sales Exp
- Tax on Sale
- Mtg. Bal.
PV NR
Net Reversion
PV CF
+
• Rent & income growth assumption is too high
– “We all know rents grow with inflation, don’t we!”?...
– Remember: Properties tend to depreciate over time
– Usually, rents within a building do not keep pace with inflation, long run
• Cap Ex &/or exit cap rate projection, are too low –
– Capital expenditures typically average at least 10%-20% of the NOI (1%2% of the property value) over the long run.
– Going-out cap rate is typically higher than going-in cap rate (older
properties are more risky and have less growth potential).
Stabilized
NOI
NIr
GIr
• Discount rate (expected return) is too high –
– This third mistake may offset the first two
– End result may be realistic estimate of current value,
– No guarantee and often not true
Real Estate Finance
Net Reversion
© JR DeLisle, Ph. D.
Sales Price
TRCm
Net Sales Price
- Sales Exp
Appreciation
CG Appr
x 20%
Land Value
Depreciation
Mortgage
CG Depr
x 25%
Amortization
Net Reversion
PV NR
Pb
Stabilized
NOI
NIr
GIr
© JR DeLisle, Ph.D.
Real Estate Finance
Lecture Review
DCF Prelude
• The Value Proposition
• Frontdoor/Backdoor Models
Introduction to Discounted Cash Flow
• DCF: A Visual Overview
• One Word: GiNiTiBtAtNR
• Basic Inputs
DCF Schedules
• Schedule 1: Pro Forma Cash Flow
• Schedules II-III: Depreciation and Loan Amortization
• Schedules IV-V: Capital Gain Taxes and Net Reversion
• Schedules VI: Financial Ratios
© JR DeLisle, Ph.D.