Chapter 19: Investment value: NPV and IRR

Chapter 19: Investment
value: NPV and IRR
Outline
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DCF framework
Discounting NOI
Investment value
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Investment value (to a particular investor) is
different from market (appraisal) value.
Commercial real estate decisions are made
with an investment motive: expecting cash
flows from the investment.
The discounted cash flow (DCF) analysis
addresses this motive.
Decision rule: if NPV > 0, accept the project.
Inputs for DCF
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The holding (investment) horizon.
Applicable required return.
Expected cash flows.
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In traditional finance, we’d like to use after
(corporate) tax cash flows, e.g., dividends or
FCFs to the firms.
In RE, there are a variety of cash flow choices,
both before taxes and after taxes.
Thus, be clear about the types of cash flows and
then use the appropriate discount rate.
Do not compare apples with oranges.
The example
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A possible purchase of a 96,000 sf building for $9 million
(V0). There are three tenants now.
Current market rent: $15 / sf, and this is expected to
increase at 4% per year.
Expected CPI rate: 4%.
This example is based on Brueggeman and Fisher (2008).
Current
Age of Remaining
Tenant
sf
rent / sf Base rent this term lease term
A
70000
14
980000
2 years
3 years
B
10000 14.5
145000
1 year
4 years
C
16000
15
240000
0
5 years
96000
1365000
CPI
adj.
0.5
0.5
0.5
CPI adjustment
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The base rent is $1,365,000, which is based on
current rent price.
Current rent prices for A and B are lower than the
market rent price because they are older leases.
Rent prices are usually adjusted based on CPI; but
this adjustment is usually partial (50% here).
Thus for Year 1, we would expect a 2% (50% of 4%
CPI) adjustment for older leases: A and B.
The lease for C is just signed, its rent price is set to
the current market price: $15 / sf.
Since this is a new lease, there would be no CPI
adjustment for C in Year 1.
Pro forma rental income and CPI
adjustments; horizon = 5
B
C
CPI adj
A
B
C
Total
A
B
C
Total rent
rent/sf
A
B
C
145000
240000
145000
240000
19600
2900
0
39592
5858
4800
145000
240000
145000
240000
175478.8 175478.8
240000 291996.7
59983.84
0
23622.14 47716.73
8875.16 11952.66
0
3509.576
9696
14689.92 19783.72
0
999600 1019592 1039984 1181107 1204729
147900 150858 153875.2 156952.7 175478.8
240000 244800 249696 254689.9 259783.7
1387500 1415250 1443555 1592750 1639992
14.28
14.79
15
1228824
178988.4
291996.7
1699809
14.5656 14.85691 16.87296 17.21042 17.55463
15.0858 15.38752 15.69527 17.54788 17.89884
15.3
15.606 15.91812 16.23648 18.24979
Expense reimbursements as
another source of income
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Expense stop: a clause often found in commercial
leases that requires landlords to pay property
operating expenses up to a specified amount and
tenants to pay the expenses beyond that amount.
Expense stop is usually stated in per sf amount.
For example, if the expense stop is $4.25 / sf and
the current expense is $4.5 / sf, the tenant must pay
the landlord 25 cents / sf as an expense
reimbursement (income to the landlord).
Suppose that expense reimbursement estimates for
Year 1-6 are 33500, 44396, 70625, 15256, 19189,
and 19670.
Formula for PGI
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Base income + CPI adj.
+ Expected reimbursement
= Potential (gross) income (PGI)
Projected NOI
1
Base income + CPI 1387500
Ex. Reimburse.
33500
Potential income
1421000
Vacancy
0
EGI
1421000
Operating expense 497350
NOI
923650
2
1415250
44396
1459646
0
1459646
510876
948770
3
1443555
70625
1514180
0
1514180
529963
984217
4
1592750
15256
1608006
80400.3
1527605
534662
992944
5
1639992
19189
1659181
82959
1576222
551678
1024544
6
1699809
19670
1719479
85973.9
1633505
571727
1061778
Vacancy is estimated to be 5% of total potential income after year 3
Operating expense is estimated to be 35% of effective gross income (EGI)
No capital expenditures
Discounting NOI
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Note that NOI is a before-tax cash flow.
Thus, when we assign a discount rate to
discount NOI, this must be a before-tax
discount rate.
Suppose that the investor requires a beforetax discount rate of 12%.
Note that this discount rate is somewhat
individual-specific; some investors have
higher costs of capital than the others.
The terminal market value
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For an NPV analysis, we need to know the
terminal market value at the end of 5-year
horizon.
V5 = NOI6 / R5, where R5 is going-out cap
rate. Suppose the going-out cap rate is
expected to be 10%.
Note that the going-out cap rate is
determined in the market; not individualspecific.
V5 = NOI6 / R5 = 1061778 / 0.1 =
$10,617,780.
NPV and IRR
0
-9000000
1
Cost
NOI
923650
Terminal value
Cash flow
-9000000 923650
Discount rate
0.12
0.12
PV
-9000000 824688
NPV
518788.3
IRR
14%
2
3
4
948770
984217
992944
948770
0.12
756354
984217
0.12
700546
5
1024544
10617780
992944 11642324
0.12
0.12
631034 6606167
Decision
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Would you purchase the building?
Other cash flows/discount rates
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The previous example does not take
taxes into consideration.
One of course can use after-tax cash
flows for the basis for DCF.
If so, the discount rate needs to be a
after-tax one.
For this, see Chapter 11, Brueggeman
and Fisher (2008).
Profitability ratios
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Going-in capitalization rate R0 = NOI1 /
V0 = 923650 / 9000000 = 10.26%.
Net income multiplier (NIM) = V0 / NOI1
= 9000000 / 923650 = 9.74.
Gross income multiplier (GIM) = V0 /
EGI1 = 9000000 / 1421000 = 6.33.
Financial risk ratios
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These ratios try to measure the
income-producing ability to meet
operating and financial obligations.
Operating expense ratio (OER) =
operating expenses / EGI; for year 1,
OER = 497350 / 1421000 = 35.00%.
Loan-to-value (LTV) ratio = mortgage
balance / acquisition price (V0).
Pros and cons of financial
ratios
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Easy to calculate and communicate.
Their calculations are usually based on
a single year’s numbers; they tend not
to consider future cash flows.
They do not have a formal decision
rule.