Outline
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The Property Cash Flow
Discounted Cash Flow
Discounted Cash Flow Model
Elements of Discounted Cash Flow
Discounted Cash Flow Principles Summarized
Key Considerations in Discounted Cash Flow Applications
Discounted Cash Flow Mathematics
Discounted Cash Flow Model and Borrowing
Property Cash Flow Problems
Worked Examples
The Property Cash Flow
Property cash flow refers to the expected future expenditures and
receipts from property asset. In the case of landed property, the
expenditures will include the buying price and incidental costs (legal and
surveyor’s fees, stamp duty and VAT if not recoverable) and any works of
improvement. The income will be rent less maintenance and
management costs not recoverable from tenants. Rent is usually fixed up
to the first rent review, when changes in the economy and in the balance
of supply and demand for similar property are likely to allow an increase,
or possibly decrease.
Attempting to assess this leads into such uncertainty that the temptation
is to abandon the attempted appraisal at this point. However,
extrapolation of past trends and the use of a technique known as implied
growth rate offer some assistance.
The duration of the cash flow will depend on the expected life
of the asset. In the case of landed property this can be a long
time, but it is convenient to make an assumption that the asset
will be sold at some point in the not-too-distant future, perhaps
at the end of a standard commercial lease of 15 or 20 years.
This puts a limit on how far the income forecast has to be made.
Discounted Cash Flow (DCF)
• What is discounted cash flow?
‘A cash flow – discounted'.
‘An arithmetic process for testing or appraising whether an
investment opportunity is worth the money, or for choosing
between alternative investments’.
• What is meant by cash flow and how is it established?
• What is discounting?
• What is investment, and when is something ‘worth’ the cost?
Discounted Cash Flow Model
Discounted Cash Flow (DCF) model is used widely in the analysis of real estate
investment properties, and specifically for the estimation of the Present Value
(PV) or the Net Present Value (NPV) of cash flows associated mainly with
commercial real estate investment.
The DCF model consists of a series of periodic cash flows associated with the
ownership of a particular property investment, which are discounted to the
present time (time 0) using a discount rate.
The Present Value model estimates the present value of anticipated cash flows
from a commercial property without taking into account the initial cash outlay or
investment cost for the acquisition of the property. In the Net Present Value
model, however, the initial cash outlay in time zero is taken into account.
The two important components that determine the net present value of a real
estate investment in the discounted cash flow model are the
series of cash flows used and the discount rate.
When is DCF Model Used?
The discounted cash flow model is used in the following cases:
1)
When the investor wants to estimate what is the maximum
price he must pay to achieve a minimum or required rate of
return. This price can be estimated by discounting the cash
flows expected from the property over the holding period using as
discount rate the investors required or minimum rate of return.
This is a present value, not a net present value, calculation since
the initial cash outlay is not known and is to be determined.
2)
When the investor wants to evaluate the return that a property
investment will provide over the investment horizon if it is acquired
at a given price. This is calculated by including the acquisition price
in the cash flows to be discounted, and estimating the discount rate
that sets the NPV equal to zero. The so estimated discount rate is
actually the internal rate of return (annual, monthly, quarterly, etc)
depending on the length of the period to which the cash flows
refer to.
The important things to have in mind about the evaluation of real estate
investment properties using the discounted cash flow model are:
1)
All periodic cash flows that are used in the discounted cash flow
model have to refer to periods of the same length (annual, semiannual, quarterly, monthly)
2)
All cash flows that are used in the discounted cash flow model
refer to the future. For this reason analysts need to use projected
rental income, operating expenses, cap rates, values, etc.
Forecasts of rental rates for different property types are provided
by various vendors at the market level. These forecasts need to
be adjusted to take into account the position of the building
under consideration vis a vis the market average.
3)
The discount rate used must represent the discount rate that
corresponds to the length of period in which the cash flows refer
to. For example, if quarterly cash flows are used then a quarterly
discount rate needs to be used.
Elements of DCF
The two main elements of a discounted cash flow calculation are:
• The expected cash flow over the period of holding the asset.
Typically this is an initial spend at the start and an income for a
number of years following.
• The discounting of this cash flow at a rate of interest - a process
which allows for the time when future money is received (or paid
out as the case may be). Fundamental to discounting is the
recognition that N1 today is better than N1 tomorrow because of
interest.
Discounting, Discount rate and Present Value
Having made the projection of future cash flows, the second element
comes into play: assessing the present value, or value as at today, of all
future income and expenditure by the application of appropriate discount
rate to the projected future cash flows. The discount rate can be defined
as the required rate of return by the real estate investor and its level
depends on a number of factors.
Discount rate is chosen from one of the following:
• borrowing cost
• opportunity cost
• target rate, reflecting risk and uncertainty
The discount rate will vary from project to project or investment situation
depending on how the financing is to be arranged. The opportunity cost is
the return that is foregone by not investing in the best alternative
investment available.
Net Present Value (NPV)
The sum of the cash flows, including the initial expenditure, after
discounting. A positive NPV indicates the investment is profitable
at the rate of interest adopted.
In Example 1 the NPVs of a simple investment is shown,
discounted at rates of 6% and 10%.
Internal Rate of Return (IRR)
Internal Rate of Return is the rate of interest which produces an
NPV of zero. In other words, all the profits are expressed as an
interest rate. If the asset is government bonds, this is the
redemption yield, which includes the value of annual interest and
the repayment of the face value of the bond at its due date. If the
asset is property, the IRR is equal to the income plus capital gain on
sale, expressed as a weighted average return on expenditure. It is
therefore comparable to the redemption yield on government
bonds. It is sometimes called an equated yield in the property
industry, to distinguish it from initial yield which is simply the
current rent as a percentage of capital.
Problems with Internal Rate of Return
The phenomenon of multiple rates of return can occur in IRR
calculations. Some investors will therefore use only NPV. For
multiple rates to occur, there has to be more than one outflow of
cash, for example a large outflow of cash late in the life of the
project, and for many property investments the problem will not
arise. An example of the problem would be where restoration was
required at the end of a mineral lease. I have included an
illustration (Example 3) where the IRR is shown to be 7%. Above
this rate, NPV would normally be negative, but it is shown as
positive at much higher interest rates and heading back to zero at
around 100% pa interest.
Mutually Exclusive Projects
Where two investment opportunities, A and B, have the same cost,
then, assuming risk factors are equal, the one having the higher NPV
(and/or IRR) will normally be chosen. However, where the cost of
investment A is greater than that of B, the criterion of NPV may
indicate that investment A should be preferred, while IRR may
indicate B.
To use NPV as the criterion when costs are not the same can be
misleading, and this favours IRR as the criterion. In these cases, it is
useful to calculate the return on the extra cost of A as a guide to the
decision. Example 4 illustrates the situation.
Principles of DCF summarized
•
DCF calculations are based upon the simple axiom that
economic value is a function of the relation between
spending and rewards, and the time over which rewards
are received. It is about money out, money in, and time.
•
The first step in a DCF calculation is to list the items of
expense and income against a timetable, the simplest
being based on the assumption that money is spent and
received at the end of each year of the life of the
investment. (Computer spreadsheets such as Microsoft
Excel do this.) Refinements for in-advance and monthly or
quarterly payments can be made, and
will be explained later.
•
The second step is to discount the cash flow items using the
formula 1/(1+r)^n, where r is the rate of return required by
the investor which will have regard to the risk inherent in
the asset being purchased or the cost of funding the
purchase.
•
The sum of the discounted cash flows (including the initial
outlay) is the Net Present Value, which is a positive amount
for a profitable investment.
When Net Present Value is zero, the discount rate
represents the interest on capital employed, which is called
the Internal Rate of Return - a useful measure to compare
with other interest rates and returns.
Key Considerations in DCF Application
The discounted cash flow model is widely used in real estate especially
for the calculation of the NPV or the internal rate of return (IRR). The
internal rate of an investment is actually the discount rate that renders
the NPV of the expected cash flows equal to 0.
Typically the following apply when using the discounted cash flow
model for the evaluation of real estate investments:
1.
Use of after-tax cash flows
2.
Cash flow at time 0 is negative as it represents investment
costs (property acquisition costs, plus any pre-acquisition
costs for due diligence, such as market studies, feasibility
studies, legal, environmental studies, etc., or other expenses).
Subsequent cash flows might be negative as well, especially
in the case of real estate development projects.
3.
Cash flows represent the sum of all anticipated revenues
and costs in each period; notice that such costs and
revenues will differ by property type and for each property
depending on its idiosyncrasies.
4.
Special attention is needed when projecting property
income and expenses in order to estimate these cash
flows. Reliable projections of a property’s net operating
income (NOI) need to take into account the property lease,
rollover schedule, expiring leases and vacancy durations,
as well as potential changes in current market rents, which
will affect income from new leases. Projecting market rents
is not an easy task.
Discounted Cash Flow Mathematics
The formula for the discounted cash flow model for the calculation
of NPV, which takes into account investment costs (cash outlays) at
time 0, is the following:
NPV=CF0 + CF1/(1+d) + CF2/(1+d)2 + a€, a€.. CFn/(1+d)n
Where CF represents the cash flow of each period within the
investment analysis horizon, d the discount rate and n the last
period of the investment horizon. As indicated earlier, the first cash
flow CF0 represents the initial cash outlay or investment cost. The
last cash flow CFn includes any income expected to be received
during the last period of the investment horizon plus the market
value or sales price of the property at that point in time. Typically
this is calculated as the ratio of the expected Net Operating Income
(NOI) in the last period of the investment horizon over an
expected exit cap rate.
The correct application of the discounted cash flow model to a
particular real estate investment requires lots of number crunching
and accounting of all potential costs and revenues over the holding
period of the property. For this reason there are several real estate
investment analysis software programs that can make this task much
easier and more automated and can help avoid mistakes.
Very important to have in mind that the d is the periodic discount rate
that corresponds to the length of period that cash flows refer to. For
example, if cash flows are quarterly then the quarterly discount rate
needs to be entered in the formula. Caution is needed here because
discount rates are usually quoted in annual terms, and one might be
tricked to use an annual discount rate with quarterly cash flows, in
which case a very incorrect result will be obtained. Furthermore,
caution is needed when deriving quarterly or other periodic discount
rates from annual discount rates to take into account the compounding
effect. The correct formula for deriving the quarterly discount rate (dq)
from the annual discount rate (da) is:
dq = (1+da)1/4 - 1
the correct formulas for deriving the monthly discount rate (dm) and
the semi-annual discount rate (ds) from the annual discount rate (da)
are:
dm = (1+da)1/12 - 1
ds = (1+da)1/2 -1
DCF Model and Borrowing
The discounted cash flow model needs to be modified when
borrowed money are used to finance part of the property
acquisition. What it does change is how the cash flows used in the
DCF formula are calculated. In particular, if the analyst wants to take
into account the effect of borrowing on the project’s PV or IRR the
mortgage loan payments over the holding period need to be
appropriately and fully incorporated in the project’s after-tax cash
flows. In particular, this would include replacing any capital costs that
are financed through borrowed money, with the respective periodic
loan payments. For example, if construction costs of N20 million are
financed by 50%, then the negative cash flow of N20 million will be
replaced by a negative cash flow of N10 million (50% of N20 million)
and a negative cash flow equal to the payment for a loan of N10
million (plus any other incurred costs in association with obtaining
the loan, such as bank fees, etc.)
Notice that in the case of construction loans, banks will allow
interest only payments during the construction period with
principal payments starting after project completion. Also in
incorporating the effect of borrowing in the discounted cash flow
model, the remaining loan balance needs to be subtracted from
the last cash flow, which should also incorporate a positive cash
flow representing the property anticipated market value or resale
price. The return that incorporates the effect of borrowing is
referred to as leveraged return. This represents a typical use of the
Discounted Cash Flow model since borrowing is commonly used in
real estate investing due to the large capital required to acquire
property.
Property Cash Flow Problems
• Inflation
• Taxation
• Rent growth forecast - past rent growth rate v. implied rent
growth forecast
• Forecast resale prices
• Future yield
• Inflation and its relation to rent growth and interest rate
• Land value price growth
• Building cost charges
Worked Examples
Example 1
Time
Cash out
1
-10000
2
3
4
5
Cash in
3000
4000
3000
2000
Net cash
-10000
3000
4000
3000
2000
Sum or NPV
PV at 6%
0.9434
0.8900
0.8900
0.8396
0.7473
PV x Cash
-9434
2670
3358
2376
1495
465
Time
Cash out Cash in
Net cash
PV at 6%
PV x cash
1
2
3
4
5
-10000
-10000
3000
4000
3000
2000
0.9091
0.8264
0.7513
0.6830
0.6209
-9091
2479
3005
2049
1242
3000
4000
3000
2000
Sum or NPV
-315
Internal Rate of Return
NPV at 6% 465
NPV at 10% -315
Difference 780
Interpolate> 465/780 x 4%
2.385
Approx IRR> 6% plus 2.385
8.385
Trial rate 8.385%
Time
Cash out
1
2
3
4
5
10000
Cash in
Net cash
PV at 6% PV x cash
3000
4000
3000
2000
-10000
3000
4000
3000
2000
0.9229
0.8518
0.7862
0.7256
0.6697
Sum or NPV
Result:
IRR close to 8.385%
-9229
2555
3145
2177
1339
-13
Example 2 Residential investment
Time
0
1
2
3
4
5
6
7
8
9
10
Cash out
-100000
1440
1440
1440
1575
1575
1575
1710
1710
1710
(Re-sale)
Cash in
0
9600
9600
9600
0500
10500
10500
11400
11400
11400
120000
Net cash flow
-100000
8160
8160
8160
8925
8925
8925
9690
9690
9690
20000
PV factor*
1
0.9091
0.8264
0.7513
0.6830
0.6209
0.5645
0.5132
0.4665
0.4241
0.3855
Net present value
*Interest at 10%
Assumptions:
1 Annual in arrears calculation is acceptable
2 Purchase and resale prices allow for fees etc.
PV x Cash
-100000
7418
6744333
6131
6096
5542
5038
4973
4520
4110
46265
-3164
Example 3
Problems with IRR: Multiple rates
Time
0
1
2
3
4
5
6
Cash in
Cash out
-15370
-100000
Net cash
-15370
20000
20000
20000
20000
20000
20000
20000
20000
20000
20000
-100000
PV at 7%
0.935
0.873
0.816
0.763
0.713
0.666
PV x cash
-15370
18692
17469
16326
15258
14260
-66634
0
PV at 20%
-15370
16667
13889
11574
9645
8038
-33490
10952
PV at 90%
-15370
10526
5540
2916
1535
808
-2126
3829
Example 4 Problems with IRR : Mutually exclusive assets
Project A
Time
1
2
3
4
5
6
7
Cash out Cash in
-50000
10000
10000
10000
14000
14000
14000
Net cash
-50000
10000
10000
10000
14000
14000
14000
PV at 10%
0.9091 -45455
0.8264 8264
0.7513 7513
0.6830 8630
0.6209 8693
0.5645 7903
0.5132 7184
NPV
933
IRR
11%
PV X Cash
Project B
Time
1
2
3
4
5
6
7
8
Cash out
-84000
Cash in
14000
14000
18000
18200
18200
22000
22000
Net cash
-84000
14000
14000
18000
18200
18200
22000
22000
PV at 10%
0.9091
0.8264
0.7513
0.6830
0.6209
0.5645
0.5132
0.4665
NPV
IRR
PV X Cash
-76363.6
11570.25
10518.41
12294.24
11300.77
10273.43
11289.48
10263.16
1146.096
10%
Example 5 Implied rent growth
Initial yield: 4%
Resale YP: 25
Time (Yrs)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Rent
(N’000)
(Purchase)
50
50
50
50
50
Growth
3%
50
50
50
50
50
57.964
57.964
57.964
57.964
57.964
67.196
67.196
67.196
67.196
67.196
(Sale, 25YP) 77.898
Cash Flow
(N’000)
-1250
50
50
50
50
50
57.964
57.964
57.964
57.964
57.964
67.196
67.196
67.196
67.196
67.196
1947.459
NPV
PV at 6.5%
PV X Cash
1
0.9390
0.8817
0.8278
0.7773
0.7299
0.6853
0.6435
0.6042
0.5674
0.5327
0.5002
0.4697
0.4410
0.4141
0.3888
0.3651
-1250
46.948
44.083
41.392
38.866
36.494
39.725
37.300
35.023
32.886
30.879
33.612
31.561
29.634
27.826
26.128
711.008
-6.634
Result: Purchase close to viability with 3% rent growth.
Actual growth rate implied is just under 3%.
Example 6 Annual equivalent rates of interest
Target rate (AER):
Equivalent rate:
Income:
10% annually
2.41% per quarter
N2000 per quarter
Present Value
Cash out
Cash in
PV factor
1
2
3
4
5
6
7
8
2000
2000
2000
2000
2000
2000
2000
2000
0.9765
0.9765
0.9310
0.9091
0.8877
0.8669
0.8465
0.8265
Value
PV X Cash
2.41%
1953
1907
1862
1818
1775
1734
1693
1653
14395
Based on annual in arrear at AER
Year
1
2
Cash in
PV @ AER 10%
8000
0.9091
8000
0.8264
Value
Result: Under-valuation due to annual base.
PV X Cash
7273
6612
13884
Example 7 Present Value of a perpetual income
Target rate:
Quarterly income
PV of N1 per quarter
10% AER
Value
Annual income
PV N1 per annum @ 10%
Result: Under-valuation due to annual base.
2000
41.494 (1/0.0241)
82988
8000
10
80000