Introduction to Real Estate
Investment Appraisal
NPV and IRR
Pat McAllister
INVESTMENT APPRAISAL
DISCOUNTED CASFLOW ANALYSIS
Investment Mathematics
• Discounted cash flow to calculate
– Gross present value
– Net present value
– Internal rate of return
• IRR is the discount rate at which the NPV
equal zero
Basically
• We need to answer four questions.
• What do we get?
• When do we get it?
• What do we pay out?
• When do we pay it out?
Definition
• Net Present Value
• The discounted or present value of a series of
future cash flows where the initial outlay is
included as an outflow. The NPV is therefore
the surplus of deficit present valued
monetary sum above and below the initial
outlay (purchase price).
Definition
• Gross Present Value
• The discounted or present value of a series of
future cash flows where the initial outlay is
not included as an outflow. The GPV is
therefore the worth of the cash flow at the
investor’s target rate of return
Internal Rate of Return
• The rate of interest (expressed as a percentage) at
which all future cash flows (positive and negative)
must be discounted in order that the NPV of those
cash flows should equal zero
Mathematically
RI 3
RI n
SPn
RI1
RI 2
Vp
......
2
3
n
n
(1 k ) (1 k ) (1 k )
(1 k ) (1 k )
Where:
Vp = Value of property
RI = Rental income
SP = Selling price
k = Target rate of return
on property
n = Holding period
As you know...
(1 +i)-n
INVESTMENT APPRAISAL
DISCOUNTED CASHFLOW
•
•
•
•
Discounted Cashflow analysis - or DCF – applies
discounting techniques to the analysis of projects or
investment opportunities;
DCF techniques are used to determine buy/sell
decisions and to decide whether or not to proceed
with projects;
There are two main techniques:
NET PRESENT VALUE ANALYSIS (NPV)
– This provides a monetary sum: a positive NPV is a
signal to proceed with a project;
•
INTERNAL RATE OF RETURN (IRR)
– This provides a % return – if the IRR% is sufficiently
high then the project should proceed.
INVESTMENT APPRAISAL
NET PRESENT VALUE
•
•
All project cashflows are discounted back to today’s
prices at a firm’s discount rate – the target rate. The
NPV is the SUM of the individual present values.
Let Ct be the cashflow in year t. Then:
NPV =
C
t
t
i
for t = 0,1, … n Recall that
t
t
i
- I0 for t = 1…..n
•
Sometimes you will see
•
where I0 is the Initial Investment or outlay.
Key elements of NPV analysis are
C
t
i
= (1+i)-t
(i) estimating/forecasting the cashflows;
(ii) deciding on an appropriate discount rate.
INVESTMENT APPRAISAL
INTERNAL RATE OF RETURN
• The IRR is the rate of return or yield of the project
or investment, expressed as a percentage.
• It is the discount rate which generates a Net
Present Value of zero
• Formally, the IRR is i% such that
C
• Or
t
t
=
i
C
t
t
i
I0
for t = 1, 2, … n
=
0
for t = 0, 1, 2, … n
• As with the NPV it is vital that we can
– estimate/forecast the cashflows;
• We must also be able to specify
– The firm’s target return (hurdle rate) for this type of
project or investment
A very simple example
• An asset offered at a price of €10,000,000
• We expect €1,000,000 for the next five years
• We will sell it for €10,000,000 in five years time.
• Our target rate of return is 10%
• What is the NPV?
• What is the GPV?
• What is the IRR?
You should be able to
guess!
Capital
Year
Income
0
Out/In
Cash flow
PV factor
PV
10,000,000 €
10,000,000 €
1.00
10,000,000 €
1
1,000,000 €
1,000,000 €
0.91
909,091 €
2
1,000,000 €
1,000,000 €
0.83
826,446 €
3
1,000,000 €
1,000,000 €
0.75
751,315 €
4
1,000,000 €
1,000,000 €
0.68
683,013 €
5
1,000,000 €
11,000,000 €
0.62
6,830,135 €
10,000,000 €
NPV
0€
GPV
10,000,000 €
IRR
10.00%
INVESTMENT APPRAISAL
WORKED EXAMPLES: PROJECTS S & B
• Consider two simplified projects:
Year
0
1
2
3
Project S (£m)
-150
+50
+75
+88
Project B (3m)
-250
+110
+110
+115
• Both last exactly three years, have an initial
investment in year zero (today) and generate
income at the end of years 1 to 3
• The cashflows in each year are net cashflows, that
is income less any costs
• In property a net cash flow is sometimes called the
“net operating income”
INVESTMENT APPRAISAL
WORKED EXAMPLES – NPV S
• Work out NPV of Project S, using a discount rate of
10% (we’re using big rates for illustration here …)
Cashflow
-150
+50
+75
+88
Discounted cashflow
t
i
1.0000
0.9091
0.8264
0.7513
-150.00
45.45
61.98
66.12
+23.55
• This is a POSITIVE NPV: at this discount rate, the
project is feasible. What if we used 20%?
Cashflow
-150
+50
+75
+88
t
i
1.0000
0.8333
0.6944
0.5787
Discounted
cashflow
-150.00
41.66
52.08
50.93
-5.33
• Now the NPV is NEGATIVE so the project is NOT
feasible, we should not go ahead.
INVESTMENT APPRAISAL
WORKED EXAMPLES – NPV B
• We can do exactly the same analysis for Project B:
Year
Cashflow
0
1
2
3
-250
+110
+110
+115
Discounted
@ 10%
-250
100
90.91
86.40
Discounted
@ 20%
-250
91.67
76.39
66.55
+27.31
-15.39
• Again, the project is feasible at 10% but not at 20%.
• The decision, then, rests on the choice of discount rate
• This will reflect, as always, anticipated inflation, time
preference, risk, alternative opportunities and the cost
of borrowing.
INVESTMENT APPRAISAL
WORKED EXAMPLES – IRR S
• The IRR generates an NPV = 0: it must lie
somewhere between 10% and 20%.
• Assume a straight line rel. between NPV & i%
(n.b. it isn’t a straight line, it’s just a convenience)
+23.55
0
-5.33
10%
IRR
20%
We can use this to give us a first estimate of the IRR
INVESTMENT APPRAISAL
WORKED EXAMPLES – IRR S
The slope of the line is
5.33 2355
.
28.88
=
or –2.89
20 10
10
That is, a 1% increase in i% leads to a 2.89 fall in NPV
Now, at 20%, the NPV is –5.33. We want NPV = 0
So, we must ADD 5.33 to the NPV. Divide by the Slope:
+5.33 / -2.89 = -1.84 We must reduce i% by 1.84%
20% - 1.84% = 18.16% is our first estimate of the IRR
If we’d worked from 10%, we have NPV = 23.55
Must reduce it by 23.55 for an NPV of zero;
Divide by slope: -23.55 / -2.89 = +8.15
10% + 8.15% = 18.15% (difference = rounding error)
INVESTMENT APPRAISAL
WORKED EXAMPLES – IRR S
• Now NB that 18.15% is just our FIRST estimate
• We assumed a straight line – an oversimplification
• We must CHECK our estimate by calculating NPV –
let’s try 18%
Year
Cashflow
0
1
2
3
-150
50
75
88
t
i
1.0000
0.8475
0.7182
0.6086
DCF
-150.00
42.37
53.86
53.56
-0.21
• That’s close enough to zero, call IRRS 18%
INVESTMENT APPRAISAL
WORKED EXAMPLES – IRR B
• We’ll do exactly the same with Project B
+27.31
0
-15.39
10%
the slope of this line is
IRR
20%
15.39 27.31
= –42.7/10 = -4.27%.
20 10
• Working from 10%, NPV = +27.31, must fall 27.31
• Divide by slope –27.31 / -4.27 = +6.4%
• 10% + 6.4% = 16.4% = our first estimate of IRR
INVESTMENT APPRAISAL
WORKED EXAMPLES – IRR B
• With a first estimate of 16.4%, we might check
16% and 16.5% …
Year
Cashflow
0
1
2
3
-250
+110
+110
+115
Discounted @
16%
-250
94.83
81.75
73.68
0.26
Discounted @
16.5%
-250
94.42
81.05
72.73
-1.80
• That’s nearer to 16% so we’ll use that as our
estimate of the IRR
• In both cases, should really check on computer …
IRRs = 17.923%, IRRb = 16.061%
IRR/NPV DECISION RULES
• Net Present Value
Decision rule - project/investment accepted if NPV zero or above
: requires the selection of a target rate of return.
• Internal Rate of Return
–Decision rule - investment is accepted if the investment’s IRR is
equal to or greater than some pre-determined target rate
Decision rules
•
•
•
•
•
•
GPV > Offer price
GPV = Asset valuation
GPV < Asset valuation
IRR > TRR
IRR < TRR
NPV/IRR debate
Buy
Hold
Sell
Buy
Sell
USE OF IRR/NPV
•
•
•
•
NPV is preferred in finance literature to IRR. (see
Lumby, 1991)
Predictably, IRR used in real estate practice more
than NPV.
The greater the discount rate the greater the
weight placed upon early rather than later cash
flows
Multiple (unreal) IRR (+ve and –ve)