Growing Annuities
 Definition –
 Mathematically:
1  g CF1  1  g  CF1    1  g  CF1
CF1
PV 

(1  r )
(1  r ) 2
(1  r )3
(1  r ) N
2
 1  1  g  1  r N
 CF1 
rg

David M. Harrison, Ph.D.
Texas Tech University
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Real Estate Investments
N 1
Growing Annuity Example #1
 Suppose your are analyzing a 10-year lease with
annual rental payments (due at the end of each year).
If the first year rent is $20 per square foot and the
contract calls for the rent to increase by 2% each year,
if the opportunity cost of capital (discount rate) is 10%,
what is the present value of this lease?
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
“Tricking” Your Calculator
 Step #1: Redefine the interest rate
 Step #2: Solve for the Present Value of a level annuity in advance
 Step #3: Convert your answer
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Growing Annuity Example #2
 A landlord has offered a tenant a 10-year lease with
annual net rental payments of $30/SF in arrears. The
appropriate discount rate is 8%. The tenant has asked
the landlord to come back with another proposal, with a
lower initial rent in return for annual step-ups of 3% per
year. What should the landlord’s proposed starting rent
be?
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Constant-Growth Perpetuity
 Definition –
1  g CF1  1  g  CF1  
CF1
PV 

(1  r )
(1  r ) 2
(1  r )3
2

CF1
rg
The entire infinite series collapses to this simple ratio!
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Perpetuities and Cap Rates
BldgVal
CF1
NOI
 PV 

r  g caprate

NOI
caprate 
PV

r
f

rg
 RP   g
 Tbill Rate  Risk Pr emium  GrowthRate
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Cap Rate Examples
 An apartment building has 100 identical units that rent at
$1000/month with building operating expenses paid by the landlord
equal to $500/mo. On average, there is 5% vacancy. You expect
both rents and operating expenses to grow at a rate of 3% per year
(actually: 0.25% per month). The opportunity cost of capital is 12%
per year (actually: 1% per month). How much is the property
worth?
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Intra- vs. Inter-Lease Rates
 A typical commercial building space may be
viewed as a perpetual series of long-term fixedrent leases. Once signed, the lease CFs are
relatively low risk, hence a low “intra-lease”
discount rate is appropriate. Prior to lease
signings, however, the future rent is more risky.
Hence, a higher “inter-lease” discount rate is
appropriate. Rent may be expected to increase
between leases, but not within!
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Intra/Inter-Lease Example
 Suppose expected first lease rent is $20/SF/yr net, on a 100,000
SF building. The first lease will be signed in one year with rent
paid annually, in advance. Leases will be for 5 years with a fixed
rent. Expected rental growth between leases is 2%/yr, with no
vacancies expected in between leases. Suppose the intra-lease
(low risk) discount rate is 8%/yr, while the inter-lease (high risk)
discount rate is 12%. What is the PV of this space?
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Measuring Return
 Current Yield
 Capital Gain
 Total Return
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Total Return Example #1
 PROPERTY VALUE AT END OF 2007 = $100,000
 PROPERTY NET RENT DURING 2008 = $10,000
 PROPERTY VALUE AT END OF 2008 = $101,000
 What is this investment’s total return?
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Calculating Total Return
 Methodology:
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David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Total Return Example #2
 Ex. Consider an investor with a 5 year investment horizon,
evaluating an income producing property. The property may
currently be purchased for $2,000,000. Last year’s NOI of
$150,000 is projected to grow at 3% annually into the foreseeable
future. At the end of the investor’s holding period, cap rates are
expected to 8% on properties of this nature. What is the total
[expected] return offered by this security?
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments
Yield Decompositions
 Potential Sources of an Investment’s Dollar Return:




Decompose the expected return on our 5 year investment
property.
Conclusions:
David M. Harrison, Ph.D.
Texas Tech University
Real Estate Investments