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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 rg David M. Harrison, Ph.D. Texas Tech University 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 rg The entire infinite series collapses to this simple ratio! David M. Harrison, Ph.D. Texas Tech University Real Estate Investments Perpetuities and Cap Rates CF1 NOI BldgVal PV r g caprate NOI caprate rg PV r f RP g Tbill Rate David M. Harrison, Ph.D. Texas Tech University Risk P r em ium GrowthRate 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: 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