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Growing Annuities

Growing Annuities. Definition – Mathematically:. Growing Annuity Example #1.

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Growing Annuities

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  1. Growing Annuities • Definition – • Mathematically:

  2. 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?

  3. “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

  4. 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?

  5. Constant-Growth Perpetuity • Definition – The entire infinite series collapses to this simple ratio!

  6. Perpetuities and Cap Rates

  7. 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?

  8. Intra- vs. Inter-Lease Rates • A typical commercial building space may be viewed as a perpetual series of long-term fixed-rent 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!

  9. 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?

  10. Measuring Return • Current Yield • Capital Gain • Total Return

  11. 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?

  12. Calculating Total Return • Methodology:

  13. 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?

  14. Yield Decompositions • Potential Sources of an Investment’s Dollar Return: • Decompose the expected return on our 5 year investment property. • Conclusions:

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