An appraiser estimates the reversion value for a retail center using a terminal capitalization rate of 7.0%. The projected NOI for Year 11 (the first year after the 10-year holding period) is $385,000. The appraiser then discounts the reversion value back to present value using a yield rate of 8.5%. What is the present value of the reversion?
Correct Answer
D) $2,127,412
First, calculate reversion value: Year 11 NOI ÷ terminal cap rate = $385,000 ÷ 0.07 = $5,500,000. Then discount to present value over 10 years at 8.5%: PV = $5,500,000 × (1.085)^−10. The present value factor for 10 years at 8.5% is approximately 0.3868 (1 ÷ 1.085^10 ≈ 0.3868). So $5,500,000 × 0.3868 = $2,127,400 (rounded to nearest $100). Option D ($2,127,412) matches this calculation within rounding tolerance. This tests correct sequencing: reversion is derived from terminal cap rate applied to *subsequent* year’s NOI, then discounted at the yield rate — per the Income Approach standards in USPAP Standards Rule 1-10 and The Appraisal of Real Estate (12th ed.), Ch. 17.
Why This Is the Correct Answer
First, calculate reversion value: Year 11 NOI ÷ terminal cap rate = $385,000 ÷ 0.07 = $5,500,000. Then discount to present value over 10 years at 8.5%: PV = $5,500,000 × (1.085)^−10. The present value factor for 10 years at 8.5% is approximately 0.3868 (1 ÷ 1.085^10 ≈ 0.3868). So $5,500,000 × 0.3868 = $2,127,400 (rounded to nearest $100). Option D ($2,127,412) matches this calculation within rounding tolerance. This tests correct sequencing: reversion is derived from terminal cap rate applied to *subsequent* year’s NOI, then discounted at the yield rate — per the Income Approach standards in USPAP Standards Rule 1-10 and The Appraisal of Real Estate (12th ed.), Ch. 17.
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A property is subject to a ground lease with 40 years remaining. The tenant (improvements owner) pays $50,000 annually to the landowner, while current market rent for the land alone is $72,000 per year. The improvements are fully depreciated, and the tenant bears all maintenance, taxes, and insurance. Under the income approach, what is the indicated value of the leasehold interest assuming a 6% overall capitalization rate applied to the annual rent differential and a 40-year term?
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A discount rate for a DCF may be supported by: