CAIA L2 - 6.5 - Valuation Methods for Private Assets: The Case of Real Estate Flashcards
Define
depreciation tax shield
’–
Formula of
PV of
depreciation tax shield
(in real estate investment)
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
depreciation tax shield is the
expected income tax savings
as a result of deducting depreciation
depreciation tax shield ‘t’ = depreciation’t’ × tax’t’
PV of depreciation tax shield = ∑ [ (depreciation’t’ × tax’t’) / (1+R’d’)^t ]
* R’d’ = R’f’ (if tax shield is certain)
* R’d’ > R’f’ (if tax shield is not certain / default is present)
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
Define
recaptured depreciation
(in real estate investment)
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
if an asset is sold above its depreciated book value
=>
recaptured depreciation = difference (selling price - depreciated book value)
Obs: This difference is only paid n periods in the future => calculate PV!!
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
Describe
depreciation
as generating an
interest free loan
(in real estate investment)
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
Depreciation generates a reduction of taxes
similar to a interest free loan.
‘–
Ex:
* annual depreciation = $1M
* marginal tax rate = 25%
* discount rate = 8%
* n = 10 years
* tax on depreciation recapture $2.5M
Determine the investor benefit (in $) of the interest-free loan
Answer:
1. depreciation tax shield’t’ = $1M x 25% = $250k. This is PMT
2. tax on depreciation recapture of $2.5M means the asset was sold for $2.5M/25% = $10M above the depreciated book value. FV = -$2.5M (obs: exercise could give the value of depreciation recapture)
3. solve
present value of this investor’s benefit is an interest-free loan of $519,537 (i.e., FV = –$2.5 million; I = 8%; N = 10; PMT = +250,000)
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
Formula
after-tax return
without tax deferral
and
with tax deferral
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
after-tax return without tax deferral = r × (1 – RTax)
Ex:
investment with a 12% pretax return,
28% marginal tax rate,
no tax deferral
=> after-tax return of 8.64% [= 12% × (1 – 0.28)]
‘——–
‘——–
after-tax return with tax deferral = { 1 + [ (1+r)^(T) – 1] × (1–tax rate)}^{1/T} – 1
Raciocínio:
* [ (1+r)^(T) – 1] => primeiro calcular quanto ganharia bruto, sem tax durante todo o “T” período
* [ (1+r)^(T) – 1] × (1–tax rate) => aí sim você cobra tax
* { 1 + after tax rate in T periods}^{1/T} – 1 => anualiza a taxa
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
List
3 tax benefits
of leveraging
in real estate acquisition
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
- Can defer taxes through the depreciation tax shield.
- Capital gains are not taxed until the property is sold. This presents a second layer of tax deferral.
- Enables a small amount of capital to produce tax-favorable gains while also harvesting more tax deductions from the interest paid on the leverage.
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
List and explain
Real Estate IRR of
1. pre-tax (= no tax)
2. depreciation is not allowed
3. Accounting Depreciation Equals Economic Depreciation
4. Accounting Depreciation Is Accelerated
5. Capital Expenditures Can Be Expensed
as a function of operating cashflow, depreciation, proceeds from a sale
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
For each 5 scenarios, CF’t’ = CFO-Dep-tax+sale proceeds-capital gain tax shield
1. pre-tax (= no tax)
CF’t’ = CFO-Dep-0+sale proceeds-0
IRR’pretax’ = 10%
2. depreciation is not allowed
CF’t’ = CFO-0-tax+sale proceeds+capital loss tax shield
IRR = 5.76% < 10% x (1- 40%) => pretax IRR = 10%, marginal tax rate = 40%
=> first principle of depreciation and returns
3. Accounting Depreciation Equals Economic Depreciation
CF’t’ = CFO-Dep-tax+sale proceeds-0
IRR = 6% = 10% x (1- 40%)
=> second principle of depreciation and returns
4. Accounting Depreciation Is Accelerated
CF’t’ = CFO-Dep-tax+sale proceeds-capital gain tax shield
IRR = 6.27% > 10% x (1- 40%)
=> third principle of depreciation and returns
5. Capital Expenditures Can Be Expensed
CF’t’ = CFO-0-tax+sale proceeds-capital gain tax shield
IRR = 10% = pretax IRR
=> fourth principle of depreciation and returns
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
List and explain
2
transaction-based indices
(in real estate investment)
list advantages and disadvantages
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
Repeat-Sales Method (RSM)
* regresses percentage price change observed on a property against a series of dummy variables for time
Advantages
1. calculates changes in a single property over time, thus eliminating comparison issues between properties with differing characteristics.
2. robust to specification error, which would normally be present when the wrong model is used to explain variations in a dependent variable.
Disadvantages
1. potential for data scarcity because the sample size of repeat sales is typically a small subset of all available transactions.
2. It assumes no changes in the property. In practice, all properties age, and some are renovated over time.
3. When the RSM is updated, it provides backward adjustments in historical returns. This means previously reported returns may change.
’–
Hedonic Pricing Method (HPM)
* market price–based method that determines pricing based on the bundle of unique attributes for a given property
Advantages
1. uses all observations, not just repeat sales. This is very helpful when time periods are short.
2. is adaptable, in the sense that it can be structured to include any attributes (a.k.a. hedonic variables) desired.
3. avoids backward adjustments of historical returns when the index is re-estimated in the future.
Disadvantages
1. requires large amounts of data on the hedonic variables.
2. may suffer from sample selection bias because unsold properties are not represented in the index.
3. is exposed to specification error because significant property attributes might not be considered.
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
List and explain
3
Appraisal-Based Indices
(in real estate investment)
list advantages and disadvantages
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
- Sales comparison approach involves evaluating one property against other similar properties that have also recently sold. Adjustments can be made for attributes like location, square footage, and amenities.
- Cost approach assumes that a buyer will not pay more than it would cost to build an equivalent property. This is essentially a replacement cost checkpoint.
- Income approach applies discounted cash-flow analysis to a series of projected operating cash flows. This is especially useful for commercial real estate, which is typically income producing.
Advantages
1. No sample selection bias - They do not generally suffer from sample selection bias because there is not a reliance on sales constraints.
2. Any property + any frequency - All properties can be appraised on any desired frequency.
Disadvantages
1. Appraisals subjectivity - Appraisals are inherently subjective, which introduces the potential for pricing errors.
2. Generate smoothed indices - Measures of volatility can be underestimated because appraisal-based indices are smoothed compared to actual value changes.
3. Appraisals rely on data from the sale of comparable properties. Highly unique properties may have an issue under this model, and there could be a time lag between the sale of comparables.
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
Define
appraisal error
(in real estate valuation)
How to reduce it?
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
difference between
an appraised value
and the true market value
To reduce random estimation error
=> need to use more transaction data
=> expand the observation window (+ older prices)
=> tradeoff between reducing noise and assuming temporal lag.
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
Define
temporal lag bias
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
occurs when there is a
time lag between
the sale of a comparable property and
its use in the appraisal process
Example:
a negotiated price might be arranged months before the actual sale (prices could change during this time period).
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
Explain
The Square Root of N Rule
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
error of an estimated market value = 1/√n
n = number of observations
Ex:
n = 2 => error = 1/√2 = 71%
n = 8 => error = 1/√8 = 35%
6.5 - Valuation Methods for Private Assets: The Case of Real Estate
Complete with higher/lower
_____ tax bracket investors will benefit more from depreciation tax shield than ____ tax bracket investors
Higher tax bracket investors will benefit more from depreciation tax shield than lower tax bracket investors
