# Bep for Rental Income by rob14866

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```									                                                                                                    Joseph M. Davis, MAI, PhD

Project Feasibility Using
Breakeven Point Analysis

Using the breakeven point formula, an appraiser can quickly determine the
feasibility of a project from several points of veiw. An expanded breakeven
point formula combines the possibilities of the land and building residual tech-
niques with cash flow model analysis. The article illustrates the importance of
making revisions to the original formula—which is commonly found in real es-
tate investment texts—to include leasing commissions and tenant improvements
in office or retail space analysis.

W       hen a client asks the question, what is
my breakeven cost on this project, he is re-
BEP =
TC
TR
= 1 = Breakeven

ally asking, “When will my project have a                Breakeven cash flow analysis: Breakeven
breakeven cash flow if I obtain typical financ-          cash flow (BECF) analysis, as used in real
ing?”                                                    estate with financing and after income taxes,
Important questions like this can be an-            is shown below:
swered using the breakeven point (BEP), which
is really a single year’s cash flow model. The                             PGI – V&RL =
formula answers the following questions: How                                  EGI – OE =
much is the land worth for a proposed use?                                   NOI – DS =
What rental rate will be needed, given the cost                          BTCF – TAXES = ATCF
of constructing the improvements and buying              where,
the land? Given market rental rates, what can                   PGI = Potential gross income
the operating expenses be and still meet the                   V&RL = Vacancy and rent loss
lender’s requirements?                                          EGI = Effective gross income
Breakeven economic analysis: Just as finance                     OE = Operating expenses
and real estate disciplines had their origins in                NOI = Net operating income
economics, the breakeven point formula is                        DS = Debt service + interest
closely associated with the breakeven point                    BTCF = Before-tax cash flow
analysis of a perfectly competitive firm.                     TAXES = Federal and state income taxes
As shown in figure 1, when total revenue                  ATCF = After-tax cash flow
(TR) = total cost (TC), breakeven points exist:

Joseph M. Davis, MAI, PhD, is president of Joseph M. Davis and Associates, Tempe, Arizona, and is a
professor of real estate at Arizona State University. He received his PhD in real estate from the University of
Georgia, Athens, and has previously written for The Appraisal Journal. Contact: (602) 705-0007. Fax (602)
705-0006. Email joseph.davis@asu.edu.

41
Let:                                                  Value is a function of:
OE + DS
BECF (before-tax) =           = BEP = 1
EGI                                Value = f (Building value, land value)
If [OE + DS ] = EGI                         Building value = f (Building square footage, price per
OE + DS                                        square foot)
BECF (after-tax) =         + TAXES = BEP = 1
EGI                          Land value = f (Land square footage, price per
Thus, the BEP is:                                                        square foot or acre)
OE + DS
BEP =
EGI
Income or revenue is a function of:

This simple formula can be used to do many            Retail and office:
types of real estate analysis.                          PGI = f (Leasable area, price per square foot per year,
Breakeven point analysis: The simple BEP                        other income)
formula is only the tip of an iceberg that leads      Apartments (300-unit project):
to numerous applications. Generally, it illus-          PGI = f [(100 1BR/1BA × \$500 × 12) + (100 2BR/2BA
× \$550 × 12) + (100 3BR/3BA × \$600 × 12)
trates the following:                                           + other income]
• BEP shows the percentage of the effec-                                       or
tive gross income (EGI) at which the be-            PGI = f [(100 1BR/1BA × Y × 12) + (100 2BR/2BA
fore-cash tax flow or BTCF is 0.                            × 1.10Y × 12) + (100 3BR/2BA × 1.2Y × 12)
+ other income]
• If EGI – (OE + debt service or DS) = 0,
EGI = f (PGI – V&RL)
then, BEP = 1 and BTCF = 0.
V&RL = f (%, PGI)
• If (OE + debt service or DS) < EGI,
then, the BTCF is positive.
Operating expenses (OE) are a function of:
• If (OE + DS) > EGI,
then, the BTCF is negative.                          OE = f (Property taxes, insurance, utilities, manage-
The financing, as expressed in the DS com-                      ment, utilities, etc.)
ponent of the BEP formula, is a function of
(f) the following:                                        The BEP formula can be used to derive
an estimate of any of the variables listed. The
DS = f (AMC, loan amount)          formula can be used to:
AMC = f (i, Term)
• Determine how much to pay for the land
Loan amount = f (LTV, V)
or how much can be spent on improve-
LTV = f (%, V)
ment costs
DCR = f (NOI, DS)
where,
• Determine what the apartments or leas-
AMC = Annual mortgage coefficient
able area rent must be
LTV = Loan-to-value ratio                          • Determine if the project will meet the
i = Interest rate                                 lender’s financing requirements (LTV,
Term = Amortization period                            DCR, etc.)
V = Value                                        • Determine the maximum expenditures
DCR = Debt coverage ratio                             for operating expenses per unit and still
meet the lender’s requirements

FIGURE 1 Breakeven Economic Analysis
TC = Total cost                                    \$                                                  TC   TR
VC = Variable cost
FC = Fixed cost
TR = Total revenue
π = Profit maximization
BEP1 = (TC = TR)                                                                           Decreasing

BEP2 = (TC = TR)                                                                            Returns

TR – TC = Profit                                                                 Increasing
Returns
FC
TC = VC + FC
\$ = Rent/revenue/dollars
Q = Units/Square feet/quantity                                                                           Q
BEP1             π    BEP2

42   The Appraisal Journal, January 1998
Each variable following the “function of”                       600,000 + 1,074,012
1=
or f above can be solved for and the BEP for-                    [1,140Y + 1,254Y + 1,368Y]
mula can be rewritten as needed by the                  3,762Y = \$1,674,012
analysis to include all or portions of the vari-             Y = \$445
ables.                                                       Therefore, the required rent is as follows:
Applications for the BEP formula are                 • \$445 per month for a 1-bedroom/1-bath unit
shown in the following examples.                          • \$490 per month for a 2-bedroom/2-bath unit
• \$534 per month for a 3-bedroom/2-bath unit
Example A: BEP Analysis of an                           Check (pro forma):
Apartment Project                                            \$534,000 (1-bedroom/1-bath is 100 × \$445 × 12)
1. The lender’s requirements are as follows:                \$588,000 (2-bedroom/2-bath is 100 × \$490 × 12)
\$640,800 (3-bedroom/2-bath is 100 × \$534 × 12)
1.30 = DCR (minimum)                               \$1,762,800 (PGI—rental income)
25 years = Term                                       –     88,140 (V&RL—5%)
8.5% = Interest rate (monthly payments)              1,674,660 (EGI)
75% = Maximum loan-to-value ratio                 – 600,000 (OE—300 units × \$2,000)
9.4% = Acceptable capitalization rate                 1,074,660 (NOI)
– 826,163 (DS—8.5% for 25 years in monthly
payments)
2. A 300-unit project is planned on a 15-acre
\$248,497 (BTCF)
parcel of land. Current vacancy rates of
1,074,660
comparable projects in the area average                                DCR =            = 1.30
826,163
5%. Comparable rents for tenant-paid
DS    826,163
utilities projects show that:                                    Loan amount =         =
AMC 0.09662725
= \$8,550,000
1.00Y = 1BR/1BA (100 units)
8,550,000
1.10Y = 2BR/2BA (100 units)                          LTV ratio (cost) =              = 0.7500
11,400,000
1.20Y = 3BR/2BA (100 units)                                               8,550,000
LTV ratio (market) =                 = 0.7479
11,432,553
Property managers’ records and pub-                           NOI 1,074,660
VMKT =         =       = 11,432,553
lished data indicate that the average an-                     0.094   0.094
nual operating expense per unit is \$2,000.
3. According to a preliminary sketch of the           Example B: BEP Analysis of Retail Center
project from an architect and estimates             1. Given the following lender’s require-
of a general contractor, the project could             ments:
be built for \$28,000–\$32,000 per unit plus
\$8,000 per unit for the land, or a total of                1.30 = DCR (minimum)
\$38,000 per unit.                                      25 years = Term
4. What must the apartments rent for each                   8.50% = Interest rate (monthly payments)
month to satisfy the lender’s require-                     75% = Maximum loan-to-value ratio
ments? The problem is solved using                      10.00% = Acceptable capitalization rate
breakeven point analysis:
2. A 160,000-square-foot leasable area retail
OE + DS
BEP =                                                      center is planned on a 15-acre parcel of
EGI
land. The estimate is based on compa-
Y = Required apartment rent for 1-bedroom/1-bath
rable rents and expenses and property
OE + 1.30DS
1=                                                     managers’ records of similar projects.
[0.95(100)(1Y)(12) + [0.95(100)(1.10Y)(12)
+ 0.95(100)(1.20Y)(12)]                                The annual stabilized NOI pro forma
OE = \$2,000 × 300 units = \$600,000                       is:
DS = (AMC) (loan amount)
DS = (0.09662725)(0.75) (cost)                               \$1,760,000 (PGI—\$11 per square foot)
Cost = \$38,000 per unit × 300 units                          –    88,000 (V&RL—5%)
= \$11,400,000                                             1,672,000 (EGI)
DS = [0.09662725 (0.75) (11,400,000)]                       – 480,000 (OE—\$3 per square foot)
DS = \$826,163                                                \$1,192,000 (NOI)
1.30DS = \$1,074,012                                              \$1,200,000 (rounded)

Davis: Project Feasibility Using Breakeven Point Analysis        43
3. The maximum amount of the lender’s                   Breakeven cash flow occurs at 80.7204%
loan is estimated using the following           of the EGI, or restated:
methods:
PGI – V&RL = EGI × 80.7204% = BEP = [(OE + DS)
DCR method:                                                         – 0.807204 EGI = 0]
DCR = 1.30

DCR =
NOI                           Working backward, BE occurs at 23% va-
DS                        cancy; market vacancy is 5%.
1,200,000
1.30 =
DS                                 \$1,760,000 (PGI)
1,200,000                                410,355 × V&RL = (0.233156 × PGI)
DS =            = \$923,077              –
1.30
\$1,349,645 (EGI)
DS
= Loan amount maximum                \$1,672,000 (EGI)
AMC
923,077                                      × 80.7204% (BEP)
= \$9,552,968 Maximum loan
0.096627                                       \$1,349,645 (EGI)
amount
Check (pro forma):
Loan-to-value ratio method:                                   \$1,349,645 (EGI)
NOI
V=                                   – 480,000 (OE)
R
869,645 (NOI)
1,200,000
V=            = \$12,000,0000                     – 869,645 (DS)
0.10
\$          0 (Breakeven cash flow)
LTV ratio = 75% maximum
\$12,000,000 × 0.75 = \$9,000,000
Loan amount maximum = \$9,000,000                          Given a 75% LTV ratio from the lender,
an AMC of 0.09662725, and building costs
(BC) of 9,600,000, the appraiser then solves
In conclusion, the lender will offer only
for land value (LV):
\$9 million at 8.5% for 25 years with a
maximum loan-to-value ratio of 75%.                       OE + DS
BEP =
4. A preliminary sketch and footprint of the                   EGI
retail center drawn by an architect has                   OE + [0.75 (BC + LV) AMC]
BEP =
been obtained. According to the                                       EGI
builder’s estimate, the cost for gross                    480,000 + [0.75 (9,600,000) + LV) AMC]
BEP =
1,672,000
building area is \$55–\$65 dollars per
480,000 + [0.75 (0.09662725) (9,600,000 + LV)]
square foot (includes all direct and indi-         0.81 =
1,672,000
rect costs), or about \$60 per square foot.
1,349,645 = 480,000 + [(0.072470)(9,600,00 + LV)]
The gross building area is equal to the
1,349,645 = 480,000 + 695,716 + 0.07247044 LV
leasable area. Thus, the estimated build-
1,349,645 – 480,000 – 695,716 = 0.07247044 LV
ing cost is 160,000 square feet × \$60 =
173,929                     \$2,400,000
\$9,600,000.                                                    = Land value =
0.07247044                     15 acres
5. How much can the investor afford to pay                          Land value = \$160,000 per acre
for the land and meet the lender’s re-                           Land value = \$3.67 per square foot
quirements?
The total cost for the building and land is:
Land residual method:
\$12,000,000 (Lender’s property value)                 \$9,600,000 (Building)
– 9,600,000 (Building cost)                          + 2,400,000 (Land—160,000 × 15 acres)
\$2,400,000 (Land residual value)                   \$12,000,000
\$160,000 per acre
\$3.67 per square foot                                     CONCLUSION
Breakeven point analysis solution:
OE + DS                        Using the expanded BEP formula, an ap-
BEP =
EGI                          praiser can quickly determine the feasibility
480,000 + 869,645              of a project from several points of view by
BEP =
1,672,000
including many other variables. As de-
BEP = 80.7204%

44   The Appraisal Journal, January 1998
scribed, the BEP formula combines the pos-              Generally, leasing commissions and ten-
sibilities of the land and building residual       ant improvements will apply when retail and
techniques with cash flow model analysis.          office space are analyzed. Apartment projects
However, an appraiser should consider re-          account for these categories in operating ex-
vising the formula when leasing commis-            penses: management, maintenance, and re-
sions and tenant improvements are part of          pairs. The revised BEP formula gives the
the analysis, so that the revised formula is:      owner or purchaser a more realistic cash flow
breakeven expectation. The formula, whether
OE + DS + LC + TI              revised for LC and TI or not, can also be writ-
BEP =
EGI                      ten to reflect an after-tax analysis by adding
where,                                             income taxes in the numerator.
LC = Leasing commissions
TI = Tenant improvements

Davis: Project Feasibility Using Breakeven Point Analysis   45

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