BARTRAM & COCHRAN

Real Estate Math for Attorneys

Marc Louargand, Ph.D., CRE®, FRICS&

Maura Cochran, CRE®

BARTRAM & COCHRAN

Real Estate Math for Attorneys

• VALUATION– Capitalization Rate, Discount Rate, Cash on

Cash return, Internal Rate of Return

• FINANCING– Interest rates – fixed and variable, rate versus

spread, reference rates, term versus amortization, 360 day convention versus actual interest rate calculations – effect on cost of funds. APR’s and Amortization

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Annual Percentage Rate (APR) 6.06%Interest Rate 4.47%

Amortization Constant 1.59%

Property and Market ConditionsSq. Ft. 70,000

$/ Sq.Ft. 200$

Rent 22.00$ Op. Exp. 8.00

NOI 14.00$ Capital 1.50

EBIT 12.50$

FinancialsOccupancy 100%

Effective Gross Revenue 1,540,000$ Cash on Cash 6.7% Actual Net Operating Income 980,000 Total Return Annual EBIT 875,000 (Current Y ield + Growth) 9.7% Debt Service 605,885

Free Cash Flow 269,115 Revenue Growth Rate 3.0%

Office Building Deal

Price 14,000,000$ Cap Rate 7.0% Equity 4,000,000

Loan to Value Ratio LTV 71% Debt 10,000,000 Interest Rate 4.47%

Debt Service Coverage Ratio APR 6.06%or DCR 1.62 Debt Service 605,885

DCR=NOI/Loan Payment

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Interest Payments Decline, Principal Payments Increase

1 11 21 31 41 51 61 71 81 91 101111121131141151161171181191201211221231241251261271281291301311321331341351

$50,490.43 payment

Principal Payment

Interest Payment

$37,250.00

$13,240.43

Month

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Capitalization Rate – simple relationship of Net Operating Income (NOI) to price or value

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Cash on Cash Return – net cash flow after all costs and debt service

Let’s revisit our deal to see the Cash on Cash return……….

Cash on Cash is like Dividend Yield on a stock

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Office Bulding Deal II(What Actually Happened)

Price 14,000,000$ Equity 4,000,000 Cap Rate 7.0%

Debt 10,000,000 LTV 71%Interest Rate 4.47%

APR 6.06%DCR 605,885 DCR 1.21

Annual Percentage Rate (APR) 6.06%Interest Rate 4.47%

Amortization Constant 1.59%

Property and Market ConditionsSq. Ft. 70,000

$/ Sq.Ft. 200$

Rent 22.00$ Op. Exp. 8.00

NOI 14.00$ Capital 1.50

EBIT 12.50$

FinancialsOccupancy 75%

Effective Gross Revenue 1,155,000$ Actual Net Operating Income 735,000 Effective Cap Rate 5.3%

Annual EBIT 656,250 Cash on Cash (Yield) 1.3%Debt Service 605,885 Total Return

Free Cash Flow 50,365 (Current Y ield + Growth) 4.3%Revenue Growth Rate 3.0%

But Vacancy is 25%

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Discount Rate – desired total rate of return from the investment applied to all cash flows

Cap rate reflects current income while the discount rate values the income and appreciation from the whole ownership period

Discount Rate captures Cap Rate in every period +

Value Change at end of ownership

The Discount Rate is used to solve for the Present Value of all the cash flows

The Internal Rate of Return (IRR) is the particular discount rate that makes the Present Value be equal to the cost

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• The Discount Rate, k is the desired total rate of return from the investment applied to all cash flows

• Cost = $10,000 with a life of 4 years

• In this case, the IRR is 10% since that’s the discount rate that made the PV equal to the cost

• IRR = Discount Rate when PV = Cost 

𝑃𝑉= 𝐶𝐹11+ 𝑘+ 𝐶𝐹2ሺ1+ 𝑘ሻ2 + 𝐶𝐹3

ሺ1+ 𝑘ሻ3 + 𝐶𝐹4ሺ1+ 𝑘ሻ4

𝑃𝑉= 1,0001.10 + 1,0001.21 + 1,0001.33 + 11,0001.464

𝑃𝑉= 10,001.07

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• FinancingInterest Rates – Fixed and Variable

Fixed interest rates are the same for the life of the loan Variable Rates are adjusted periodically to reflect changes in some reference rate of interest Reference rates include Treasury instrument rates, LIBOR, Federal Reserve rates or anything parties desire.

Components of a fixed rate loan payment

Annual Percentage Rate (APR) =Total Fixed Rate Payment per Year = (interest for the period + amortization + the effect of any points paid)

Loan Amount

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Components of a variable rate loan payment or a locked spread loan

(reference rate for the period + loan spread + amortization paid)

Often quoted as, “150 over the coterminous Treasury, 10 years with a 30 year amortization schedule” 10 year Treasury Note = 2.97% (12/ 2/ 2010) Spread = 1.50% (150 basis points, b.p’s or “bips”) 30 year amortization constant = 1.58% (increasingly important at low interest rates)

Debt Service = 6.05%

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For a loan of $10 million, monthly payments would be $50,490 and balance at end of year 10 would be $8,001,258.67 which is due and payable then Debt Service and APR are not affected by the method of calculation, actual days versus 360 day “years” in a standard mortgage. In this case, the difference in different length months would be

30/ 360 Actual DaysFebruary (28) 37,250.00$ 34,290.41 J uly (31) 37,250.00$ 37,964.38 November (30) 37,250.00$ 36,739.73 Whole Year 447,000.00$ 447,000.00

If it was interest only. The actual effect is less due to amortization. The 360 day convention DOES affect closing pro-rations and interest pre-payment and increases interest in a loan that calculates interest on a daily basis.

Day's Interest

365 days(.0447/ 365) x 10,000,000 = 1,224.66$

360 days(.0447/ 360) x 10,000,000 = 1,241.67$ 17.01$

so on a 15 day prepayment borrowerwould pay $255.15 more.

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Same concepts as Finance, just different names

Real Estate Model 𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑡𝑢𝑟𝑛 = 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑅𝑎𝑡𝑒= 𝐶𝑎𝑠ℎ 𝑜𝑛 𝐶𝑎𝑠ℎ+ 𝐺𝑟𝑜𝑤𝑡ℎ 𝑖𝑛 𝐶𝑎𝑠ℎ 𝑜𝑛 𝐶𝑎𝑠ℎ

Stock Market Model

𝑉𝑜= 𝐷1 (Dividend is analogous to NOI) 𝑘𝑒 – g (Discount rate or return on equity – growth is cap rate)

Price Earnings (PE) Ratio is the Cap Rate backwards

Price / Earnings instead of Earnings/ Price

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Discount and Cap Rate Variations• “Trailing Cap”- last 12 months’ NOI/Price• “Going-in Cap” – pro-forma year 1 rents/Price• “Trended Rents Cap” – pro-forma using rent growth assumptions in year 1/

Price• Exit Cap Rate – when using a discount rate to find the Present Value or IRR

an assumption about what the property will sell for at the end of the analysis – usual “conservative” estimate is 50 basis points above the going-in cap rate.

• Reported Cap Rate – Seller’s is always lower than the Buyer’s but higher than the Broker’s

• IRR – universally accepted as if it’s real when in fact it’s totally fiction• IRR Flaws – it is only correct if interim cash flows are reinvested at the same

rate. Never happens.• If there are negative cash flows during ownership the IRR may have multiple

solutions or no solution• People in investment committee meetings waste endless hours discussing

them as if they existed prospectively when their only legitimate use is retrospectively for keeping score.

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Decomposing Returns

• Spread Investing – see the spread over Treasuries as a risk premium because that’s what it is

• 5% Real – typical pension plan return target = Inflation rate + 5%• Partitioned IRR – using a discounted cash flow model to indicate

how much of total return is coming from income and how much from expected appreciation. That’s where the exit cap rate becomes a tempting tool. As each cycle ages, the balance shifts overwhelmingly toward appreciation, a signal that it’s time to go.

•  Weighted Average Cost of Capital – WACC – each component of the capital stack times it’s rate, added up – Loan to Value Percent x APR + Equity Percent x equity’s required rate of return =

WACC or Overall Cap Rate

BARTRAM & COCHRAN19781979

19801981

19821983

19841985

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19901991

19921993

19941995

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20100.0400000000000001

0.0500000000000001

0.0600000000000001

0.0700000000000001

0.0800000000000001

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0.1

NCREIF Office Cap RatesNCREIF Office Cap Rates

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