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Chapter 19

Investment Decisions: NPV and IRR

McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.19-2

Overview

� Major theme: most RE decisions are made with an investment motive

� magnitude of expected CFs--and the values they create—are at the center of investment decision making

� Chapter 18 focuses on widely used, single-year, return measures, ratios, & income multipliers

� These criteria are relatively easy to calculate & understand—an advantage in the eyes of many industry professionals

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Overview

� Many investors also perform multi-year analyses of potential acquisitions

� When using multi-year discounted CF decision making methods, investor must

1. estimate how long she expects to hold property

2. make explicit forecasts of:

� property’s net CF for each year,

� net CF produced by expected sale of property

3. Select rate of return at which to discount all future CFs

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Centre Point Office Building

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Centre Point:

5-Year Operating Pro Forma

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Centre Point: Reversion Sale Price

0875.0469,180,1$

6NOI=

0875.0

291,103$469,180,1$ =

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@4%

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19-7

Levered vs. Unlevered Cash Flows

� Levered CFs measure property’s income after subtracting mortgage payments

� Valuation of levered CFs?

� Discount expected BTCFs rather than stream of NOIs

� Why is owner’s claim on a property’s CFs referred to as a “residual claim”?

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Effects of Leverage on Centre Point

Cash Inflows & Outflows

� Loan Terms� 75% loan, 30 years, 6.5% annual interest rate, total up-front fees = 3%

of loan amount

� Net loan proceeds:

= $792,000 − (0.03 x 792,000)

= $768,240

� Required equity = $1,056,000 - $768,240 = $287,760

� Payment: $5,005.98 or $60,072 per year� Can you compute this?

� What is the Mortgage Balance after 5 years?

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19-9

Centre Point 5-Year Pro Forma with

Leverage

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19-10

Present Value of Levered Cash Flows:

Centre Point

Why was the discount rate increased to 14%?

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Net Present Value of Centre Point

NPV = PVin − PVout

NPV = $319,591 − $287,760

PVout in this example is equal to original equity investment of $287,760

NPV = $31,831

Decision: Accept Centre Point investment opportunity because doing so will increase equity investor’s wealth by $31,831

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Effect on NPV of Variation in

Discount Rate

At a discount rate of 16.8727%, NPV = 0, this is the going-in IRR

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So…From Where Do Discount Rates Come?

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Selecting Discount Rates

� Discount rate is composed of two parts:E(Rj) = r = Rf + RPj

� Rf is risk-free rate

� yield/return available on U.S. Treasury securities with maturity equal to the expected holding period of the property

� This benchmark rate is readily observable

� RPj is risk premium for “subject” property

� This component of discount rate is difficult to determine

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U.S. Example: Class A Apartment

PropertiesSource: quarterly survey conducted by Real Estate Research Corporation (www.RERC.com)

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Selecting Discount Rates

� Since risk premiums vary, so do required yields

� High quality, relatively safe RE investments: currently 6-8% required returns

� Development Project: 15%-30% or more (much more risky)

� So…how do investors determine required risk premiums(RPjs)?

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19-17

Why IRR Is Technically Inferior to

NPV as an Investment Criterion

� IRR & NPV will always give the same accept-reject signal w.r.t. an individual investment

� But…..

� IRR may rank investment opportunities differently than NPV

� NPV ranking is always consistent with wealth maximization

� If projected CFs change signs more than once over expected holding period, there may be multiple IRRs

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A simple example

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� Buy a building for $10,000,000 that has an NOI of $1,000,000 each year. Sell after 10 years for $10,000,000.

� If you use no leverage, what is the IRR of this investment?

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A simple example

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� Buy a building for $10,000,000 that has an NOI of $1,000,000 each year. Sell after 10 years for $10,000,000.

� If you use no leverage, what is the IRR of this investment?

� A bank offers you a 50% LTV bullet loan at 6% for 10 years. What is the IRR of this investment?

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A simple example

20

� Buy a building for $10,000,000 that has an NOI of $1,000,000 each year. Sell after 10 years for $10,000,000.

� If you use no leverage, what is the IRR of this investment?

� A bank offers you a 50% LTV bullet loan at 6% for 10 years. What is the IRR of this investment?

� Another bank offers you a 75% LTV bullet loan at 6% for 10 years. What is the IRR of this investment?

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When Will Leverage Increase NPV

& IRR?

� Increased leverage will increase calculated NPV when….

� opportunity cost of equity capital (discount rate) exceeds effective borrowing cost

� Increased leverage will increase going-in IRR when….

� unlevered going-in IRR exceeds effective borrowing cost

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Borrower’s Decision Making

Process: Loan Size

� Reasons for use of debt by investors:� Limited financial resources/accumulated wealth

� Debt alters risk & equity return of investment

� “Magnifies” rate of return on invested equity

� This magnification known as positive (or negative) leverage

� Diversify investment portfolio (that is can buy more buildings)

� Increase after tax return

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19-23

When is Use of Leverage Expected

to be Favorable?

� Increased leverage will increase expected return when….

� the rate of return without leverage exceeds the cost of debt

� This is called positive leverage

� MM Eqn:

�RL = RU + D/E(RU-RD)

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19-24

Effects of Leverage on NPV & IRR

But…leverage also increases risk to equity investor, thus required equity return should increase with leverage

Increased leverage usually increases both NPV and IRR—holding mortgage rate and all other assumptions constant

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Impact of Leverage on Risk of

Equity Investment

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Income Taxes, Cash Flows & Returns

� Cash flows and returns most important to investors are after-tax cash flows &returns

� The following after-tax analysis assumes a 30 percent income tax rate

� More detail on the tax calculations is provided in Chapter 20

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Centre Point: After-Tax Cash Flows

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How is Required After-Tax

Discount Rate Determined?

� Assume: required before-tax return = 14%� Assumed income tax rate on additional income = 30% � After-tax required return = 14% − (0.30 x 14%)

= 14% x (1 − 0.30)= 9.8%

� That is, a reasonable assumption is:after-tax return = before-tax return x (1−TR)

whereTR is investor’s “marginal” tax rate

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Centre Point: After-Tax NPV & IRR

Note: IRR falls less than 30%: (16.9 – 12.8) ÷ 16.9 = 0.24

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Effective Tax Rate Formula

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� Effective tax rate on the project =

� (BTIRR – ATIRR)/BTIRR

� From previous slide:

� (16.9 – 12.8)/16.9 = 0.24 = 24%

� Note: This is less than the 30% marginal tax rate on ordinary income

� Real Estate Investing may lower Effective Tax Rates!

� Alternately stated, real estate can be a tax shield

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Comparison of Three Scenarios

Some conclusions:� Leverage increases expected Centre Point equity returns

� Taxes significantly reduce net investor CFs and returns

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Reality Checks on Investment Value

�Claim of project organizer (promoter) on returns� Compensation for idea, time, effort, & knowledge

�Claim of taxes on returns� Federal taxes (IRS): Up to 43.4%

� State taxes: Up to 10%

� Complexity of tax computations

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Varying the Assumptions

� Sensitivity analysis

� Most likely scenario

� Worst-case scenario

� Best-case scenario

� Value of computer

� Excel spreadsheets – Let’s try this!

� Specialized software such as ARGUS

� Monte Carlo simulation

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Nathan Collier on Quantitative

Analysis

“NPV and IRR are major ways in which investment decisions are evaluated. Each method has its strengths and weaknesses. Proper analysis of investment real estate requires a pro forma, an estimate of income and expenses over a period of time, usually 5 to 10 years. I can create the template for a rough pro forma from scratch in a couple of hours, a complete pro forma with all the bells and whistles and looking crisp could easily take a few days. It is amazing how many people in real estate and finance have never created a pro forma from scratch and couldn’t to save their lives.”

“I’ve told my COO that the requirement to be a financial analyst for The Collier Companies should include the ability to at least create a rough pro forma from scratch solo. Otherwise, how can you truly understand what you are doing? I’m a big “back of the envelope” kind of guy. If the deal is so close that it does not pencil out on a napkin at the table, I’m pretty sure I don’t want to go for it. But before we proceed we double and triple check our gut feel via sifting the deal numbers through a great pro forma.”

Nathan Collier: Chairman, The Collier Companies, a major owner/operator of student apartment communities

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End of Chapter 19