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# Real Options in Real Estate - PowerPoint PPT Presentation

Real Options in Real Estate. Theory and Evidence. Overview. Options Real Options Development Option Empirical Evidence Applications. Options. Call option: The right (not the obligation) to purchase a share of stock at a date T in the future for price P. Option Valuation. Stock price

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### Real Options in Real Estate

Theory and Evidence

• Options

• Real Options

• Development Option

• Empirical Evidence

• Applications

• Call option: The right (not the obligation) to purchase a share of stock at a date T in the future for price P.

• Stock price

• Strike price

• Interest rate

• Volatility of stock return

• Time to maturity

• Black-Scholes formula: C ( S, K, r, σ, T)

• No downside cost, so no downside risk.

• Upside payoff, so risk is good.

• Method of valuation:

• Call option payoff can be locally matched by borrowing, and holding some amount of the stock.

• As S changes, this “replicating portfolio” must be adjusted.

• We know the price of the stock and the bond at each moment, so we can calculate the equivalent price of the option.

• Fisher’s NPV criterion: take any project that project that provides a positive Net Present Value.

• Suppose, however, that taking one project costs you the opportunity to take another positive NPV project?

• Take the highest NPV of the two.

• Cost of Plant: \$100 million

• Net after-tax cash flow/yr. in perpetuity from plant: \$3 million.

• Cot of capital = current interest rate.

• Current cost of capital today: 3%.

• NPV = \$3 m/ .03 = \$100 m.

• Build the plant?

• Interest rates go up or down each year by 100 BP.

• If they are certain to go to 2% next year:

• NPV = [\$3 m/.02 - \$100m]/(1.03) = \$48.54 m

• Wait one year to build!

• Each project competes with itself delayed by one period.

• But ONLY if both projects cannot be undertaken!

• Irreversible investment.

• Irreversible investment involves a timing decision.

• Relevant stochastic variables:

• Interest rates

• Demand

• Investment cost

• Autocorrelation of variables are relevant.

• Rents vary through time, with some momentum.

• Rents are locked in for 10 years when you lease.

• Costs to build are fixed (as are interest rates): \$ 400/square foot. Build and lease instantaneously.

• Current rents are \$40/square foot.

• Current cost of capital is 10%.

• Rents are trending up: prob 60% of rents going to \$50/sq.foot and 40% chance of \$30/square foot.

• NPV = \$40/.1 - \$400 = 0

• Exp. Value: .6(\$500-\$400)/(1.1) + .4(0)= \$90.9

• What if rent (t) = a + b*rent(t-1)+e ?

• Wait for rents to tip and then build?

• Issues:

• Construction time.

• Build but hold vacant.

• Laura Quigg (JF, 1993)

• Examines Seattle market for undeveloped land.

• Estimates building prices, development costs and models development costs as stochastic.

• Value with and without std of DC = 0.

• Rena Sivitanidou & Petros Sivitanides (RE Econ 2000)

• Construction starts should depend upon option value.

• Higher volatility of rents should cause delay of construction.

• Time-series of commercial property completions in U.S. Office markets: CC

• Data: Torto-Wheaton Research: 1982 – 1998.

• Model:

• Completions = a+ a1*Completions t-1 + a2*Income + a3*EmpGrowth+ a4*EmpVolatility +a5*Interest +a6*Cost + a7*Commute +a8 Temperature

• Also used Rents and Vacancies in other models

A = constant: + insignificant

A1 = Lag Comp: + significant

A2 = Income: + significant

A3 = EmpGrowth + significant

A4 = Volatility-- significant

A5 = Interest Rate -- significant

A6 = Cost -- insignificant

A7 = Commute -- significant

A8 = Climate + significant

• Other variables: Income and Rents both are positive and significant in other models. Vacancies are negative and significant in other models

• Some evidence that development in 1990’s took optionality more into account.

• Conservatism or increased volatility expectation?

• Empirical results suggest that developers already value optionality:

• Land prices are higher than simple present values.

• Volatility in demand causes construction delay.

• Vacant land represents an option.

• Option exercise triggered by peak valuation

• Demand, construction costs, financing.

• Strategic considerations.

• Rents.

• Complex issues

• Time to build.

• Competitor decisions.

• One exercise, all exercise.

• Each floor is a separate option.

• High volatility of rents implies value in short-term lease/ vacancy.

• Peaking rents a sign to lease up.

• Low rents a sign to keep vacant space.

• Low rents + vacancy = negative economic sign – or not?

• Low vacancy + high rents = positive sign – or not?

### Agency Theory and Real Estate

Theory, Insights and Applications

• Ross (1973) "The Economic theory of agency: the principal's problem.“

• “Agency relationship when one, designated as the agent, acts for, on behalf of, or as representative for the other, designated the principal, in a particular domain of decision problems.”

• Agent and Principal agree on a fee structure.

• Agent takes actions that are not directly monitored or observable.

• Fees determined by outcomes and external events, perhaps.

• Agent motivated to act in his/her own interest.

• Imperfect information

• Management

• Complex organizations

• Co-operative ventures

• Negotiation

• What fee structure will best align interest of P & A?

• Is it possible to find something that achieves a “first best” solution which maximally motivates the Agent?

• What additional mechanisms exist to align interests/motivate Agent?

• Costly auditing/ monitoring an option

• There are agency costs

• Shirking

• Pilferage

• Risk-shifting

• Near alignment of interests possible

• Stock option programs a major solution

• Solutions must be incentive-compatible and individually rational.

• Real Estate Agents

• Local knowledge essential (before web)

• Commission earned on transaction.

• Effort unobservable.

• Result: Realtors leave their own home on the market longer and get higher adjusted prices for it.

• Home-ownership and urban quality

• Home ownership aligns upkeep incentives.

• Rental home are not well-maintained.

• Externalities imposed.

• Real estate development and management is local.

• Real estate portfolios are diversified.

• Principal = national owner, Agent = local manager.

• Understand differing motivations

• Where will conflicts arise?

• Understand differing strengths

• These provide the gains to trade.

• Understand the IR and IC constraints on both

• This means the deal will not fall through in the future.

• A solution should be possible (Ross result) for a wide range of agents and principals.

• Negotiation process should help reveal the relative strengths and motivations (Raiffa result).

• Use the power of incentive alignment

• Equity sharing.

• Look for judicious use of monitoring.