1Evaluation of Flexibilityfor a Primary ResidenceMichael PasqualMIT ESD.71, Fall 2009 Outline• Motivation• System Definition• Model• Uncertainties• Design Concepts• Decision Analysis• Lattice Analysis• Simulation• Conclusions2Motivation• Fiance and I need a home for when we get married• Housing market is perfect– Low prices– Low mortgage rates System Definition• The system is our primary residence• Demand-capacity challenge– Capacity: #bedrooms in home– Demand: #family members• Benefits– My focus: shelter– Many others: stability, security, tax benefits, equity• Design variables– My focus: #bedrooms– Many others: location, age, external/internal features, aesthetics, appreciation potential3Model• Timeline (30 years)– Buy home in Year 0– Have children until Year 10– Family lives in home until Year 30– Sell home in Year 30• Home prices– Constant at current median prices– Rationale: we are buying in near future, inflation-adjusted house prices usually steady over time• Benefits– Occupied BR delivers $6000/year• Based on ½ value of a $1000/mo 1BR apartment– Children can share rooms if necessary– Unoccupied rooms deliver no valueUncertainties• Family size– Probability of having a child in a 2-year period is p = 0.8– #children N2Min 2M years is a binomial distribution:– E[N10] = 4, σN10= 0.89• Home/building prices– Assume constant for model, but obviously uncertain too– Median prices rounded to nearest $50K (zillow.com)– Adding bedrooms cost $50K/BR (costhelper.com)() (1)nMnMPN n p pn−⎛⎞== −⎜⎟⎝⎠0 1 2 3 4 500.20.40.60.81nP(N = n)Distribution of N10(#children in 10 years)5005BR House4504BR House4003BR Condo3502BR CondoMedian Price ($K)Home Type4Design Concepts• Big House (fixed)– Buy 5BR house for $500K in Year 0 – Delivers $30K/yr at capacity– Sell 5BR house for $500K in Year 30– Note: 5BR determined to be optimal fixed design• Small House (flexible)– Buy 3BR house for $400K in Year 0– Delivers $18K/yr at capacity– Expansion capability in Year 8: add BRs for $50K/BR– Sell 3BR house for $400K in Year 30• Condo (flexible)– Buy 2BR condo for $350K in Year 0– Delivers $12K/yr at capacity– Expansion capabilty in Year 8 : sell condo and buy a 4BR or 5BR house• Incur seller closing cost of $35K– Sell condo or 4/5BR house in Year 30Cash Flows300or$New Home6(N10+1)6(N8+1)or6(N8+1)+315 - $New Home6(N6+1)6(N4+1)6(N2+1)6-350Condo400 + 50 x #BRs Added6N10+1)6(N8+1)-50x #BRs Added6(N6+1)6(N4+1)6(N2+1)6-400Small House5006(N10+1)6(N8+1)6(N6+1)6(N4+1)6(N2+1)6-500BigHouse3010-298-96-74-52-310YearDesign Concept5Decision Tree• 2-stage decision tree– Stage 1: choose design concept in Year 0, then have children for 6 years– Stage 2: choose how/whether to expand in Year 8, then have children for 4 more yearsSolve Decision TreeStage 2• e.g., Small House – maximize E[NPV] of 2nddecision6Solve Decision TreeFold-back• e.g., Small House – Stage 2 pruned and folded backDecision AnalysisResults• Multiple Criteria• Value-At-Risk-Gain (VARG) curve• Conclusion– Small House is best by all metrics (except CAPEX)– Big House is second best8.3%3505547-2229Condo18.0%40010094-872Small House9.4%5008567-3047Big HouseROI(E[NPV] / CAPEX)CAPEX($K)P90($K)P50($K)P10($K)E[NPV}($K)CriteriaDesignConceptVARG0.00.10.20.30.40.50.60.70.80.91.0-300 -200 -100 0 100 200NPVCDFBig Small CondoBig Avg Small Avg Condo Avg7Lattice Development#childrenLattice Analysis• Start with Small House• Call option: to add 2BRs for $100K• Is it optimal to expand in next period?• Expand if…– 2 children by Yr 4– 2 children by Yr 6– 3 children by Yr 108Simulation• Monte Carlo simulation– 4000 trials for each design concept• VARG curves match those from Decision Analysis (as expected)VARG0.00.10.20.30.40.50.60.70.80.91.0-300.00 -200.00 -100.00 0.00 100.00 200.00NPVCDFBig Small CondoBig Avg Small Avg Condo AvgConclusions• Design concept ranking– Small House – defers & avoids costs– Big House – meets point estimate– Condo – hurt by seller closing costs• Lattice analysis most helpful because it allowed expansion in any period– DA and simulation only allowed expansion in Yr 8• Familiar now with mechanics of methods• Proficient in
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