1. Improving the versatility of D.C.F. models by simple computer applications Dr. LI Ling Hin Associate Professor Dept. of Real Estate and Construction The University of Hong Kong

2. Useful references : §1) Glenn Kautt and Fred Wieland “Modeling the future: The full monte, the Latin hypercube and other curiosities”, Journal of Financial Planning; Denver; Dec 2001; Vol. 14, Issue 12, pp78-88; §2) Craft, R. Kim “Using spreadsheets to conduct Monte Carlo experiments for teaching introductory econometrics”, Southern Economic Journal, Jan. 2003Vol.69, Iss. 3; pg. 726, 10 pgs, § 3) Rouse, Paul, “Constructing Monte Carlo Simulations on Lotus 1-2-3”, Journal of Accounting Education, Spring 1993, Vol. 11, Issue 1, p.113

3. Introduction §D.C.F. model of valuation provides mode sensible interpretation of real estate value, provided sensible assumptions are made. §Since major variables applied in the D.C.F. model do vary to a certain extent according to different market circumstances, this may affect the validity of the model.

4. §By incorporating the estimation of the “likelihood” of achieving a certain value for all the relevant variables by way of Monte Carlo simulation, the use of D.C.F. in property appraisal and analysis becomes more versatile.

5. §This paper shows that average appraiser with a basic computer knowledge can provide a further option of appraising real estate investment by way of D.C.F. simulation model, with relatively little difficulty. §The only limitation, however, is the quality control in the estimation of the input variables.

6. Monte Carlo Simulation §Simply put, where the probability distributions (and hence the cumulative probability) of most or even all of the variables are known, simulation techniques can be applied to analyze the expected outcome based on randomly drawn probability of these variables.

7. §Hence a randomly drawn figure for each of the variables will be generated in each single simulation process. §These “random” figures become the input variables to be used in the D.C.F. model for appraisal or analysis purposes. §The end result of this appraisal or analysis becomes the first set of “expected” value.

8. §When this simulation process is repeated to a certain times, such as one thousand or more times, the randomly drawn figures would be vary close to represent the probability of these figures actually appearing in the real world. §With these one thousand or more simulated values, an average mean value can be obtained so that the final expected outcome can be estimated.

9. Example - Investment Project §Total retail floor space allowed85,000 sq.ft. §ground floor30,000 sq.ft §second floor30,000 sq.ft §third floor25,000 sq.ft §Total office space allowed725,000 sq.ft. §lower level (15 floors)225,000 sq.ft §middle level (20 floors) 300,000 sq.ft §high level (20 floors)200,000 sq.ft §Total car-parking spaces allowed 430 units §Loan-to-value ratio of mortgage on land 60% §Maximum mortgage loan term 10 years §Land Price HK$1,200 million

10. Summary of Simulation Analysis  Expected Net Profit HK$m (before tax) : $2,179.4695 §Minimum value :$1,178.7371 §Maximum value : $3,975.3138 §Standard deviation :$397.62 §Expected Overall net rate of return :87.631% §(ie. discounted net profit / discounted total cash outflows ) §Expected IRR (p.a.)24.28% §Expected IRR (per quarter.)5.90%  Minimum value (per quarter) :4.20%  Maximum value (per quarter):7.81% §standard deviation :0.58%