1. Improving the versatility of D.C.F. models by simple computer applications

2. 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.

3. §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.

4. §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.

5. 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.

6. §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.

7. §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.

8. DCF-Simulation Model for Estimation of Land Value §Let’s assume that we need to estimate the value of a piece of land for commercial development with an office tower and a shopping mall. The investor intends to keep the retail portion of the project in his portfolio for ten years (including construction period of the first two years) as investment. The office tower will be sold off upon completion of the development.

9. §1) Design : §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 allowed430 units §Loan-to-value ratio of mortgage on land 60% §Maximum mortgage loan term 10 years

10. §2) Rentals §Rentals for the retail component vary quite substantially according to the actual location of the unit within the mall due to the value of accessibility and pedestrian flow. For simplicity reason, rental values are only divided into three ranges, namely ground floor, second floor and third floor rentals. §By the same token, estimated sale prices for offices also vary with floor height only. Hence, as a matter of simplicity in this example, there are only three price levels according to floor height for offices. §The rental levels for car-parking spaces are also categorized into three groups, but not on the basis of floor height. The range of car park rentals cover the fixed or designated parking spaces for monthly parking, “floating” monthly parking spaces and hourly parking spaces. Obviously, the fixed spaces would command the highest rental as the users will be guaranteed a fixed or designated location for parking in the building. The floating monthly car-parking spaces are less expensive as the users will have to spend time to locate vacant floating spaces in the car-park every time he is trying to park.

11. The Simulation §The whole issue of improving the assessment ability of finding the most probable expected land value from this D.C.F. simulation model evolves around the computer’s ability to conduct the automatic looping calculations among different worksheets. This is achieved by the macro commands. §What these macro commands direct is to perform the calculation in the relevant cells for the number of times set in the counter key, which in this case is 1000.

12. §As a result, this macro commands will return one thousand simulated land values from the D.C.F. analysis. By arranging these values in descending order according to the macro commands, one may find the minimum and maximum values, apart from the mean value. §In this case, the mean or expected land value is HK$3584 million, based on the average of these one thousand simulated values. The maximum value is HK$4603.09 million and the minimum simulated value is HK$2539.29 million. The analysis also provides with information on the standard deviation (HK$353.14 million), which shows the dispersions of the simulate values.

13. Simulation and feasibility analysis : §In this feasibility study, we assume that the land cost is HK$1,200 million with 60% financed by a mortgage loan and the rest of the cost injected as equity portion by the developer §expected average profit from the one thousand simulated values can be observed as seen in the summary table

14. §The model can also provide other indicators for the development’s feasibility, such as the periodic IRR and annual IRR, the overall rate of return, depending on the purposes of the analysis

15. 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

16. 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%