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Gangming	
  Liang


                                                                                                                                                The Relationship between NPV & Discount Rate                                                                                                                                                                                                                                                                                                                                                    Black-­‐Scholes	
  Price	
  versus	
  Intrinsic	
  Value	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         16.00	
  	
  
                                                                   1200




                                                                                                                                                                                                                                                                                                                                                                                                                 Call	
  Price	
  and	
  Intrinsic	
  Value	
  ($)	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         14.00	
  	
  
                                                                    900
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         12.00	
  	
  
                                                NPV	
  ($MM)	
  




                                                                                                                                                                                                                                                                                                                                                                                                                                                                         10.00	
  	
  
                                                                    600
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           8.00	
  	
  
                                                                    300
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           6.00	
  	
  

                                                                                                                                                                                                                                                                                                                                                                                                                                                                           4.00	
  	
  
                                                                        0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           2.00	
  	
  
                                                                   -300
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           0.00	
  	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          5	
                 7.5	
                  10	
              12.5	
                   15	
                17.5	
             20	
          22.5	
                 25	
            27.5	
                        30	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Stock	
  Price	
  S	
  ($)	
  
                                                                                                                                                                                                      Discount	
  Rate	
                                                                                                                                                                                                                                                                                                                                          Call	
  Price	
             Intrinsic	
  Value	
  

                                                                                                                                                                                                Years	
  
                                                                                   1	
                          2	
                         3	
                           4	
                  5	
        6	
                              7	
                       8	
                   9	
                       10	
                                                                                                                                                                                                                               The	
  Rela9onship	
  Between	
  FV	
  &	
  Years	
  
                                                       -­‐$500	
                                                                                                                                                                                                                                                                                                                                                                                        2400	
                                                                                                                                                                                                                         0	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       0.05	
  
                                         -­‐$2,000	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                        2000	
                                                                                                                                                                                                                         0.1	
  
   Payment	
  




                                         -­‐$3,500	
                                                                                                                                                                                                                                        I	
  PMT	
                                                                                                                                                                                                                                                                                                                                                                                 0.15	
  
                                                                                                                                                                                                                                                                                                                                                                                                        FV	
  
                                                                                                                                                                                                                                                                                            L	
  PMT	
                                                                                                        1600	
                                                                                                                                                                                                                                                                   0.2	
  
                                         -­‐$5,000	
  

                                         -­‐$6,500	
                                                                                                                                                                                                                                                                                                                                                                                                    1200	
  

                                         -­‐$8,000	
                                                                                                                                                                                                                                                                                                                                                                                                                       800	
  
                                                                                                                                                Rela9onships	
  between	
  I	
  PMT,	
  L	
  PMT,&	
  Years	
  	
                                                                                                                                                                                                                                                                                     0	
                              1	
                                  2	
           Years	
   3	
                                         4	
                               5	
  
                                                                                                                                                                                                                                                                                                                         y	
  =	
  1.5807x	
  +	
  0.0075	
  
                                                                                                            Rela9onship	
  Between	
  Stock	
  A	
  Return	
  and	
  S	
  &	
  P	
  500	
  R	
  eturn	
                                                                                                                             R2	
  =	
  0.5911	
                                                                                                                                                                 Rela9onships	
  betwwen	
  Return	
  &	
  Beta	
  of	
  Stock	
  A,	
  Stock	
  B,	
  &	
  
                                                                   0.2	
                                                                                                                                                                                                                                                                                                                                                                                      0.15	
  
                                                                                                                                                                                                                                                                                                                        Stock	
  A	
  Beta	
  =	
  1.5817	
                                                                                                                                                                                           SML	
  	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                              0.12	
  
         Stock	
  A	
  Return	
  




                                                         0.12	
                                                                                                                                                                                                                                                                                                                                           Return	
  (%)	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                SML	
                                                                                                                     A	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                              0.09	
  
                                                         0.04	
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            B	
                                   Market	
  Index	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                              0.06	
  
                                                     -­‐0.04	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                              0.03	
  
                                                     -­‐0.12	
                                                                                                                                                                                                                                                                                                                                                                                                                   0	
  
                                                            -­‐0.06	
                                                             -­‐0.03	
                                             0	
                      0.03	
                                               0.06	
                                                                                                                                                                                                                  0	
                         0.2	
                       0.4	
                              0.6	
                   0.8	
                      1	
                       1.2	
                             1.4	
  
                                                                                                                                                                                   S	
  &	
  P	
  500	
  Return	
                                                                                                                                                                                                                                                                                                                                                                                  Beta	
  
                                                                                                                                                                                 QUARTERLY	
  SALES	
  
                                                                                                                                          (Data	
  values	
  are	
  shown	
  as	
  solid	
  circles,	
  forecasts	
  as	
  a	
  heavy	
  jagged	
  line,	
                                                                                                                                                                                                                                                                                                                Average Forecast
                                                42000	
                                                                                                        and	
  the	
  projected	
  CMA	
  as	
  a	
  dashed	
  line.)	
                                                                                                                                                                                                                                                        0.1
                                                40000	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  0.08
                                                38000	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  0.06
         QUARTERLY	
  SALES,	
  $	
  MILLION




                                                36000	
  

                                                34000	
                                                                                                                                                                                                                                                                                                                                                                                                                          0.04
                                                32000	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  0.02
                                                30000	
  
                                                                                                                                                                                                                                                                                                                                                                                                                              %




                                                28000	
                                                                                                                                                                                                                                                                                                                                                                                                                                           0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              2011                             2012                        2013                         2014                    2015                      2016                         2017
                                                26000	
                                                                                                                                                                                                                                                                                                                                                                                                                       -0.02
                                                24000	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              -0.04                                                                                                                                                                     GNP
                                                22000	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Inflation
                                                20000	
                                                                                                                                                                                                                                                                                                                                                                                                                       -0.06
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        T- Bills
                                                                    17	
             18	
              19	
             20	
           21	
               22	
            23	
   24	
     25	
      26	
            27	
            28	
           29	
        30	
              31	
              32	
        33	
                34	
                       35	
                         36	
  
                                                                                                                                                                            QUARTER	
  NUMBER	
  (Quarter	
  17	
  is	
  the	
  first	
  quarter	
  of	
  1995.)
                                                                                                                                                                                                              -0.08                                                                                                                   Years                                             30- Year T- Bonds

Sale	
  Year

                                                                         2E+09	
  
                                                                                                                                                       2004
                                                                                                                                                                                       AQR	
  Distribu9on	
                                                                                                                           400	
                                                                                                                                                                                                                         2004	
  Sales	
  Ac9vi9es	
  
                                                                                                                                                       Data
Sale	
  Month                                                                                                                                          Sum	
  of	
  Sales	
  ($)                                               Number	
  of	
  Deals                                                             Sale	
  Month                      Sum	
  of	
  Sales	
  ($) Number	
  of	
  Deals                                                                        18000000	
                                                                                                                                                                                                         80	
  
                                                                                                                                                   1                                                            4,827,000                                                            30                          January              350	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  4,827,000
                                                                                                                                                                                                                                                                                                                                        	
  	
  	
                                              30

                                                                    1.6E+09	
  
                                                                                                                                                   2
                                                                                                                                                   3
                                                                                                                                                                                                                8,797,000
                                                                                                                                                                                                               15,824,036
                                                                                                                                                                                                                                                                                     40
                                                                                                                                                                                                                                                                                     67
                                                                                                                                                                                                                                                                                                                 February
                                                                                                                                                                                                                                                                                                                 March
                                                                                                                                                                                                                                                                                                                                        	
  	
  	
   8,797,000
                                                                                                                                                                                                                                                                                                                                                     	
  	
  	
  	
  	
  	
  
                                                                                                                                                                                                                                                                                                                                                                         15,824,036
                                                                                                                                                                                                                                                                                                                                                                                                40
                                                                                                                                                                                                                                                                                                                                                                                                67
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           16000000	
                                                                                                                                                                                                         70	
  
                                                                                                                                                   4                                                            8,672,692                                                            42                          April                300	
          	
  	
  	
  	
  	
  	
  	
  	
  8,672,692  42                                                                         14000000	
                                                                                                                                                                                                         60	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    #	
  of	
  Deals	
  
                                                                                                                                                   5                                                            5,575,000                                                            27                          May                                 	
  	
  	
  	
  	
  	
  	
  	
  5,575,000  27
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           12000000	
  
                                                                                                                                                                                                                                                                                                                                                                                                                  Amount	
  




Grand	
  Total                                                      1.2E+09	
  
                                                                                                                                                   6                                                            8,042,000
                                                                                                                                                                                                               51,737,728
                                                                                                                                                                                                                                                                                     42
                                                                                                                                                                                                                                                                                    248
                                                                                                                                                                                                                                                                                                                 June
                                                                                                                                                                                                                                                                                                                                      250	
          	
  	
  	
  	
  	
  	
  	
  	
  8,042,000  42
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              50	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                           10000000	
  
                                                                                                                                                                                                                                                                                                                                                                              #	
  Deals	
  
   Dollars	
  




                                                                                                                                                                                                                                                                                                                                      200	
                                                                                                                                                                                                                                                                                                                                                   40	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            8000000	
  
                                                   800000000	
                                                           Statement of Cash Flow, For the Year Ended Dec. 31, 2004 ($ 000's)                                                                                                                                           150	
                                                                                                                                 6000000	
                                                                                                                                                                                                         30	
  
Cash Flows from Operations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            4000000	
                                                                                                                                                                                                         20	
  
Net Income                                                                                                                                                                                                             44.22
                                                                                                                                                                                                                                                                                                                                      100	
  
Depreciation Expense
Change in Accounts Receivable
                                                   400000000	
                                                                                                                                                         20.00
                                                                                                                                                                                                                      -50.80                                                                                                                                                                                                                                                2000000	
                                                                                                                                                                                                         10	
  
Change in Inventories                                                                                                                                                                                                -120.80                                                                                                          50	
                                                                                                                                        0	
                                                                                                                                                                                                         0	
  
Change in Accounts Payable                                                                                                                                                                                             29.60

                                                                                             0	
                                                                                                                                                                                                                                      0	
                                                                                                                                                                               January	
                February	
                           March	
                   April	
                 	
                           June	
  
                                                                                                                1	
                        2	
                           3	
                 4	
           5	
                         6	
                   7	
                   8	
                       9	
                                                                                                                                                                                                                                                                                   Month	
                             May	
  
                                                                                                                                                                                                         AQR	
  

                                                                                                                                                          Histogram	
  for	
  Tobacco	
  Industry	
                                                                                                                                                                                                                                                                                                                                                           Stove Sales by State

                                                                                                     0.3	
  
                                                                             Freqyency	
  




                                                                                                     0.2	
                                                                                                                                                                                                                                                                                                                                                                      Maine
                                                                                                      0.1	
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Circle

                                                                                                        0	
                                                                                                                                                                                                                                                                                                                                                              Vermont                                                                                                                                                                                                                Box
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Star
                                                                                                                                 19	
              21	
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         West
                                                                                                                                                                          23	
             25	
                                                                                                                                                                                                          Massachusett
                                                                                                                                                                                                              27	
                 29	
                                                                                                                                                                       s
                                                                                                                                                                                                                                                         31	
  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         0         50000              100000               150000              200000              250000          300000         350000                 400000         450000
                                                                                                                                                                                                 Ages	
  
Cash Flow Projections - Utilities NOT Included

                                                                                                                 General Information (Flexible)                                                                                                                                            Sq.Ft. & Lease Rates                                                                                                                                                                                                                       Cost Breakdown
                                                                                                                                                                                                                                                                                                                                                          Lease Rate
                                                                                                                                                                                                                                                                                                                 Total Leasable                            without                                   Lease Rate
Total Sq. Ft. Constructed:                                                                                                                                                              22,757                                                         Floor                                       Purpose           Space                                 Utilities                                with Utilities                                                                                                      Hard Costs               $5,120,325
Per SF Const. Cost:                                                                                                                                                                    $225.00                                                           1                                  Retail (Sq. Ft.)              3,000                                  $2.50                                 $2.65                                                                                                            5% Contingency HC        $256,016
Construction Costs:                                                                                                                                                                   $7,376,341                                                       2 to 5                             Residential (Sq. Ft.)          13,344                                  $4.00                                 $4.15                                                                                                            Land                     $2,000,000
Rent Inflation Estimate:                                                                                                                                                                3.00%                                                            1                                 Parking (Spaces)                   12                              $200.00                                 $200.00                                                                                                           Soft Costs                    $0
Fully-stabilized Income Cap Rate                                                                                                                                                        4.50%                                                                                                                                                                                                                                                                                                                           5% Contingency SC             $0
Not fully stabilized Income Cap Rate                                                                                                                                                    5.00%                                                                                                                                                                                                                                                                                                                           Subtotal                $7,376,341
                                                                                                                                                                                                                                                          Building Completion Schedule                                                                                     Cost Breakdown                                                                                                                               Ramp-Up Cost Year 1           $0
                                                                                                                                                                                                                                                       Month                              Floors CompletedAvail. To Rent Hard Costs                                                                 $5,120,325                                                                                                          Grand Total             $7,376,341
                                                                                                                                                                                                                                                        12                                          1,2,3                 1,2,3                     5% Contingency HC $256,016
NPV Discount Rate Relationship
NPV Discount Rate Relationship
NPV Discount Rate Relationship
NPV Discount Rate Relationship

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NPV Discount Rate Relationship

  • 1. Gangming  Liang The Relationship between NPV & Discount Rate Black-­‐Scholes  Price  versus  Intrinsic  Value   16.00     1200 Call  Price  and  Intrinsic  Value  ($)   14.00     900 12.00     NPV  ($MM)   10.00     600 8.00     300 6.00     4.00     0 2.00     -300 0.00     5   7.5   10   12.5   15   17.5   20   22.5   25   27.5   30   Stock  Price  S  ($)   Discount  Rate   Call  Price   Intrinsic  Value   Years   1   2   3   4   5   6   7   8   9   10   The  Rela9onship  Between  FV  &  Years   -­‐$500   2400   0   0.05   -­‐$2,000   2000   0.1   Payment   -­‐$3,500   I  PMT   0.15   FV   L  PMT   1600   0.2   -­‐$5,000   -­‐$6,500   1200   -­‐$8,000   800   Rela9onships  between  I  PMT,  L  PMT,&  Years     0   1   2   Years   3   4   5   y  =  1.5807x  +  0.0075   Rela9onship  Between  Stock  A  Return  and  S  &  P  500  R  eturn   R2  =  0.5911   Rela9onships  betwwen  Return  &  Beta  of  Stock  A,  Stock  B,  &   0.2   0.15   Stock  A  Beta  =  1.5817   SML     0.12   Stock  A  Return   0.12   Return  (%)   SML   A   0.09   0.04   B   Market  Index   0.06   -­‐0.04   0.03   -­‐0.12   0   -­‐0.06   -­‐0.03   0   0.03   0.06   0   0.2   0.4   0.6   0.8   1   1.2   1.4   S  &  P  500  Return   Beta   QUARTERLY  SALES   (Data  values  are  shown  as  solid  circles,  forecasts  as  a  heavy  jagged  line,   Average Forecast 42000   and  the  projected  CMA  as  a  dashed  line.)   0.1 40000   0.08 38000   0.06 QUARTERLY  SALES,  $  MILLION 36000   34000   0.04 32000   0.02 30000   % 28000   0 2011 2012 2013 2014 2015 2016 2017 26000   -0.02 24000   -0.04 GNP 22000   Inflation 20000   -0.06 T- Bills 17   18   19   20   21   22   23   24   25   26   27   28   29   30   31   32   33   34   35   36   QUARTER  NUMBER  (Quarter  17  is  the  first  quarter  of  1995.) -0.08 Years 30- Year T- Bonds Sale  Year 2E+09   2004 AQR  Distribu9on   400   2004  Sales  Ac9vi9es   Data Sale  Month Sum  of  Sales  ($) Number  of  Deals Sale  Month Sum  of  Sales  ($) Number  of  Deals 18000000   80   1 4,827,000 30 January 350                      4,827,000       30 1.6E+09   2 3 8,797,000 15,824,036 40 67 February March       8,797,000             15,824,036 40 67 16000000   70   4 8,672,692 42 April 300                  8,672,692 42 14000000   60   #  of  Deals   5 5,575,000 27 May                5,575,000 27 12000000   Amount   Grand  Total 1.2E+09   6 8,042,000 51,737,728 42 248 June 250                  8,042,000 42 50   10000000   #  Deals   Dollars   200   40   8000000   800000000   Statement of Cash Flow, For the Year Ended Dec. 31, 2004 ($ 000's) 150   6000000   30   Cash Flows from Operations 4000000   20   Net Income 44.22 100   Depreciation Expense Change in Accounts Receivable 400000000   20.00 -50.80 2000000   10   Change in Inventories -120.80 50   0   0   Change in Accounts Payable 29.60 0   0   January   February   March   April     June   1   2   3   4   5   6   7   8   9   Month   May   AQR   Histogram  for  Tobacco  Industry   Stove Sales by State 0.3   Freqyency   0.2   Maine 0.1   Circle 0   Vermont Box Star 19   21   West 23   25   Massachusett 27   29   s 31   0 50000 100000 150000 200000 250000 300000 350000 400000 450000 Ages   Cash Flow Projections - Utilities NOT Included General Information (Flexible) Sq.Ft. & Lease Rates Cost Breakdown Lease Rate Total Leasable without Lease Rate Total Sq. Ft. Constructed: 22,757 Floor Purpose Space Utilities with Utilities Hard Costs $5,120,325 Per SF Const. Cost: $225.00 1 Retail (Sq. Ft.) 3,000 $2.50 $2.65 5% Contingency HC $256,016 Construction Costs: $7,376,341 2 to 5 Residential (Sq. Ft.) 13,344 $4.00 $4.15 Land $2,000,000 Rent Inflation Estimate: 3.00% 1 Parking (Spaces) 12 $200.00 $200.00 Soft Costs $0 Fully-stabilized Income Cap Rate 4.50% 5% Contingency SC $0 Not fully stabilized Income Cap Rate 5.00% Subtotal $7,376,341 Building Completion Schedule Cost Breakdown Ramp-Up Cost Year 1 $0 Month Floors CompletedAvail. To Rent Hard Costs $5,120,325 Grand Total $7,376,341 12 1,2,3 1,2,3 5% Contingency HC $256,016