SOLUTION: Asset X generates a perpetual stream of cash flows of $100,000 every 3 months. The relevant interest rate is 12%, compounded quarterly. How much would you pay to buy Asset X today

The question is as follows:


    If you have enough amount of money Y, what is better for you:
       
         deposit this amount Y "all in one time" today into a bank at 12% compounded quarterly
                 or to buy today an asset X for Y dollars, from which you will deposit 
                     $100,000 every 3 months to a bank at 12% compounded quarterly?



First option generates  the amount of A =  =  = 1.125509*Y  dollars in one year.



Second option works as an Annuity Due saving plan and generates the amout 

    B =  =  = $430913.58  (rounded) in one year.


Therefore, the reasonable value/price to buy the asset X for one year is no more than 

    Y =  = $382861.07  dollars.


Thus, we calculated the reasonable value/price to buy the asset X for one year.


    Next, let's consider more longer time intervals of n = 3, 5, 10, 20, 50 and 100 years.


We should calculate  A(n) and B(n) using the formulas


   A(n) = ,  B(n) =  


and the ratio  Y(n) = , which is the reasonable value/price to buy the asset X for n year.


The table for the values of n, B(n) and Y(n) is shown/computed below


     n             Y(n)          B(n)
  -----------------------------------------     
     1		 430914		 382861
     3	        1461779		1025262
     5	        2767649		1532380
    10		7766330		2380822
    20		3310039         3110679
    50	      1264688299	3424038
   100      468384665935	3433308


From the table, it is seen that the values of B(n) raise significantly for n = 1, 3, 5, 10, 20 years, 
but after that, for n = 50, 100 years tends to some limit (to stabilization).


As everybody understands, the 12% percentage account is non-realistic for such long time as 20-30-50 years 
- - - therefore, I made my calculations in this lesson to present you more realistic picture.