FOREST FIHAHCE 7 



(G) 



0. Op 



The aft-value of single payments, annuities and periodical payments at 

 the end of an indefinite period is itself indefinite ( OO )• 



The pre-value of a single payment due after an indefinite period of years 

 is equal to zero. 



The pre-value (V) of annuities or periodical payments running for an 

 indefinite number of years is, however, something very definite, namely, dis- 

 counted backwards to the present day, in the case of an annuity: 

 R 



V - (I) 



0. Op 

 or 

 P R 



100 V 



It appears at a glance that this pre-value (V) derived from never-failing 

 annuities — is merely the capital from which a perpetual revenue of p% is 

 expected. Unknowingly, the investor usually figures at indefinitely long per- 

 iods of never failing returns when capitalizing such returns at a given rate 

 of interest. It is only too well known, however, that all investments, except- 

 ing pure real estate investments, have a merely temporary lease of life. As 

 an illustration, we might mind the fact, that the majority of all insurance 

 policies are surrendered, — the insured being unable to pay his dues when he 

 meets with financial reverses : Business investments, in the majority of cases, 

 seem to end unluckily for the investor. 



The pre-value (V) of periodical payments (R) hereafter due at the end 

 of every "mth" year until infinity is 

 R 



V - (J) 



1. Op" — 1 



The influence on present values exercised by payments (receipts or ex- 

 penses), expected after 100 and more years, is very small. 



For the financial prospects of an enterprise, the current expenses and 



receipts of the first (n) years are 



(l.op°-l) 

 times as influential as the current expenses and receipts of any and all years 

 following after the nth year. 



The above factor of influence, viz. (1. op" — 1), equals 10 within 

 60 years, in case of 6% investments; 

 63 years, in case of 4% investments; 

 83 years, in case of 3% investments. 



