40 BULLETIN 1224, U. S. DEPARTMENT OF AGRICULTURE. 
this constant increase to prevail in the future, and it was not pro- 
jected into the future until it had continued for a number of years. 
Furthermore, the buyers and sellers of land in this period still had 
vividly in their minds those years preceding 1896, when agricultural 
prices and land incomes were declining. They were, therefore, not 
so ready to project past increases in land incomes into the future as 
were the farmers in 1920. 
ANTICIPATED RATE OF RETURN ON INVESTMENTS IN FARM LANDS. 
There are two problems in connection with the anticipated rate of 
return on the investment: (1) What are future incomes expected to 
be? (2) what is the rate at which these expected incomes are dis- 
counted to a present worth ? 
If land incomes were constant year after year and were to continue 
so for all time, then the formula for land value would be v — — where 
r 
a is the annual net rent and r is the rate of interest at which these 
future constants rents are discounted to a present worth. Under 
these conditions the anticipated rate of return on the investment and 
the actual rate of return would be identical, and both rates would be 
identical with the rate of capitalization. This is true because the 
expected rate of return is the rate of capitalization at which these 
known future incomes are discounted to a present worth. For ex- 
ample, if the rate of capitalization were 5 per cent and the annual 
5 
rent $5, the present value would be $100, that is, v = -^ = $100, and 
conversely, the rate of return on this $100 would be r = - or tkfl = 5 per 
v 100 r 
cent. If the rate of interest were also constant, the rate of return 
on the investment and the rate of return on sale price in any given 
year would be identical. 
If land incomes are increasing, however, the above formula for 
land values no longer applies. Under these conditions the formula 
becomes v = — + — • If the future increases in a are known, then 
r r- 
again the anticipated and actual returns on the investment are the 
same and both are equivalent to the rate of capitalization. But here 
neither rate of return on the investment nor the rate of capitalization 
are equivalent to the rate of return on the value at a given time. 
In the years immediately following the investment, the rate of return 
will be low, but as time goes on the annual return will be greater 
and greater, so that in the long run the average return on the invest- 
ment will be equivalent to the rate of capitalization. In the early 
years the rate of return is lower than the rate of capitalization, but 
in the later years it is higher. The rate of return on the selling 
value at any given time, however, will always be lower than the 
rate of capitalization. Under conditions where v, a, and i are 
known, the rate of capitalization, or the long-run return on the 
a % 
investment, can be determined by solving the equation v = — -\--^i or r. 
Under actual conditions, the future increases in income are not 
known and have to be estimated. Since the future increases as 
