44 MISC. PUBLICATION 218, U. S. DEPT. OF AGRICULTURE 
of these distant taxes and of the immediate future taxes which must 
be paid during the period of waiting is $5,820. The present value 
of the capital before taxes is $15,820, and the tax ratio is 36.8 percent. 
Since the value of the capital after taxes is $10,000, however, just 
what the second brother received in his legacy, he has no complaint 
against his tax burden. 
A similar conclusion can be drawn with respect to the third brother. 
In his case the present value at 3 percent of all taxes which he will be 
required to pay before his legacy has vanished is $264. The present 
value of the capital before taxes is then $10,264, and the tax ratio 
2.6 percent. Here again the value of the capital after taxes is $10,000, 
the amount that was received in his legacy. He thus gains no advan- 
tage from the comparatively low taxratio. The details of the incomes 
for the several brothers and the corresponding values of the respec- 
tive capitals and taxes from year to year are shown in table 20. 
TABLE 20.—Capital, tax, and income of three brothers, each having different income 
streams } 
| First brother Second brother | Third brother 
Time (FRR anaphora ay 
| Capital | Tax | Income | Capital | Tax Income | Capital | Tax | Income 
a 
At beginning_____ 10s O00) sae |ise eee ee S10;0003/ ees ae eee $10) 000): Bane Re | seeaerwes 
In 1 year_____.-._| 10,000 | | $100 $400} 10,400} $100.00 0 7,200 '$100.00 | $€2, 500 
In 2-years_2._ 1 | 10,009} 100 400 | 10,816 104. 00 0 5,720} 79.00} 2,500 
In 3 years___-.-_--| 10, 609 100 400 11, 249 108. 16 0 3,450 | 57. 2! 2, 500 
In 4 years_--._--.-; 10, 000 100 400 11, 699 112. 49 0 1, 080 34. 50 2, 500 
Impoiyears = 252 | 10, 000 100 400 12, 167 116. 99 0 0| 10.80 1, 130 
linkosyearses-s2o a= | 10, 000 100 400} 12,683 121. 67 0 0 . GO | 0 
THaVeals= seo see | 10, 000 100 400; 18,159 126. 53 0 0 . 00 | 0 
yes) yearsess2 as sk | 10,000 100 430 13, 686 131. 59 0 0 . 00 0 
tile) AOR See 10, 000 100 400 14, 233 136. 86 0 0 . 00 0 
Tn 20'years=-= 0. 3-- 10, 000 100 400 14, 802 142. 33 0 0 . 00 0 
nm iinyears=-25 =. 10, 000 100 400 15, 395 148. 02 0 0 . 00 | 0 
In J2 years__-.---- 10, 000 100 400 16, 010 153. 95 0 0 . 60 | 0 
Tr svears-i22 7 - 10, 0600 100 400 16, 651 160. 10 0 0 . 6d | 0 
14 years________ 10, 000 100 400 17, 317 166. 51 0 0 . 00 | 0 
tiv earsass sere) 10, 000 100 400 | 18,009 79. 17 0 0 . 00 0 
16 years__..___- 10, 000 100 400! 18, 730 180, 09 0 0 . 00 0 
l7syears= === = 10, 000 100 400 19, 479 187. 30 0 0 . 00 0 
18svearseee 10, 000 100 400 20, 000 194.7 $267 0 . 00 0 
in 19 years and | 
| 0 . 00 0 
| 
thereafter______- 10, 000 100 400 | 20,000 | 200. 00 800 
1 Assessment date is at beginning of year. Tax is paid at end of year; tax rate, 1 percent. Capital is the 
sum of all future net incomes after tax discounted at 3-percent interest. 
With proper capitalization of taxes, therefore, owners who acquired 
their capital after the present tax was established can charge no 
present Injustice to the property tax on account of the tax ratio as 
long as the tax rate remains the same. It is probable, however, that 
taxes are seldom completely capitalized, owing to the inherent 
optimism of buyers and sellers and to their ignorance of what the 
future tax burden will be. In addition, land values are frequently so 
inelastic that apparently neither taxes nor any other expected item 
of expense or income can be said to be completely capitalized. In 
such cases prices are more or less traditional. To whatever extent 
capitalization of real estate taxes may fail to become fully effective, 
there is direct discrimination against real estate investments of the 
deferred-yield type. 
