292 NATURE OF CAPITAL AND INCOME [Cmar. XVI
houses in the average would be worth $10,000 each were it
not for the risk of fire; in other words, that $10,000 is the
capitalized value of the services to be rendered by each
house, assuming that it lives out its natural life. The
value of the total number of houses would then be
$100,000,000. This is the “riskless value.” Tt is the
capitalized value of the income which the 10,000 houses
would bring in, were there no loss by fire. If interest is
at 5 per cent, the income which is thus capitalized is
$5000,000 a year. If now we suppose that the annual
risk of fire is one chance in 200, there will be about 50
houses annually burned. Reckoning the value thus de-
stroyed at an average of $10,000 for each house, there
will be $500,000 annually lost by fire. We must now de-
duct this from the $5,000,000, which would be the
income were it not for fires. We have left $4,500,000,
the capitalization of which is only $90,000,000. In
other words, the total property of 10,000 houses is
worth in “ mathematical value” $90,000,000 instead of
$100,000,000, the reduction being because of the prospect
of fires. If we suppose all of these houses to be owned by
one corporation, this mathematical value of $90,000,000
might also be the actual value, for such a corporation
could count on about 50 houses burning annually almost
as a certainty. Each house would then be worth, on an
average, $9000. But if such an individual house is owned
by an individual person, this mathematical value would
not be its ‘ commercial value,” on account of the element
of caution. Let us say that the caution coefficient is §, in
which case the house would be worth $7000. In other
words, we have $10,000 as the “riskless” value of the
house, $9000 as its “mathematical” value, and $7000 as
its actual “commercial” value, assuming that there is not
as yet insurance. Now if the owner of such a house could
secure insurance on a purely mathematical basis of the
risk, which, as we have seen, is one half of one per cent,
