The Fargo forum and daily republican. [volume] (Fargo, N.D.) 1894-1957, 1917-01-25

remain similar, but from q practical
viewpoint, an increase in capitalize
ton would be necessary In order to
meet the Increased cost.
Many important problems ariEing
in engineering practice may be solved
by making use OF what Is sometimes
termed capitalized cost BY capital
ICED cost, we mean the first cost, plus
the present value OF the cost OF indee-
mite renewals. An extension OF this
idea is to be found In the following:
Suppose a railroad company wishes to
find out how much may be expended
in treating ties costing TIC each laid
on the road-bed. to extend the life Of
tie from seven to fifteen years. The
principle involved as far as mathe-
matics Is concerned is to determine
what amount may be expended upon
an article costing a given sum, in or
der to extend its life from n given
number OF years to a desired number
of years.
"The problem to be solved consists
In determining the present value OF
the cost for the number Of years OF
extended life of the article, also the
present value of the annuity neces-
sary to meet the added expenditure.
I'm the cross-tie problem just given,
the result from the mathematical OPP
erations as just stated is 59c. That is
the railroad company can afford to
expend sec when money is worth 8
per cent in treating ties. provided the
life of the tie is extended from seven
to fifteen years.
The Cost of Paving.
Another illustration of this prin-
ciple is seen in the following: II BIZ
tulithic paving costs $500 per square
yard and has a probable life of twenty
years. $1.29 additional may be ex-
pended at time of construction, IL
money is worth per cent. in order
twenty to thirty years. That is an
expenditure Of 1929 per square yard
is warranted provided the life is ex-
tended ten years. Likewise 7Sc may
be expended provided the life Of the
paving is doubled.
'It can be proven in general that
the amount that may be expended in
original cost multiplied by the present
value of the cost due in years,
where k years is the life Of the ar
ticle without added expenditure.
Nov / wish to turn to q phase of
the mathematics Of investments when
mathematics itself bears a slightly
different relation than in our pre-
ceding illustrations and let US consid-
err the following problem:
'If city bonds itself for $250,000
for twenty years in order to erect a
new high school building what sum
must be set aside annually to meet
the debt when it falls due?
Fargo High School Cost.
This problem brings us at once to
the question of sinking funds, and our
problem in this case is the determi-
nation Of the amount Of the annual
payment that will extinguish the
debt in twenty years. If money is
worth 5 per cent the annual payment
required is $7,560.65. This is an an
nual payment to a sinking fund, when
money is invested at per cent effec-
tive, of $7,560.65 will extinguish the
debt in twenty years. OF course you
can readily see that there is an addi-
tional feature that mNst be met ann
ually exclusive of the sinking fund
the interest on the principal. How
ever, that has nothing to do with the
sinking fund ITSELF 1t may be OF in
terest at this particular time to know
that assuming the assessed valuation
of the city at $7,O0O,O00, the annual
cost Of $250,000 school building
to q taxpayer owning a residence
assessed at $1,000, would be approx
mately $3.50. In other words the tax
on a $1,000 residence property is $3.50
per year for 20 years, for the pro-
posed new high school building.