Principles of Mining: Valuation, Organization and Administration

ation (Co

RTIZATION OF CAPI

he theory of amortization before consider

d as a return of capital. Therefore, before the yield on a mine investment can be determined, a portion of the annual earnings must be set aside in such a manner that when the mine is exhausted the original investment will have been restored. If we consider the date due for the return of the capital as the time when the mine is exhausted, we may consider the annual instalments as payments before the due date, and they can be put out at compound interest until the tim

nvestor. Mining business is one where 7% above provision for capital return is an absolute minimum demanded by the risks inherent in mines, even where the profit in sight gives warranty to the return of capital. Where the profit in sight (which is the only real guarantee in mine investment) is below the price of

t on it pending recovery. This is true, but as mines are seldom dealt with on the basis of profit in sight alone, and as the purchase price includes usually some proportion for extension in depth, an unknown factor is introduced which outweighs the known quantities. Therefore the application of the culminative effect of interest accumulations is much dependent upon the sort of mine under consideration. In most cases of uncertain continuity in depth it introduces a mathematical refinement not w

need of its introduction in calculations. Especially is this so where the cost of equipment is large proportionately to the annual return. Further, it may be said that such calculations are of decreasing use with increasing

ion of certain mines or mining investments. That is, by a sort of inversion such calculations can be made to serve as a means to expose the amount of risk,-to furnish a yardstick for measuring the amount of risk in the very speculations of extension in depth and price of metals which attach to a mine. Given the annual income being received, or expected, the problem can be formulated into the determination of how many years it must be continued in order to amortize the investment and pay a given rate of profit. A certain length of life is evident from the ore in sight, which may be called the life in sight. If the term of years requ

examples may be of assist

or estimated factors. It is then possible to determine the present value of this annual income after providing for amor

,000,000, thus recoverable in ten years. On a basis of a 7% return on the investment and amortization of capital (Table I), the factor is 6.52 x $200,000 = $1,304,000 as the present value of the

BL

er - Years at -% and Replacing Capital

6% 7% 8

4 .93 .9

2 1.78 1.7

3 2.56 2.5

8 3.27 3.1

9 3.93 3.7

4 4.53 4.3

6 5.09 4.8

3 5.60 5.3

7 6.08 5.7

98 6.52 6.

45 6.94 6.

90 7.32 6.

32 7.68 7.

72 8.02 7.

09 8.34 7.7

45 8.63 7.9

78 8.91 8.1

.10 9.17 8.

.40 9.42 8.

.68 9.65 8.

.95 9.87 8.

.21 10.08 9

.45 10.28 9

.68 10.46 9

.90 10.64 9

.11 10.80 9

.31 10.96 9

50 11.11 10.

68 11.25 10.

85 11.38 10.

01 11.51 10.

17 11.63 10.

31 11.75 10.

46 11.86 10.

59 11.96 10.

72 12.06 10.

84 12.16 10.

96 12.25 10.

07 12.34 10.

18 12.42 11.

from Inwoo

sent value of a fixed sum payable at the end of a given term of years, interest being disco

LE

￡1, payable in - Years

4% 5

.952 .9

.907 .8

.864 .8

.823 .7

.783 .7

.746 .7

.711 .6

.677 .6

.645 .5

.614 .

.585 .

.557 .

.530 .

.505 .

.481 .

.458 .

.436 .

.415 .

.396 .

.377 .

.359 .

.342 .

.325 .

.310 .

.295 .

.281 .

.268 .

.255 .

.243 .

.231 .

.220 .

.210 .

.200 .

.190 .

.181 .

.172 .

.164 .

.156 .

.149 .

.142 .

from Inwoo

loss of interest in delay and the cost of equipment. In this case the present value of $1,304,000 in two years, interest at 7%, the factor is .87 X 1,304,000 = $1,134,480. From this comes off the cost of equipment,

LE

terest, and in addition to furnish annual instalments which, if reinves

% 7% 8

41

8.0

6 28.

21.6 28

7.7 21.6

.0 17.7 21

.0 15.0 17

.5 13.0 15

3 11.5 13.

10.3 11.5

6 9.4 10.

9 8.6 9.4

3 7.9 8.6

.8 7.3 7

.4 6.8 7

.0 6.4 6

.7 6.0 6

.4 5.7 6

.1 5.4 5

.9 5.1 5

.7 4.9 5

.5 4.7 4

.3 4.5 4

.1 4.3 4

.9 4.1 4

, especially in weighing the risks involved in the portion of the purchase or investment unsecured by the profit in sight. Given the annual percentage income on the investment from the dividends of the mine (or on a non-producing mine assuming a given rate of production and profit from the factors exposed), by reference to the table the number of years can be seen in which this percentage must continue in order to amortize the investment and pay various rates of interest on it.

the ore in sight is ten years, then the extensions in depth must produce ore for 11.6 years longer-1,160,000 tons. If the ore-body is 1,000 feet long and 13 feet wide, it will furnish of gold ore 1,000 tons per foot of depth; hence the ore-body must extend 1,160 feet deeper to justify the price. Mines are seldom so simple a proposition as this example.

point of view under "Ratio of Output." If the plant on this mine were doubled and the earnings increased to 20% ($400,000 per annum) (disregarding the reduction in working ex

nsion. Similarly, the present value of the ore in sight is $268,000 greater if the mine be given double the equipment, for thus the idle money locked in the ore is brought into the interest market a