538

THE COLLIERY GUARDIAN.

March 14, 1913.

84 years. On behalf of the owner, he met the mineral
valuer stationed at Bradford. They agreed upon all the
factors affecting the valuation—that is, the deferred
period, the active period of the royalty, the area of the
field, thickness and price per foot per acre, and the rate
of discount—but on calculating the present value from
all the known factors they found there was a wide
difference between them, the district valuer’s amount
being 10 times his own amount. As none of the data
were in dispute, the difference was one solely of calcula-
tion—in fact, a difference of interpretation as to the
meaning of one of the functions—and on further
correspondence it was found that they did not attach
the same meaning to the expression “ discounted at the
rate of 10 per cent, per annum.” The writer thereupon
asked his son and partner, Mr. Daniel Stephen, to
ascertain as far as possible all the meanings which had
been attached to the expression, and to find out any
fallacies in them. He had put the result in the form of
a pamphlet (see p. 542 of this issue) as a contribution
to the subject of that afternoon’s discussion.

Mr. Stephen observed that the expected rents from
a mine could be quite correctly considered as a deferred
annuity, and the value calculated by finding a capital
sum to accumulate during the deferred period, and then
to provide the annuity and a sinking fund during the
active period. If this was done there were three rates of
interest to be determined:—(1) The rate for the deferred
period, (2) the rate for the active period, (3) the rate for
the sinking fund.

The method of dealing with tie problem was extremely
complex, gave rise to much difference of opinion with
respect to the various rates of interest to be charged,
but when calculated, after taking into account all the
conditions, gave the same result as obtained in the
method advocated. The modern practice by public
authorities of borrowing money, and providing a sinking
fund for repayment, had probably suggestedthe method
of dealing with the present values of mining royalties
in the same way. The problems in the two cases were
best solved by different methods, and it was much
simpler in the theory of the calculation of the present
values of mining royalties, instead of using the annuity
and sinking fund method, to use the discount method,
and deal with each expected year’s rent by itself
as a capital sum, and find its present value, as was
done in last chapter of the pamphlet. If this method
was followed only one question arose, and that was:
“At what rate shall a capital sum be discounted
for a given number of years?” When this rate
had been decided, each year’s expected rent could
be discounted by itself as a capital sum for the
determined number of years, and the total present
value obtained by adding each of the present values
together. When it was admitted that the method of
calculation put forward in the pamphlet was correct in
principle, there might be a further objection raised that,
with the rate of interest so high as 10 per cent., the
result of the calculation did not correspond with the
amounts, known to be paid as the result of experience in
the open market. This objection was foreign to the
pamphlet itself, which was concerned solely with the
method of calculation, and applied just as truly whether
the rate was taken at 10 per cent, or 8 per cent, or any
smaller percentage. The rate of interest had first to be
determined as a rate for discounting capital sums, and
this could be done oply from general considerations
quite independent of and prior to the determination of
how the calculation should be made. It was submitted,
however, that the calculated result substantially agreed
with experience. Estates were put up to auction which
were expected to have coal underneath them, but where
neither the depth, thickness, nor quality of the seams
were known. The intervening strata might be water-
bearing, and there was no expectation of working being
commenced within 30 years. In such cases it was a
general experience that very little if any more money
was paid than if the coal was not expected to be there.
If, however, in any case there was a discrepancy, it was
properly overcome by reconsidering the rate of interest
and not by the substitution of an erroneous method of
calculation. The Finance Act, 1909-10, by itself had
raised the question of the present values of deferred
mining rents to a position of much more importance
than it was previous to the passing of the Act, on
account of the more detailed and local machinery
provided by the Act for ascertaining the present values.
This was, however, of small importance in comparison
with the change proposed to be made by the valuers
themselves in the method of calculation.

Mr. W. M. Miller (Edinburgh) wrote that he did
not think Mr. O’Donahue, in his reply to his (Mr.
Miller’s) former remarks had appreciated the points he
was desirous of making. For instance, fears as to future
legislation could scarcely be met by a deduction from

estimated revenue. Again, if Mr. O’Donahue wished
the formula referred to by him to be adopted for general
application, he (Mr. Miller) thought it was incumbent
on him to explain how it could be satisfactory when
it produced paradoxical results, in very ordinary
instances, such as had been set forth in the discussion.
Mr. O’Donahue referred to “ Mr. Miller’s intuitive
method of valuing without rules or tables.” It must
surely have been apparent from his (Mr. Miller’s)
remarks that he was in the habit of using Hoskold’s
tables, and of course selecting the rate of interest
accordingly. The discussion tended to confirm him in
his view that attention was rather being directed to
what a person ought to give for a property than to what
he would give. It was of no use telling a purchaser of
minerals that he was only entitled to interest on his out-
standing capital, and not on his original outlay, and
that he must apportion part of the annual return for
redemption purposes and invest it at a particular rate,
which he might very probably not be able to obtain.
He wanted something more practical than that, and
particularly where there was no immediate revenue in
prospect he was very chary about purchasing. One had
only to look at the amount of mineral property in the
market seeking purchasers, and not even attracting an
offer, to realise that an extraordinarily high rate of
interest must be allowed, if Mr. O’Donahue’s formulae be
used, to arrive at valuations which there was any like-
lihood of a purchaser considering reasonable. Differing
from Mr. Smith, he (Mr. Miller) was of opinion that
there is an additional increment of risk due to deferment
such as to warrant the substitution of compound interest
at the high rate in calculating the accumulation of
capital during the deferred period. He could see little
use in extreme refinement of calculation when the lowest
valuation might be upset within a year by the imposition
of a Mineral Rights Duty of Is. per £, or when a valua-
tion might be rendered useless by a minimum wage or
similar Act being passed, converting it from a profitable
to an unprofitable concern; or even as regards a very
profitable colliery when a profit tax such as that
announced in France a few days ago might be imposed
at any time appropriating to the Government up to
one-third of the profits earned. In his opinion Hoskold’s
deferred tables did not make more than sufficient allow-
ance for such contingencies. If it were agreed in a
particular case with a life of, say, 30 years, that 10 per
cent, was a reasonable rate of interest, his (Mr. Miller’s)
contention was that if the first five or ten years were
cut out and only the remainder were for sale, then it
required the valuation to be not higher than that given
by Hoskold to find a purchaser. If the valuation was
made on Mr. O’Donahue’s system, then a higher rate of
interest must be used for the deferred period than was
considered suitable for the full period, otherwise a
purchaser would not be got. Something more than
formulae and tables were required for valuing mineral
property.

Dr. R. S. Heath (Birmingham University), in a
written communication, said the only question at issue
was whether 10 per cent, was a fair percentage to
anticipate during what he might call the “ period of
incubation” of the property as well as the period of
actual working. Discussing the problem enunciated by
Mr. Stephen, he said the purchaser presumably had
many securities to choose from, some free from risk,
producing say a safe 3 per cent, as well as that some-
what risky mining investment. All through the period
of incubation the purchase money was locked up in
mining securities ; the purchaser must therefore
estimate the profit at 10 per cent. The whole return
was speculative—each instalment of £3,750 which was to
accrue later was tinged with that speculative character,
and might through the risks of mining enterprise turn
out to be far less than the estimate. The purchaser
would not be justified in making the purchase unless
he could estimate the return at the rate of 10 per cent,
from the first and all through the period of incubation.
It was indeed all through the period of incubation just
as much as during the subsequent working of the
property, that the owner was exposed to special risks.
It was, therefore, his opinion that each deferred pay-
ment of rent should be discounted at the full 10 per cent.
He had arrived at tke same conclusion as Mr. Stephen
through his argument of probabilities.

Mr. R. F. Percy (Nottingham) also wrote to say that
the truth appeared to be that whatever the particular
method preferred by the valuer, if he appreciated the
mathematics of the formula and its proper application
to the particular case, he would arrive at a fair value.
There could be no absolute or exact value, for indefinite
properties must have indefinite values. Two valuers
attacking the same problem would probably arrive near
the same point although proceeding by different routes
—that was, provided they both endeavoured to reach a

just solution ; but if they approached the problem with
no intention of arriving at an equitable mean, one
seeking to find a high value and the other a low one,
the capital values they deduced would inevitably exhibit
marked disparity. He fully subscribed to Mr.
O’Donahue’s remark that the “ two-rate-throughout ”
method, “ although open to criticism of principle, is the
only satisfactory method for general application.” It
should be borne in mind that the argument which
defeated Hoskold’s method of deferment is equally fatal
to Inwood’s. To arrive at present values by the 1906
method, the writer some years ago constructed a slide
rule, which proved to be a very handy instrument, but
he afterwards replaced this by tables similar to that
given by Mr. O’Donahue later. These tables were
computed for seven rates, and are nearly complete for
100 years, but they were only correct to three figures.
In conclusion, Mr. Percy said he ventured to give the
following rules:—

Hoskold’s Values.—Take the amount of £1 per annum
at the low rate for the term, and multiply it by the
figure in the table for the same period.

Example.—The value of £1 per annum for 20 years at
8 per cent, for remuneration and 3 per cent, for redemp-
tion is 26’870 x -3175 = £8-531.

Deferred Annuity Two-rates-throughout.—Take the
amount of £1 per annum at the low rate for the period
of enjoyment and multiply by the figure in the table for
the total period (deferment plus enjoyment).

The example given would be thus simplified:—
11464 x *3497 x 1,000 = £4,008. It was very desirable
for mining engineers to adopt a uniform method if
possible; and if Mr. O’Donahue could make his theo-
retical method workable by designing a formula by
which the high rate of remuneration should alone be
deemed to be yielded by the capital value, and which at
the same time provided that with the repayment of the
capital the high rate dividends should correspondingly
decrease, the writer would be ready to bring it into
practical use without delay, and do his best to persuade
other mining engineers to adopt it also.

Mr. W. A. Mason (Birmingham) wrote to suggest
that the two contentions might be stated thus:—

1.	Is the investment to be considered “ wild cat ”
for 120 years ?

2.	Or is it to be considered “ gilt edge ” for 36 years
and “ wild cat ” for 84 years ?

Personally, he could not see any reasons to suggest
that the risks of the first period were less than those of
the second.

Mr. G. M. Cockin thought they were all agreed that
a high rate of interest was expected—at least 10 per
cent. But a great difference of opinion prevailed as to
the interest to be allowed for redemption of capital, and
these differences in the interest to be allowed gave widely
differing results. People talked about high and low
valuations ; but what was required was a true valuation.

Mr. Alexander Smith (Birmingham) said that on
a previous occasion he had given his views; and although
he could not agree with Mr. Donahue through all his
methods, he supported his view as to the treatment of
annuities during a period of deferment. He held that
the essence of all investment was that the original
capital outlay should be kept intact, and the transaction
should arrange for the annuity giving the interest
earned, and such an amount for redemption fund as
could be invested immediately without trouble, which
would be something gilt-edged, and accumulate to the
outlay at the end of the term. He therefore could not
agree with one rate of interest, as it was not convenient
to deal with sums at high rates; neither was it in
keeping with the safe return of the capital, as the high
rates gave much increased risk. Neither did he agree
with Mr. O’Donahue’s ingenious methods of showing
that as the investor was getting his capital reduced by
each payment of the redemption fund, he should be
allowed interest on the outstanding capital only, as the
calculation was for an interest to reproduce the capital
sum during the period of the annuity. That, however,
was a minor matter, and the tug of war came in dealing
with the deferred annuities. If one were a buyer, he
would like to adopt Mr. Stephen’s method, and if selling
that of Mr. O’Donahue; but one must be consistent,
and he would like to remove an impression that the
Government valuers were out for plunder, as this could
not be, for what they gained in death duties they would
lose in increment. As he stated in the last discussion,
he agreed with Mr. O’Donahue, that it was only fair to
take the two rates of interest during the time of defer-
ment, as the whole risk was covered by the high rate
adopted, and there was no such additional increment of
risks due to the deference of payment as to warrant the
substitution of compound interest at the high rate in
calculating the accumulation of capital during the
deferred period. When they came to the tables and the