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SHIPPING DEPARTMENT RECEIPT

Received of
the following described goods returned:

Returned because

Clerk in Charge.

Fig. 5

tomer or source from which return comes, one to be retained by shipping department, and one to be sent to the accounting department. (See Fig. 5.)

The shipping department should send goods out only on receipt of an order from the sales department. The sales orders

No._19

Feb. 19_ 1908
SALES ORDER
To SHIPPING DEPARTMENT:

P. & R. Freight
Please ship via

James Brown place 117 X St., Phila. the following:

Two 10 H. P. Gasoline Motors.

Terms 30 days

J. A. FULLERTON

Salesman.

A. L. MATTERSON

Sales Manager.

Fig. 6

should be made out in triplicate, the original to be retained in sales department, duplicate and triplicate sent to the shipping clerk. The shipping clerk will fill out the order as far as possible, checking off all the items he has been able to deliver, then send the triplicate to the accounting department where it will be used as an original record for the ledger credits while he will retain the duplicate for his own reference files, taking care to notify the sales department of any inability to fill out all the requirements of any order.

The two figures 6 and 7 illustrate a form for the sales order and the ledger respectively. Once such a system is established it is no harder to carry out and adds very little relatively to the costs of manufacture and selling than the ordinary method which records all sales in the Sales Ledger only. When inventory time comes around it affords a very large saving and it always possesses the great advantage of telling one at any time the exact condition of the stock on hand.

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Stock Value of a Bond.

BY CHARLES E. SPRAGUE, Ph. D. C. P. A. The longer time a bond has to run, the greater is its premium or discount, but the differences from year to year become gradually less. Thus a 5 per cent. bond on a 4 per cent. basis is worth per dollar, if it has five years to run..

1.044913 ten years to run.

1.081757 fifteen years to run.

1.111982 twenty years to run.

1.136777 twenty-five years to run.

1.157118

* * *

ninety-five years to run.

1.244194 one hundred years to run.

1.245237 three hundred years to run...

1.249909 The difference between a ninety-five and a one hundred year maturity is far less than between a five and a ten year maturity. There is : limit heyond which the value cannot pass, no matter how long the time, and this limit is the value of a perpetual bond, which we call the stock value, being like the value of a share of preferred stock guaranteed to pay a fixed dividend but bought on a certain income basis.

If we know the cash interest (c) and the income basis (i) it is easy to find the stock value. The stock value multiplied by i must give c; therefore c divided by i must give the stock value.

In the example above, the stock value, obtained by dividing .05 by .04, is 1.25, and this is the limit which the values given above constantly approach, yet never pass. 25 might be called the stock premium.

If the income basis were less than the cash received the stock value would be less than 1. If c = .04 and i = .05, the stock value would be .80, and the stock discount would be .20.

In order to be able to embrace in one name both premiums and discounts, we will speak of the variance from par as variance; referring to the stock values, the stock variance.

The stock variance is - I, or in another form, op

Example. Let c = .6 and i = .045; the stock value is 1.50 and the stock premium is .50.

Let c = 5 and i = 6: the stock value .8333 and the stock discount is .1667.

Mr. Arthur S. Little, of St. Louis, has devised an ingenious method of calculating the value of a terminant bond by first finding its stock value and then applying a difference derived therefrom.

A Stock value does not change; it is true for all future time. Thus the stock value of a 5 per cent. bond yielding 4 per cent. is 1.25 and will be the same at all future times, say twenty-five years from now....

.. 1.25 Let us suppose that the new condition is introduced, that the bond will be paid off in twenty-five years, that is, its value will then be......

. 1.00

The difference is......

.25 not at present but in twenty-five years.

Reduced to the present time, the difference is the present worth of .25, due twenty-five years from now that is.....

.095882

the stock value being. and the difference..

.1.25

.092882

the twenty-five year value is......

.1.157118 The difference between the stock value and the term value is the present worth, for the unexpired time, of the stock variance. This is substantially the rule laid down by Mr. Little. Symbolically this difference may be represented thus

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But this same difference must exist between the stock-variance
and the term-variance. The expression for the term-variance is
therefore
c-i chi

c-i
x
(1+i)"

(1+i)"

which is the form given on page 54, Problems and Studies. It may be read: “The term-variance is the compound discount of the stock-variance.”

All the methods of computing bond values bring the same result and may be transformed algebraically each into the others. We may note the following, premising that + is used in the algebraic sense .and may result in decrease thru the addition of negatives.

1. Present worth of Par + present worth of annuity of all coupons.

2. Par plus present worth of annuity of interest difference.
3. Stock value minus present worth of stock-variance.
4. Par plus compound discount of stock-variance.

Besides these methods which give the isolated result required, are the following successiv methods which derive each result from that of the next lower number of periods.

5. The present worth for one period, of the previous value and a coupon taken together.

6. The previous value + the interest-difference discounted back one more period, that is, once for each period elapst.

Or, instead of beginning at par, proceed in the opposit direction, after finding the value at the longest maturity by methods 1, 2, 3, or 4.

7. The previous value + interest thereon at the incomebasis minus the coupon.

8. The previous variance + interest thereon at the income basis minus the interest-difference.

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