*The Vista Publishing Perspectives report entitled “Profiting from Future Customers” states that an additional turn adds the same profit for a bookseller as 15 additional points of discount. In his speeches at the Conferences presenting the report (in London on June 5 and in New York on June 26), Mike Shatzkin put the equivalent to a turn of *7* additional points. For both calculations, he had relied on his father and master publishing mathematician, Leonard Shatzkin. The difference in the calculations and the way to do them is explained here by Leonard Shatzkin. *

I have been asked to explain why the value of one additional stock turn was calculated to be fifteen points of discount in the Vista report, and at a later time, calculated to be only seven points in the talk delivered by Mike Shatzkin on June 5 and 26.The shortest, to the point explanation is that I, Len Shatzkin, made an error in the first calculation. Looking back, the most likely cause is my stubby fingers pounding the fine keyboard of a pocket calculator.

The fact is that the value of one additional stock turn varies somewhat depending on the average discount and the rate of stock turn. To clarify that:

Return on investment depends on the margin earned per dollar invested (discount divided by cost) multiplied by the number of times the invested dollar is sold (the stock turn).

At 40% discount, the margin (.40 divided by .60) equals 66.7 cents per dollar. At three turns, the return on investment (66.7 cents times three) is $2.00 per dollar invested. To reach the same result in two turns, the margin must equal one dollar on each dollar invested, which it does at 50% discount (.50 divided by .50 equals one).

Therefore, at 40% discount, at a turn of two, one additional turn is worth 10 points of discount.

At 43% discount, the margin per dollar (.43 divided by .57) equals 75.4 cents. At a turn of three, the return on investment (75.4 cents times three) is $2.26. To achieve that return at a stock turn of two would require a discount of 52.5% (.525 divided by .475 equals 1.105, times two equals $2.21). At 43% discount, going from two turns to three turns is worth 9 and one-half discount points.

At 43% discount and four turns, the return on investment is $3.016 per dollar. To achieve the same return in three turns would require a discount of 50%. (.50 divided by .50 equals 1.00, which multiplied by three equals a return on investment of $3.00 per dollar.) At 43% discount, going from three turns to four turns is worth 7 points of discount.

At 43% discount and five turns, the return on investment is $3.77 per dollar. To achieve the same return in four turns would require a discount of 48.5%. (.485 divided by .515 equals .941, which multiplied by four equals a return on investment of $3.76 per dollar.) At 43% discount, going from four turns to five turns is worth 5.5 points of discount.

Calculations at other discounts and other stock turns can be made easily, providing you are careful to match the computer keyboard to the fineness of your fingering.