 There is the conventional manner in which this calculation is completed, as we noted above. Most everyone takes the final hammer price times the BP, and then adds the final hammer price. While this method is acceptable, there is an easier way to do this calculation if one has a calculator handy.

Our quicker method involves the principle that adding a percentage to a number is the same as multiplying it by [1+that percentage]. For example, adding 10% is the same as multiplying by 1.10 where “10%” is expressed as the decimal “.10”

Therefore, when adding a BP, convert it to a decimal, and add it to 1 and multiply the final bid by this number for the total including the BP. Some examples:

• \$150,000 home selling with a 15% BP: 150,000*1.15 = 172,500
• \$1,050 wristwatch selling with a 10% BP: 1,050*1.10 = 1,155
• \$45,000 horse selling with an 8% BP: 45,000*1.08 = 48,600

Let’s move on to calculating what the high bid was, if we know the number which includes the BP.

For example, someone says that a John Deere tractor recently sold at auction for \$60,500 including a 10% BP. How would we figure what the hammer price was?

By taking the \$60,500 total price for the John Deere tractor, and dividing  by 1.10 we get \$55,000, which must have been the high bid, prior to adding the BP.

Therefore, when backing out a BP, convert it to a decimal, and add it to 1 and divide the total price by this number for the high bid excluding the BP. Some examples:

• \$253,000 price including 15% BP: 253,000/1.15 = 220,000 bid price
• \$2,100 price including 5% BP: 2,100/1.05 = 2,000 bid price
• \$55,000 price including 10% BP: 55,000/1.10 = 50,000 bid price

## In Conclusion:

How is just the BP calculated, based upon either the high bid price, or the total sales price including the BP?

If the high bid price is known, the BP is calculated by taking the BP as a percentage times the high bid price. For example, a diamond ring sells for \$4,900 and a 10% BP is charged. The BP alone would be 4,900*.10 = \$490.

If the total sales price is known, including the BP, we can calculate what the BP was by taking the total sales price times [buyer’s premium / 1+buyer’s premium]. For example, our aforementioned diamond ring sells for \$5,390 including a 10% BP. If we want to know how much the BP was, we take 5,390*.10/1.10 = \$490. Some other examples: