Why Did the Previous Owner Lose Money on a Sculpture Sold at Auction?
What was the previous owner's annual rate of return on a sculpture he purchased in 2012 and sold at auction in 2016?
The annual rate of return on the sculpture is approximately -3.80%. This indicates a negative return, meaning the previous owner experienced a loss on the investment over the 4-year period.
Calculating Annual Rate of Return
Annual rate of return = [(Ending value / Beginning value)^(1/number of years) - 1] * 100
Given Values:
Ending value = $10,313,500
Beginning value = $12,386,500
Number of years = 2016 - 2012 = 4
Substitute Values:
Annual rate of return = [($10,313,500 / $12,386,500)^(1/4) - 1] * 100
Annual rate of return ≈ -3.80%
The previous owner's annual rate of return on the sculpture was approximately -3.80%, resulting in a loss on the investment. This negative return can be attributed to the difference between the purchase price in 2012 and the selling price at auction in 2016. Despite the initial high purchase price, the sculpture's value decreased over the 4-year period, leading to a negative rate of return.