Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, an auction house sold a sculpture at auction for a price of $10,391,500. Unfortunately for the previous owner, he had purchased it in 2000 at a price of $12,537,500.
What was his annual rate of return on this sculpture? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Annual rate of return %
The correct answer and explanation is :
The annual rate of return can be calculated using the compound annual growth rate (CAGR) formula:
[
r = \left(\frac{V_f}{V_i}\right)^{\frac{1}{t}} – 1
]
where:
- (V_f) = final value = $10,391,500
- (V_i) = initial value = $12,537,500
- (t) = number of years = 2003 – 2000 = 3 years
Step-by-Step Calculation:
- Divide the final value by the initial value:
[
\frac{10,391,500}{12,537,500} = 0.8288
]
- Take the cube root (since (t = 3)):
[
0.8288^{\frac{1}{3}} = 0.9415
]
- Subtract 1 to get the rate of return:
[
0.9415 – 1 = -0.0585
]
- Convert to a percentage:
[
-0.0585 \times 100 = -5.85\%
]
Final Answer:
[
\mathbf{-5.85\%}
]
Explanation:
The sculpture’s annual rate of return is -5.85%, meaning it lost value at an average rate of 5.85% per year over three years. This negative return highlights the risk in art investments, where appreciation is not guaranteed. While some artworks gain significant value, others may decline due to market trends, shifting collector preferences, or economic downturns.
In this case, the previous owner suffered a loss because the sculpture depreciated in value from its purchase price of $12,537,500 to its auction sale price of $10,391,500. Despite art being a prestigious and sometimes lucrative asset, this example emphasizes the importance of careful market research and understanding that collectible investments can be highly volatile.