Question

In 2017, Leonardo da Vinci's painting Salvator Mundi sold for a record $450.3 million. In 1958, it sold for $125, equivalent in purchasing power to about $1,060 at 2017 prices. The painting was originally commissioned by King Louis XII of France in about 1500. The Wall Street Journal guesstimated that the king may have paid Leonardo the equivalent of $575,000 in 1519.

a. What was the annual rate of appreciation in the price of the painting between 1958 and 2017 adjusted for inflation?

b. What was the annual estimated rate of appreciation in the price of the painting between 1519 and 2017 adjusted for inflation.

Answer 1

Adjusted for inflation rate of appreciation means that real rate of return is to be calculated.

a). Number of years = 2017-1958 = 59

Inflation adjusted price in 1958 = 1,060.

Price in 2019 = 450,300,000

If the rate of appreciation is r, then

450,300,000 = 1,060*(1+r)^59

r = [(450,300,000/1,060)^(1/59)] - 1 = 24.56%

b). Inflation adjusted price of 1519 = 575,000

Number of years = 2017-1519 = 498

450,300,000 = 575,000*(1+r)^498

r = [(450,300,000/575,000)^(1/498)] -1 = 1.35%