In: Finance
“Before there was Paris Hilton, there was Consuelo Vanderbilt Balsan – a Gilded Age heiress and socialite, renowned for her beauty and wealth. Ms. Balsan’s onetime Hamptons home was slated to hit the market priced at $38 million with Tim Davis of the Corcoran Group.
Located on Ox Pasture Road in Southampton, the shingle-style home was built around 1910 and is known as “Gardenside” or “Cara-Mia”. Ms. Balsan, the great-granddaughter of railroad magnate Cornelius Vanderbilt, owned the house until her death in 1954.
According to public records, the estate is owned by Robert G. Goldstein, executive vice president and president of global gaming operations at Las Vegas Sands Corp, and his wife Sheryl, who purchased the house in 2002 for $17.4 million.” (The Wall Street Journal, August 1, 2014, M2)
Let us first understand the owners of the home with timelines-
Now, let us understand the meaning of compound annual growth rate (CAGR), CAGR signifies that if growth rate is assumed to be constant in each year what will be value of home between different time period. i.e. in year 1 the growth is X%, year 2 growth is X%, year 3 the growth is X % and so on.
The formula to Calculate CAGR is-
CAGR= (value in end period / value in beginning period)^(1/period)-1 |
1. In this question we need to calculate CAGR when Robert G Goldstein and his wife sheryl was owner of the home i.e. for a period of 12 years (from 2002 to 2014)
CAGR= (value in end period / value in beginning period)^(1/period)-1
value in end period (sale price of home) = $38 million , value in beginning period (purchase price)=$17.4 million
time period for which Robert was owner is 12 years
i.e. CAGR in % terms = 0.067*100 = 6.70%
2. It is mentioned in question to assume that the CAGR calculated above to remain constant for next 30 years. So , we can say that for next 30 years CAGR will be 0.067.
It has been asked to calculate the price of house after 30 years since Robert G Goldstein sold the house.
CAGR= (value in end period / value in beginning period)^(1/period)-1
CAGR is given i.e. 0.067, value in beginning period is $38 million i.e. price at which Robert sold the home , period = 30 years as we need to calculate value of home after 30 years, value at end =x (say)
Therefore, price of home after 30 years at CAGR of 0.067 is $265.62
3. It is mentioned in question to assume that the CAGR calculated above to remain constant today since home was sold in 2014. So, we can say that for the period of 2014 when home was sold till toady 2019 (2014-2019 i.e. period of 5 years) CAGR will be 0.067.
It has been asked to calculate the price of house today since Robert G Goldstein sold the house.
CAGR= (value in end period / value in beginning period)^(1/period)-1
CAGR is given i.e. 0.067, value in beginning period is $38 million i.e. price at which Robert sold the home , period = 5 years as we need to calculate value of home today, value at end =x (say)
Therefore, price of home today at CAGR of 0.067 is $52.44
4. We need to calculate price of home in 1910 from today (i..e period of 109 years from 1910 till 2019) assuming CAGR is same i.e. 0.067
CAGR= (value in end period / value in beginning period)^(1/period)-1
CAGR is given i.e. 0.067, value of home today is $52.44 million , period = 109 years, as we need to calculate value at beginning =x (say)
Therefore, price of home in 1910 at CAGR of 0.067 is $0.04464