Question

In: Finance

“Before there was Paris Hilton, there was Consuelo Vanderbilt Balsan – a Gilded Age heiress and...

“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)

  1. Calculate the annual compound growth rate of the house price during the period when the house was owned by Robert G. Goldstein (since 2002). (Round the number of years to the whole number). Please show your work.
  2. Assume that the growth rate you calculated in question #1 remains the same for the next 30 years. Calculate the price of the house in 30 years after it was sold by Robert G. Goldstein. Please show your work.
  3. Assume that the growth rate you calculated in question #1 remains the same since the house was sold. Calculate the price of the house today. (Round the number of years to the whole number). Please show your work.
  4. Assume the growth rate that you calculated in #1 prevailed since 1910. Calculate the price of the house in 1910. Please show your work.
  5. Assume the growth rate that you calculated in #1 prevailed since 1910. Calculate the price of the house in 1954. Please show your work.
  6. You were using the time value of money concept to answer question #5. Think about the time line for that problem. What is the time point 0 in that problem? Please explain your answer.
  7. Reflection – the students also should include a paragraph in the initial response in their own words reflecting on specifically what they learned from the assignment and how they think they could apply what they learned in the workplace.

Solutions

Expert Solution

Let us first understand the owners of the home with timelines-

  • The home was built around 1910 and Ms. Balsan was the owner since 1910 till 1954 (until her death).
  • Since 2002, the home was owned by Robert G Goldstein and his wife Sheryl. The purchased the home for value of $17.4 million. They sold the home to Tim Davis of Corcon group in the year 2014 for $38 million. So, Robert G Goldstein and his wife sheryl was owner of the home for a period of 12 years (2002 to 2014 rounded off)
  • Since 2014, the owner of home was Tim Davis of Corcon group.

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


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