Question

“Before there was Paris Hilton, there was Consuelo Vanderbilt Balsan – a Gilded Age heiress and socialite, re-nowned for her beauty and wealth. Now Ms. Balsan’s onetime Hamptons home is slated to hit the market priced at $28 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 1964.

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 2003 for $17.4 million.” (The Wall Street Journal, August 1, 2014, M2)

1. 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.

2. Assume the growth rate that you calculated in #1 prevailed since 1964. Calculate the price of the house in 2000. Please show your work.

3. You were using the time value of money concept to answer the question #6. Think about the time line for that problem. What is the time point 0 in that problem? Please explain your answer.

Answer 1

Annual Compound Growth rate = [ (Ending Value / Beginning Value) ^ 1/n] - 1

n = 2014-2003 = 11

Ending Value = $28 million

Beginning Value= $17.4 million

= [(28/17.4) ^ 1/11] -1

= 4.419 %

First we have to calculate the price in 1910

1. Price in 2018 = Price in 2014 * [( 1 + growth rate ) ^(2018-2014)]

Growth Rate= 4.419 %

= $28,000,000* [( 1+0.0441) ^ 4]

= $33,275,639 (rounded off)

2. Price in 2000 = Price in 2003 / [( 1 + growth rate ) ^(2003-2000)]

= 17,400,000 / [(1+0.0441) ^ 3]

=15,287,024

3. Question 6 is not posted to answer this.