Question

The Hamptons Home of a Famed Socialite Hits the Market “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 $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 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)

PLEASE HELP ANSWERING THESE 5 QUESTIONS. THANK YOU

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. Assume the growth rate that you calculated in #1 prevailed since 1910. Calculate the price of the house in 1910. Please show your work.

4. Assume the growth rate that you calculated in #1 prevailed since 1910. Calculate the price of the house in 1954. Please show your work.

5. 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.

Answer 1

1) Annual compound growth rate (CAGR) of the house price during the period when the house was owned by Robert G. Goldstein (since 2002):

CAGR = (Value in 2014/value in 2002)^(1/number of years)

CAGR = ($28 million/$17.4 million)^(1/12) = 4.0441%

2) Value of house after 30 years compounded at same CAGR:

Future Value = (Present Value) *( 1+CAGR)^number of years

Value after 30 years = ($28 million) * (1.040441)^30 = $91.974 million

3) Price of house in 1910:

Present Value (in 1910) = Future Value (in 2002) / [( 1+CAGR)^number of years]

Value in 1910 = ($17.4 million)/((1.040441)^92) = $ 0.4535 million

4) Price of house in 1954:

Price in 1954 = (Price in 1910) *( 1+CAGR)^number of years

Price in 1954 = ($ 0.4535)*(1.040441)^44 = $ 2.5948 million

5) Here point 0 is 1910 and year number 44 is 1954, year number 92 is 2002 and year number 104 is 2014