Question

Read the following article then answer questions below:

“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)

QUESTIONS:

1. Calculate the annual compound growth rate of the house price during the period when the house was owned by Robert G. Goldstein (since 2003). (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. Which price was paid for the house in 1964? Please show your work.

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

7. 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

Soln : 1) Let the compounded annual grwoth rate = g

Now, we can calculate the g by using the eqn : g = (Ending value of investment/Initial value of investment)^1/n -1

Ending value = $28mn, Initial value =  $17.1 mn , n = 2014-2003 = 11 years

g = (28/17.1)^1/11 - 1 = 0.04585 = 4.585%

2) Let P be the price of the house after 30 years, assuming the grwth rate as calculated above and present value = $28 mn

P = (1+g)ⁿ * 28 = (1.04585)³⁰ *28 = $107.46 mn

3) We are assuming here that today means in 2018 and house was sold in 2003 as last known . So, value of the house at the time it is sold = 17.1 million, n = 15

P = (1+g)ⁿ * 17.1 = (1.04585)¹⁵ *17.1 = $33.5 million will be the value today with this growth rate

4) Now, let g = 4.585% is the growth rate since 1910 and assuming the value of house in 2003 = 17.1 million

Let X be the price in 1910 and n = 2003-1910 = 93 years

Using the CAGR equation , We can get X = 17.1/(1+g)ⁿ = 17.1/(1.04585)⁹³ = 0.2644 mn would be the price in 1910