Problem 1 In 1970, Mr. Smith bought a house for $20,000 in cash. The average inf

Question

Problem 1

In 1970, Mr. Smith bought a house for $20,000 in cash. The average inflation rate between 1970 and 2010 is nearly 4% annually, while the average bond rate of return is nearly 5%. The house value follows the real estate appreciation in the same neighborhood as follows:

Year Appreciation 1980 25%
1990 20%
2000 15%

2010 10%

a) Determine the expected minimum sale price (A$) of the house in 2010

b) Determine the expected minimum real value (R$) of the house in 2010 based on

1970 dollar real value

c) Determine the expected actual value (A$) of the purchase price in 2010 if Mr. Smith

invested in bonds

d) Determine the expected real value (R$) of the purchase price in 2010 based on

1970 dollar real value if Mr. Smith invested in bonds

e) Determine the real interest rate for the bond investment

f) Was buying the house a good choice for Mr. Smith rather than investing in bonds?

Explanation / Answer

Average Inflation = 4%                                                                    

Average Bond Rate = 5%                                                                 

Real Estate Appreciation

Year                   Rate                                                                             

1980                   25%   

1990                   20%   

2000                   15%   

2010                   10%

a)

House was bought in 1970 with $20,000

In 1980 the price was, 20,000 x (1+0.25) = 25,000                               

In 1990 the price was, 25,000 x (1+0.20) = 30,000

In 2000 the price was, 30,000 x (1+0.15) = 34,500

In 2010 the price was, 34,500 x (1+0.10) = 37,950

So the expected minimum sale price (A$) of the house in 2010 = $37,950

b) As we know inflation was 4%, and total years is = 2010 – 1970 = 40 years

So we need to discount the expected minimum price with 4% for 40 years,

The expected minimum real value (R$) of the house in 2010 based on 1970 dollar real value,

                                        = 37,950 / (1+0.04)40 = $7,904.57

c) Bond rate = 5%

Now is $20,000 was invested in bonds in year 1970, then,

Years = 2010 – 1970 = 40 years,

So expected actual value (A$) in 2010 if invested in bonds = 20,000 x (1 + 0.05)40 = $140799.8

d) Now to find out the expected real value (R$) of the purchase price in 2010 based on 1970 dollar real value if Mr. Smith invested in bonds we need to discount at inflation rate of 4% for 40 years,

The expected real value (R$) of the purchase price in 2010 based on 1970 dollar real value if invested in bonds

                                        = 140799.8 / (1 + 0.04)40 = $29,327.05

e) The real interest rate of the bond investment = Nominal interest rate of Bond investment – Inflation

                                                                                                = 5% - 4% = 1%

f) If you compare the answer of question b and question d,

The price of house in 2010 based on 1970 dollar real value = $7,904.57

The price of bond in in 2010 based on 1970 dollar real value = $29,327.05

So the price of bond is higher than price of house. So buying a house was not a good choice.

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