Question

A family purchases a new home, costing $1million, with $200,000 in cash and a mortgage to cover the remainder.

a. Write the family’s balance sheet (if it owns nothing more than the house and owes nothing more than the mortgage). What is the household’s net wealth? What is the household’s leverage ratio?

b. The family decides to improve its home by building a fancy roof-deck. The roof-deck will increase the value of the house by $100,000, but will cost $90,000. The family takes out a second mortgage to finance the entire construction project (borrows $90,000). Write the family’s balance sheet after completing the construction project. What is the family’s net wealth? What is its new leverage ratio?

c. After completing the construction project, house prices in the family’s neighbourhood decline by 20%. Write the family’s balance sheet after the decline in prices. What is its net wealth?

d. Explain why this decline in house prices could lead to a vicious cycle of depressed housing demand, low prices, and declining wealth.

e. Mian and Sufi propose eliminating mortgages and replacing them with banks taking equity shares in the houses they finance. In other words, they propose that the amount owed by households to the bank will increase and decrease in proportion to the change in the value of the house. How would the 20% decline in housing prices from part c of the question affect the family’s balance sheet, net wealth, and leverage under this alternative arrangement?

Answer 1

a.

Liabilities	Amount	Assets	Amount
Mortgage 1	800000	House	1000000
Net wealth	200000
Total	1000000	Total	1000000

Leverage ratio= Total Liabilities/Total Assets

Leverage ratio= (800000/1000000)

Leverage ratio=0.8

Leverage ratio in percentage = 80% (0.8×100%)

b.

Liabilities	Amount	Assets	Amount
Mortgage 1	800000	House (1000000+100000)	1100000
Mortgage 2	90000
Net wealth	210000
Total	1100000	Total	1100000

Leverage ratio= (890000/1100000)

Leverage ratio= 0.809

Leverage ratio in percentage = 80.9% (0.809×100%)

c.

Liabilities	Amount	Assets	Amount
Mortgage 1	800000	House	880000
Mortgage 2	90000	Net wealth	(10000)
Total	890000	Total	890000

Working Note:

House= 1100000- 20% of 1100000

House= 1100000-(1100000×20/100)

House= 1100000-220000

House= 880000

Here, Net Wealth is displayed as (10000) because it is a negative amount which means that the total liabilities of the household exceeds its assets. Thus the household is in a debt of 10000 resulting in a negative net wealth.

d.

This decline in house prices could lead to a vicious cycle of depressed housing demand, low prices, and declining wealth in the following ways:

Decrease in prices of house would lead to a decrease in the value of assets held by individuals, this decrease in value of asset would lead to debt

Now if the individual are already in debt and also they know that housing sector is failing to maintain its value and house prices are falling so they will not invest in housing sector leading to depressed housing demand.

Now, by making use of relationship between price, demand and supply a depressed demand for houses while the supply remains constant or unchanged would lead to a situation of excess supply or a situation where supply is more than demand thus resulting in fall in the prices of housing thus resulting in low prices.

Now,the value of assets ie. houses held by individuals has decreased whereas their liabilities are same as before. This decrease in the value of asset with liabilities remaining constant or uncharted would lead to a decrease in the wealth of individuals.

This is also evident from part c done above.