Although a down-payment (initial margin) of 20% is typical for a home purchase, homebuyers of modest means can qualify for a loan insured by the Federal Housing Administration (FHA) with a down payment as little as 3%. Suppose a household uses such a loan to buy a $200,000 home. To finance the acquisition, they took a mortgage with a 4% interest rate.

a) What is the dollar amount of down payment they need to bring, and what is the leverage ratio?

a. 200,000x0.03=6,000 down payment

b. 194,000/6,000=32.333 leverage ratio

b) How much equity does the homeowner have in the house? Suppose that, after the house was purchased, its price fell by 2% to $196,000

a. 6,000 equity

c) If we ignore financing costs, what is the ROI (return on investment)? (hint: use your answer to part (a))

a. ROI= (2,000/6,000)-1=-66.67%

d) How much equity (in dollars) does the homeowner have in the house? Do not forget the loan which must be repaid with interest.

a. 196,000-194,000=2,000

e) After taking into account financing costs, what is the ROI? Suppose the margin call rate is 0%, that is, the bank would not accept a negative equity. a.

f) What is the margin call price? That is, what is the house price in which the homeowners equity would reach 0%?