Question

A real estate investor has bought an office building valued at $100 million. After a 10% down payment for the property price, the investor has borrowed a one-year mortgage loan at 10% interest rate from Nopay Bank to finance the remaining purchase price. The credit rating of the investor is ABB indicating that his probability of default is 3%. The current market value of the office building is $100 million. The office building is pledged with Nopay Bank as collateral. The market value of the office building at th end of one year is expected to be either up 30% or down 30%. The risk-free rate of interest to Nopay Bank is 4%.

Questions

a) Describe the payoffs to the real estate investor.

b) Describe the payoffs to the bank.

c) If Nopay Bank requires the investor to buy default insurance, how much would the insurance

cost?

d) What is the default insurance cost if the down payment is 20% instead?

e) What is the default insurance cost if the volatility of the office price is expected to be 50% instead?

Answer 1

a. Payoffs to real estate investor:

As per 1% rule: payoffs to investor will be 1% of the Property value i.e. $ 100million x 1% which is $ 1 million pm

b. Payoffs to bank:

Property value: $100 million

Down payment: 10% = $ 10 million

Mortgage value = $100 million - $10 million = $ 90 million

Interest rate = 10%

Payoffs to bank= $90 million x 10% = $ 9 million pa = $0.75 million pm

c. Default insurance cost:

Default rate- 3%

Mortgage value- $ 90 million

Default insurance cost- $90 million x 3% = $2.7 million pa = $ 0.225 million pm

d. Default insurance cost, If the down payment is 20%=

In such a case the rate of insurance cost should be less than 3%, however in absence of information, it is assumed the rate of insurance be 1.5% on the basis of double the down payment.

Thus default Insurance cost = ($100 million - $ 20 million) x 1.5% = $1.2 million pa = $ 0.1 million pm

e. default insurance cost if the volatility of the office price is expected to be 50% instead?

Expected market value- $ 150 million

Down payment- 10%- $15 million

Mortgage amount- $ 135 million

Default insurance cost- 3% x $135 million = $4.05 million pa = $0.3375 million pm