{6 points} Leverage and limited liability

1. {1 point} You pay $1000 for a property with 9% cap rate, keep it for 5 years, and sell at the end of year 5 at the same cap rate. The selling costs are 5% of the price. What is your IRR? Enter your answer in percent, but without percent sign.

2. {1 point} You are doing the same as above but instead of paying cash, you take a 70% LTV IO loan at 5% annual rate. What is your IRR?

3. {1 point} In addition to the loan above you take a mezzanine IO loan of $200 at 8% annual rate. What is your IRR?

The neighborhood is declining, so your selling cap rate is 11% in questions 10-13. You have limited liability: you can walk awayanytime. If you walk away in year t, you also lose the net income in that year so that your cash flow for year t is zero.

4. {1 point} You pay cash as in Question 1 above. What is your IRR?

5. {1 point} You take the loan as in Question 2 above. What is your IRR?

6. {1 point} You take an additional mezzanine loan as in Question 3 above. What is your IRR?

{4 points} Mortgage-backed securities: IO & PO strips

BOA originates 1000 Fully Amortizing Fixed Rate Mortgages, each has a $100,000 balance, 6.5% interest rate (no fees), 30 year term, and annual payments. BOA immediately issues IO and PO strips backed by the pool of these mortgages and sells them to investors who discount payoffs at 5.5%.

7. {1 point} What profits does BOA make immediately?

8. {1 point} What is the value of all PO strips?

9. {1 point} What would be the value of all PO strips if the expected prepayment rate was 10% per year?

10. {1 point} What would be the value of all PO strips if instead the expected default rate was 10% per year? Assume that in case of default, BOA recovers 85% of balance.

{2 points} Mortgage-backed securities: floaters and inverse floaters

11. BOA issues $200m in CMO. 75% of the issue is floater tranche with index = LIBOR (currently 6%) and margin = 1%. The remaining 25% is inverse floater tranche that is designed to keep the total cost of financing constant. The next year LIBOR falls to 4%. What would be the interest paid to the inverse floater tranche investors? Enter your answer in percent, but without percent sign.

{4 points} Home equity and balloon

Ann would like to buy a house.

It costs $2,500,000.

Her down payment will be $50,000.

She will take out a mortgage for the remainder.

It will be a 30 year, fully amortizing, FRM, with constant monthly payments and monthly compounding.

The annual interest rate is 4.50%.

She will pay $5,000 in closing costs at origination.

She will also pay 1.75% of the balance in buy-down points at origination.

Ann is pessimistic and forecasts house prices to fall by 0.5% every month.

12. {1 point} How much home equity will she have after 10 years (120 months)?

13. {1 point} How much home equity will she have after 29 years (348 months)?

For questions 4 and 5, assume all is the same as above EXCEPT there is a $500,000 balloon due in 30 years (recalculate the mortgage payment accordingly).

14. {1 point} How much home equity will she have after 10 years (120 months)?

15. {1 point} How much home equity will she have after 29 years (348 months)?

{4 points} Mortgage insurance

Question is based on a research paper The Impact of Federal Housing Policy on Housing Demand and Homeownership: Evidence from a Quasi-Experiment by Morris Davis, Stephen Oliner, Tobias Peter, and Edward Pinto (as presented at Baruch Real Estate Seminar on November 26, 2018).

On 1/26/2015, to promote homeownership, FHA reduced its mortgage premium by 50 bp, from 1.35 percent of loan balance to 0.85 percent. The paper uses this event to estimate the sensitivity of housing demand to interest rate. But how important is a 50bp premium cut? Is it equivalent to the same 50bp reduction in interest rate? We will answer this question using the data from the original paper, for an average mortgage in their data sample.

Ann borrowed $199,755 to buy a $207,000 house (that is pretty high LTV!). The closing costs of 1.75 points are added to the loan balance (thats not like we used to calculate mortgages, but that was the case in the data). The mortgage payment is calculated based on this larger balance, while the mortgage insurance is 1.35% of the original $199,755 balance. She also pays 1.2% property tax and 0.35% house insurance premium (both based on the value of the house). The monthly payment we are interested in consists of the mortgage payment, mortgage insurance payment, property tax, and house insurance.

The table below summarizes the information we have and calculates the total loan amount after the points are added, as well as the total monthly payment as explained above. Compute total loan and payment using the information in the first seven lines of the table and make sure your answers match the last two lines.

House price	207000
Loan amount	199755
Interest rate	0.04
Upfront premium (points)	0.0175
Annual Mortgage Insurance Premium	0.0135
Taxes	0.012
Insurance	0.0035
Total loan	203251
Monthly payment	$1462.45

16. {2 points} Compute the payment if the annual mortgage insurance premium falls by 50bp

17. {2 points} Compute what should be the mortgage interest rate (it was 4% in part 1) that would lead to the same payment as in part 2 if the insurance premium stays the same as in part 1 (i.e. 1.35%). Enter your answer in percent, but without percent sign.