Part1 10 on each question except 7 which has 10 on each part)
1. Make assumptions as follows for a pass-through mortgage backed security (MBS):
a. initial principal balance (after seasoning) between $300 million and $800 million;
b. weighted average coupon (WAC): between 3% and 6%;
c. weighted average maturity (before seasoning) (WAM): between 335 and 355 months;
d. percent of PSA: between 75 and 200, but not 100;
e. seasoning: between 2 and 5 months;
f. fees: servicing fee between 25 and 50 basis points and issuer fee/credit enhancement of 85 basis points;
g. investor yield: a required return for investors purchasing the MBS that is 0.75% to 1.25% less that the WAC.
h. sponsor yield: a required return for the sponsor that is 3% to 5% greater than the WAC.
2. What is the pass-through coupon rate?
3. What is the conditional prepayment rate in the first month of the MBS?
4. What is the single monthly mortality in the first month of the MBS?
5. Using the standard MBS payment schedule:
a. Determine the scheduled payment in the first month of the MBS?
b. How much of the scheduled payment for the first month is interest? How much of that interest is paid to the mortgage backed security holders?
c. How much of the scheduled payment for the first month is principal?
d. What is the extra principal payment in the first month of the MBS?
6. Answer questions 4a through 4d for the payments in the 30th month.
7a. How much will the sponsor receive from sale of the MBS securities to investors?
b. What is the aggregate value of the pass-through MBS securities to investors?
c. What is the average time to repayment of principal for the pass-through MBS?
d. What is the duration of the pass-through MBS?
Part 2
1. Assume the MBS from Part 1 is divided into Interest Only (IO) and Principal Only (PO) pass-through securities and these are sold separately to investors that have the same required return as 1g in Part 1.
a. What is the value of the IO securities?
b. What is the average time to repayment of principal for the IO securities?
c. What is the duration of the IO securities?
d. What is the value of the PO securities?
e. What is the average time to repayment of principal for the PO securities?
f. What is the duration of the PO securities?
Part 3 1a. How does the value of the pass-through MBS (7b), change (indicate both change in dollar value and percentage change) if the investors' yield (from 1g in Part 1) increases by 0.75% and the percent of PSA (from 1d in Part 1) decreases by 45 (that is, for example, the required return increases from 4% to 4.75%, and the PSA rate decreases from PSA 110 to PSA 65).
b. How does the value of the pass-through MBS (7b), change (indicate both change in dollar value and percentage change) if the investors' yield (from 1g in Part 1) decreases by 0.75% and the percent of PSA (from 1d in Part 1) increases by 45 (that is, for example, the required return decreases from 4% to 3.25%, and the PSA rate increases from PSA 110 to PSA 155).
2a. If the MBS is divided into IO and PO securities, how does the value of the IO pass-through change with the same changes in yield and PSA rate as in question 1a in this Part?
b. If the MBS is divided into IO and PO securities, how does the value of the IO pass-through change with the same changes in yield and PSA rate as in question 1b in this Part?
3a. If the MBS is divided into IO and PO securities, how does the value of the PO pass-through change with the same changes in yield and PSA rate as in question 1a in this Part?
b. If the MBS is divided into IO and PO securities, how does the value of the PO pass-through change with the same changes in yield and PSA rate as in question 1b in this Part?
4. Briefly discuss your findings.
You may work with one other person on this assignment. Please show enough of your work that I can determine how you obtain your answers, (e.g., by turning in the spreadsheet you use to do the calculations).
For questions 3 and 4, all differences are additive; if the value is 1a is 4% and 3a asks for a rate that is 2% higher, the new rate is 6%, not 4%*(1.02):
If you need to make any other assumptions, please state them clearly.
1. Select values for the following for a commercial loan:
a. The base rate (the lender's cost of funds - depending on the lender, it may include overhead in addition to borrowing costs), between 3% and 6%.
b. A credit risk premium, between 1% and 5%.
c. Origination fees, between 0.25% and 0.75%.
d. A compensating balance, between 5% and 10%.
e. Reserve requirement (set by management rather than by a regulator), between 5% and 10%.
f. The probability of repayment, between 90% and 97.5%.
g. The recovery in the event of default, between 15% and 75%.
2. For parts a and b, assume that if the borrower defaults, the lender does not recover any of the loan interest or principal (that is, as if the assumption in part g above is 0%).
a. What is the contractually promised return on a loan described in question 1. (Reserves are maintained with respect to compensating balances.)
b. What is the expected return on the loan described in question 1.
c. What is the expected return on the loan described in question 1 if the lender recovers the portion of the loan proceeds from 1g.
3. How does the answer to question 2a change if the values in part 1 change one at a time as indicated (that is for part a below, the assumptions from 1b-1f are the same as in question 1 but the base rate is as indicated; for part b, 1a and 1c-1f are from 1 but the credit risk premium is as indicated; and etc.)?
a. The base rate is 2% higher than in 1a.
b. The credit risk premium is 2% higher than in 1b.
c. The origination fee is double the amount in 1c.
d. The compensating balance is 2% larger than in 1d.
e. The reserve requirement is 2% higher than in 1e.
4. a. How does the answer to question 2b change if all values are the same as in question 1 except the probability of repayment is 5% lower than indicated in 1f?
b. How does the answer to question 2c change if all values are the same as in question 1 except the recovery in the event of default is 5% lower than indicated in 1g?
5. Find the following from the most recent annual financial statements for a publicly traded company of your choice:
the ratio of net working capital to total assets, x1
the ratio of retained earnings to total assets, x2
the ratio of earnings before interest and taxes to total assets, x3
the ratio of market value of equity to book value of long term debt, x4
the ratio of sales to total assets, x5.
Using those ratios, compute the Altman Z score for the company and explain what it indicates about the company's risk of default. (The Z score equation is Z=1.2x1 + 1.4 x2 + 3.3 x3 +0.6 x4 +1.0 x5).
6. For a proposed loan of $10 m, select:
a. an annual interest rate between 5% and 10% (assume this rate is also equal to the average rate on comparable loans),
b. a loan duration between 4 and 8 years (the duration will not be an integer but have at least one decimal place, e.g., 3.6 years),
c. a lender's cost of funds between 3% and 6% but less than the amount selected in 6a,
d. an expected maximum change in the loan rate due to a change in the credit risk premium for the loan between 0.75% and 2.75% (assume this the number selected is the change in credit risk premium for the worst 2.5% of comparable loans over some prior period).
7a. What is the lender's risk adjusted return on capital at risk?
b. Will a lender approve this loan if it requires a 25% risk adjusted return on capital?
c. (If the answer to 7b is no, skip this question.) Find the risk adjusted return on capital for a loan that has an interest rate spread that is half as large as that used in part b and a duration that is 2.5 years longer than the loan in part b, if the maximum change in risk premium is 1.5% greater than the loan in part b. Will a lender requiring a 25% risk adjusted return on capital approve this loan?
d. (If the answer to 7b is yes, skip this question.) Find the risk adjusted return on capital for a loan that has an interest rate spread that is 1.5% greater than that used in part b and a duration that is 2.5 years less than the loan in part b, if the maximum change in risk premium is half of that for the loan in part b. Will a lender requiring a 25% risk adjusted return on capital approve this loan?
8a Obtain 5 years of monthly returns for a public company of your choice.
b. Calculate the standard deviation of monthly returns.
c. Determine the market value of the company and of its debt (you can use book value of debt as a proxy for market value of debt).
d. Determine the probability that a decline in the company's value over the next two years will cause it to have insufficient funds to repay its debt.