Question

use the following information:

Base rate	4.5%
Credit risk premium	3%
Origination fees	0.35%
Compensating balance	6.5%
Reserve requirement	10%
Probability of payment	97.5%
Expected recovery in event of default	35%

1. What is the contractually promised return (the contract rate) on the loan?

2a. How does the answer to question 1 change if all values are the same as in the table above except the base rate is 2% higher?

b. How does the answer to question 1 change if all values are the same as in the table above except the credit risk premium is 1% higher?

c. How does the answer to question 1 change if all values are the same as in the table above except the origination fee is doubled?

d. How does the answer to question 1 change if all values are the same as in the table above except the compensating balance is 2.5% higher?

e. How does the answer to question 1 change if all values are the same as in the table above except the reserve requirement is 2.5% lower?

3a. What is the expected return on the loan from question 1 if the lender expects no recovery if the loan defaults?

b. What is the expected return on the loan from part a of this question if the probability of payment is 2.5% lower?

4a. What is the expected return on the loan from question 1 if the expected recovery in the event of default is as indicated in the table above?  

b. What is the expected return on the loan from part a of this question if the expected recovery rate is 10% greater than indicated above?

5. Find the following from the most recent annual financial statements for a publicly traded company of your choice:

a. the ratio of net working capital to total assets, x₁

b. the ratio of retained earnings to total assets, x₂

c. the ratio of earnings before interest and taxes to total assets, x₃

d. the ratio of market value of equity to book value of long term debt, x₄ (be sure that you adjust as necessary if book value is stated in thousands of dollars and equity value, in dollars).

e. the ratio of sales to total assets, x₅.

6a. Using the ratios from question 5, compute the Altman Z score for the company. (The Z score equation is Z = 1.2 x₁ + 1.4 x₂ + 3.3 x₃ +0.6 x₄ +1.0 x₅).

b. Explain what it indicates about the company’s risk of default.

7. A proposed loan of $8m has total annual interest rate 6.125% and fees of 0.20%. The loan’s duration is 7.64 years. The lender’s cost of funds is 4.625%. Comparable loans have a yield of 6.125%. The expected maximum change in the loan rate due to a change in the credit risk premium for the loan is 1.15%. (This value is based on actual change in credit risk premium for the worst 1% of comparable loans over some prior period.)

a. What is the risk adjusted return on capital (RAROC) on this loan?

b. If the lender requires RAROC to exceed 25%, how could the terms of the loan be changed to make this loan acceptable?

8. A financial institution has made a 3-year commercial loan. If estimates the likelihood of default on this loan in the first year is 1.3%, the likelihood of default in the second year is 2.1%, and the likelihood of the default in the third year is 3.3%. What is the likelihood of repayment for the loan?

9a. If the expected default rate on a credit card is 7.6%, what interest rate must a financial institution charge on the credit card in order for its expected return to equal its 4.00% cost of funds if the financial institution assumes a 0% recovery rate in the event of default?

b. If the expected default rate on a 1-year home equity loan is 2.69% and the financial institution expects to recover 52% of the total loan return in the event of default, what rate must a financial institution charge on the automobile loan in order for its expected return to equal the risk free rate of 4.00%?

10. Assume that a company has a loan equal to 11% of its market capitalization that must be repaid in 4 years.  If the risk-free interest rate is 2.25% and the standard deviation of returns on the company’s stock is 0.570, what is the probability the company will default on the loan?

11. (optional) A financial institution estimates that a 2-year loan that pays an annual coupon in year 1 and 2 and repays the entire principal at maturity has a probability of payment in years 1 and 2 equal to: p₁ = 97.0%, and p₂ = 94.0%. Expected recovery rates in the event of default are: g₁ = 65%, g₂ = 45%. The 1-year risk free rate, i₁, is 1.25%, and the 1-year forward rate for lending one year from now, f_1,1, is 1.751%. What risk premium must a financial institution charge on this loan in order to have an expected return equal to 1.5%, the risk-free return on a 2-year loan?

Answer 1

Solution:

1)Contractual Return(k)=   Amount Earned / Amount Committed

Let the loan amount issued by the bank be $1000,000 for a year.

Interest rate=Base rate+ Credit Risk premium i.e, 4.5+3=7.5%

• Interest Earned =($1000,000*1.075)-$1000000=$75000
• Originaton Fee Income=($1000,000*0.0035)=$3500
• Compensating Balance=($1000,000*0.065)=$65000
• Reserve Requirement=($65000*0.10)=$6500

Amount Earned=Origination Fee +Interest earned i.e, $3500+ $75000=$78500

Amount Committed= Loan Amount-Compensating Balance+Interest Expenses+Reserve Requirement i.e, $1000,000-$65000+6500=$941500

K=$78500/$941500*100=8.34%

Hence Contract Rate on loan is 8.34% (In the given question Interest Exp is Nil since nothing has specified where compensating balance will be deposited)

2a) Contractual rate of return if base rate is 2% high

Interest rate=Base rate+ Credit Risk premium i.e, 6.5+3=9.5%

Interest Earned =($1000,000*1.095)-$1000000=$95000

Other factors are same, Amount earned=$3500+$95000=$98500

K=$98500/$941500=10.46%

2b) Contractual rate of return if credit risk premium is 1% high

Interest rate=Base rate+ Credit Risk premium i.e, 4.5+4=8.5%

Interest Earned =($1000,000*1.085)-$1000000=$85000

Other factors are same, Amount earned=$3500+$85000=$88500

K=$88500/$941500=9.40%

2c) Contractual rate of return if origination fee is doubled

Originaton Fee Income=($1000,000*0.007)=$7000

Other factors are same,Amount Earned=Origination Fee +Interest earned i.e, $7000+ $75000=$82000

K=$82000/$941500=8.71%

2d) Contractual rate of return if compensating balance is 2.5% higher

Compensating Balance=($1000,000*0.09)=$90000

Reserve Requirement=($90000*0.10)=$9000

Amount Earned=Origination Fee +Interest earned i.e, $3500+ $75000=$78500

Amount Committed= Loan Amount-Compensating Balance+Interest Expenses+Reserve Requirement i.e, $1000,000-$90000+9000=$919000

K=$78500/$919000*100=8.54%

2e) Contractual rate of return if reserve requirement is 2.5% lower

Reserve Requirement=($65000*0.075)=$4875

Amount Earned=Origination Fee +Interest earned i.e, $3500+ $75000=$78500

Amount Committed= Loan Amount-Compensating Balance+Interest Expenses+Reserve Requirement i.e, $1000,000-$65000+4875=$939875

K=$78500/$939875*100=8.35%