CH-10 Credit risk I: individual loan risk – Financial Institutions Management : Book Guide

Chapter 10 Credit risk I: individual loan risk Solutions for end-of-chapter questions Questions and problems 1 Why is credit risk analysis an important component of FI risk management? What recent activities by FIs have made the task of credit risk assessment more difficult for both FI managers and regulators? Credit risk management is important for FI managers because it determines several features of a loan: interest rate, maturity, collateral and other covenants. Riskier projects require more analysis before loans are approved. If credit risk analysis is inadequate, default rates could be higher and push a bank into insolvency, especially if the markets are competitive and the margins are low. Credit risk management has become more complicated over time because of the increase in off-balance-sheet activities that create implicit contracts and obligations between prospective lenders and buyers. Credit risks of some off-balance-sheet products such as loan commitments, options and interest rate swaps are difficult to assess because the contingent payoffs are not deterministic, making the pricing of these products complicated. Differentiate between a secured and an unsecured loan. Who bears most of the risk in a fixed-rate loan? Why would FI managers prefer to charge floating rates, especially for longer maturity loans? A secured loan is backed by some of the collateral that is pledged to the lender in the event of default. A lender has rights to the collateral, which can be liquidated to pay all or part of the loan. In a fixed-rate loan, the lender of the loan bears the risk of interest rate changes; if interest rates rise, the opportunity cost of lending is higher. If interest rates fall, then the lender benefits. Since it is harder to predict longer term rates, FIs prefer to charge floating rates for longer term loans and pass the risks on to the borrower. 3 How does a spot loan differ from a loan commitment? What are the advantages and disadvantages of borrowing through a loan commitment? A spot loan involves the immediate takedown of the loan amount by the borrower, while a loan commitment allows a borrower the option to take down the loan any time during a fixed period at a predetermined rate. This can be advantageous during periods of rising rates in that the borrower can borrow as needed at a predetermined rate. If the rates decline, the borrower can borrow from other sources. The disadvantage is the cost: an upfront fee is required and may also include a back-end fee for the unused portion of the commitment. 4 Why does greater access to credit information and disintermediation of the borrowing function have the potential to affect commercial lending volumes? As buyers of commercial paper are more easily able to access credit information, it makes it easier for such non-bank suppliers of funds to buy commercial paper and so directly supply funds to commercial borrowers. Especially for larger rated corporates, this will make borrowers less reliant on banks and broaden the range of NBFIs and investors who can supply funds. The overall trend is towards increased disintermediation of the borrowing function. 5 What are the primary characteristics of residential mortgage loans? Why does the ratio of adjustable-rate mortgages to fixed-rate mortgages in the economy vary over the interest rate cycle? When would the ratio be highest? Residential mortgage contracts differ in size, the ratio of the loan amount to the value of the property, the maturity of the loan, the rate of interest of the loan, and whether the interest rate is fixed or adjustable, capped for a period of time or offered with some lower initial rate for, say, one year, sometimes called a ‘honeymoon rate’. In addition, mortgage agreements differ in the amount of fees, commissions, discounts and points that are paid by the borrower. The ratio of adjustable-rate mortgages to fixed-rate mortgages is lowest when interest rates are low, because borrowers prefer to lock in the low market rates for long periods of time. When rates are high, the adjustable-rate mortgages allow borrowers the potential to realise relief from high interest rates in the future when rates decline. 6 How do revolving loans differ from non-revolving loans? Consumer loans can be classified into revolving loans and other consumer loans that typically include fixed-term personal loans. Fixed-term personal loans, or non-revolving loans, usually have a maturity date at which time the loan is expected to have a zero balance. Revolving loans usually involve credit card debt, and as a result the balance will rise and fall as borrowers make payments and utilise the accounts. These accounts typically have maturities of one to three years, but the accounts normally are renewed if the payment history is satisfactory. 7 How does the credit card transaction process assist in the credit monitoring function of financial institutions? Which major parties receive a fee in the typical credit card transaction? Do the services provided warrant the payment of these associated fees? Credit card transactions typically must be authorised by the cardholder’s bank. Thus, verification of satisfactory credit quality occurs with each transaction. During the transaction process, fixed fees are charged to the merchant, the merchant’s bank and the card issuer. The fees cover the data processing and technology services necessary to ensure that the revolving credit transaction process is accomplished. 8 What are compensating balances? What is the relationship between the amount of compensating balance requirement and the return on the loan to the FI? A compensating balance is the portion of a loan that a borrower must keep on deposit with the credit-granting depository FI. Thus, the funds are not available for use by the borrower. As the amount of compensating balance for a given loan size increases, the effective return on the loan increases for the lending institution. 9 County Bank offers one-year loans with a stated rate of 9 per cent but requires a compensating balance of 10 per cent. What is the true cost of this loan to the borrower? How does the cost change if the compensating balance is 15 per cent? If the compensating balance is 20 per cent? The true cost is the loan rate ÷ (1 – compensating balance rate) = 9 per cent ÷ (1.0 – 0.1) = 10 per cent. For compensating balance rates of 15 per cent and 20 per cent, the true cost of the loan would be 10.59 per cent and 11.25 per cent respectively. Note that as the compensating balance requirement increases at a constant rate, the true cost of the loan increases at an increasing rate. 10 Metrobank offers one-year loans with a 9 per cent stated or base rate, charges a 0.25 per cent loan origination fee, imposes a 10 per cent compensating balance requirement and must pay a 6 per cent reserve requirement to the central bank. The loans typically are repaid at maturity. (a) If the risk premium for a given customer is 2.5 per cent, what is the simple promised interest return on the loan? The simple promised interest return on the loan is L + m = 0.09 + 0.025 = 0.115 or 11.5 per cent. (b) What is the contractually promised gross return on the loan per dollar lent? (c) Which of the fee items has the greatest impact on the gross return? The compensating balance has the strongest effect on the gross return on the loan. Without the compensating balance, the gross return would equal 11.75 per cent, a reduction of 1.22 per cent. Without the origination fee, the gross return would be 12.69 per cent, a reduction of only 0.28 per cent. Eliminating the reserve requirement would cause the gross return to increase to 13.06 per cent, an increase of 0.09 per cent. 11 Why are most retail borrowers charged the same rate of interest, implying the same risk premium or class? What is credit rationing? How is it used to control credit risks with respect to retail and wholesale loans? Most retail loans are small in size relative to the overall investment portfolio of an FI, and the cost of collecting information on household borrowers is high. As a result, most retail borrowers are charged the same rate of interest that implies the same level of risk. Credit rationing involves restricting the amount of loans that are available to individual borrowers. On the retail side, the amount of loans provided to borrowers may be determined solely by the proportion of loans desired in this category rather than price or interest rate differences, thus the actual credit quality of the individual borrowers. On the wholesale side, the FI may use both credit quantity and interest rates to control credit risk. Typically, more risky borrowers are charged a higher risk premium to control credit risk. However, the expected returns from increasingly higher interest rates that reflect higher credit risk at some point will be offset by higher default rates. Thus, rationing credit through quantity limits will occur at some interest rate level even though positive loan demand exists at even higher risk premiums. 12 Why could a lender’s expected return be lower when the risk premium is increased on a loan? In addition to the risk premium, how can a lender increase the expected return on a wholesale loan? A retail loan? An increase in risk premiums indicates a riskier pool of clients who are more likely to default by taking on riskier projects. This reduces the repayment probability and lowers the expected return to the lender. In both cases the lender often is able to charge fees that increase the return on the loan. However, in both cases also, the fees may become sufficiently high as to increase the risk of non-payment or default on the loan. 13 What are covenants in a loan agreement? What are the objectives of covenants? How can these covenants be negative? Positive? Covenants are restrictions that are written into loan or bond contracts that affect the actions of the borrower. Negative covenants in effect restrict actions; that is, they are ‘thou shall not ...’ conditions. Common examples include the non-increase of dividend payments without permission of the borrower, or the maintenance of net working capital above some minimum level. Positive covenants encourage actions such as the submission of quarterly financial statements. In effect, both types of covenants are designed and implemented to assist the lending firm in the monitoring and control of credit risk. 14(a) Identify and define the borrower-specific and market-specific factors which enter into the credit decision. What is the impact of each factor on the risk premium? The borrower-specific factors are: Reputation: Based on the lending history of the borrower; better reputation implies lower risk premium. Leverage: A measure of the existing debt of the borrower; the larger the debt, the higher the risk premium. Volatility of earnings: The more stable the earnings, the lower the risk premium. Collateral: If collateral is offered, the risk premium is lower. Market-specific factors include: Business cycle: Lenders are less likely to lend if a recession is forecasted. Level of interest rates: A higher level of interest rates may lead to higher default rates, so lenders are more reluctant to lend under such conditions. (b) Which of these factors is more likely to affect adversely small businesses rather than large businesses in the credit assessment process by lenders? Reputation involves a history of performance over an extended time period. Many small businesses that are fairly young in operating time may suffer due to the lack of business history. In contrast, many large businesses have more established performance so providing more information about the business for the lender to assess. (c) How does the existence of a high debt ratio typically affect the risk of the borrower? Is it possible that high leverage may reduce the risk of bankruptcy (or the risk of financial distress)? Explain. Increasing amounts of debt increase the interest charges that must be paid by the borrower, and thus decrease the amount of cash flows available to repay the debt principal. Cases have been made that high debt levels require the firm to be relatively far more efficient in its managerial decision making to reduce the probability of bankruptcy. (d) Why is the volatility of the earnings stream of a borrower important to a lender? A highly volatile earnings stream increases the probability that the borrower cannot meet the fixed interest and principal payments for any given capital structure as and when the payments fall due. 15 Why is the degree of collateral as specified in the loan agreement of importance to the lender? If the book value of the collateral is greater than or equal to the amount of the loan, is the credit risk of the lender fully covered? Why or why not? Collateral provides the lender with some assets that can be used against the amount of the loan in the case of default. However, collateral has value only to the extent of its market value, and thus a loan fully collateralised at book value may not be fully collateralised at market value. Further, errors in the recording of collateralised positions may limit or severely reduce the protected positions of a lender. 16 Why are FIs consistently interested in the expected level of economic activity in the markets in which they operate? During recessions, firms in certain industries are much more likely to suffer financial distress because of the slowdown in economic activity. Specifically, the consumer durables industries are particularly hard hit because of cutbacks in spending by consumers. Central bank monetary policy actions that increase interest rates cause FIs to sustain a higher cost of funds and cause borrowers to increase the risk of investments. The higher cost of funds to the FI can be passed along to the borrower, but the increased risk in the investment portfolio necessary to generate returns to cover the higher funding cost to the borrower may lead to increased default risk realisation. Thus, actions by the central bank often are signals of future economic activity. 17 What are the purposes of credit scoring models? How could these models possibly assist an FI manager in better administering credit? Credit scoring models are used to calculate the probability of default or to sort borrowers into different default risk classes. The models use data on observed economic and financial borrower characteristics to assist an FI manager in (a) identifying factors of importance in explaining default risk; (b) evaluating the relative degree of importance of these factors; (c) improving the pricing of default risk; (d) screening bad loan applicants; and (e) more efficiently calculating the necessary reserves to protect against future loan losses. 18 Suppose the estimated linear probability model used by an FI to predict business loan applicant default probabilities is PD = 0.03X1 + 0.02X2 – 0.05X3 + error, where X1 is the borrower’s debt/equity ratio, X2 is the volatility of borrower earnings, and X3 = 0.10 is the borrower’s profit ratio. For a particular loan applicant, X1 = 0.75, X2 = 0.25 and X3 = 0.10. (a) What is the projected probability of repayment for the borrower? PD = 0.03(0.75) + 0.02(0.25) – 0.05(0.10) = 0.0225 (b) What is the projected probability of repayment if the debt/equity ratio is 2.5? PD = 0.03(2.5) + 0.02(0.25) – 0.05(0.10) = 0.075 The expected probability of repayment is 1 – 0.075 = 0.925. (c) What is a major weakness of the linear probability model? A major weakness of this model is that the estimated probabilities can be below 0 or above 1.0, an occurrence that does not make economic or statistical sense. 19 Describe how a linear discriminant analysis model works. Identify and discuss the criticisms that have been made regarding the use of this type of model to make credit risk evaluations. Linear discriminant models divide borrowers into high or low default classes contingent on their observed characteristics. The overall measure of default risk classification (Z) depends on the values of various financial ratios and the weighted importance of these ratios based on the past or observed experience. These weights are derived from a discriminant analysis model. Several criticisms have been levied against these types of models. First, the models identify only two extreme categories of risk, default or no default. The real world considers several categories of default severity. Second, the relative weights of the variables may change over time. Further, the actual variables to be included in the model may change over time. Third, hard to define, but potentially important, qualitative variables are omitted from the analysis. Fourth, the real-world database of defaulted loans is very incomplete. Finally, the model is very sensitive to changes in variables. A change in sales of 40 per cent may cause the model to provide different accept/reject decisions, but a decrease in sales in the real world normally is not seen as hard evidence that credit should be denied or withdrawn from an otherwise successful company. 20 MNO Inc., a publicly traded manufacturing firm, has provided the following financial information in its application for a loan. Assets $ Liabilities and equity $ Cash 20 Accounts payable 30 Accounts receivables 90 Notes payable 90 Inventory 90 Accruals 30 Long-term debt 150 Plant and equipment 500 Equity 400 Total assets 700 Total liabilities and equity 700 Also assume sales = $500, cost of goods sold = $360, taxes = $56, interest payments = $40 and net income = $44; the dividend payout ratio is 50 per cent and the market value of equity is equal to the book value. (a) What is the Altman discriminant function value for MNO Inc.? Recall that: Net working capital = current assets minus current liabilities Current assets = cash + accounts receivable + inventories Current liabilities = accounts payable + accruals + notes payable EBIT = revenues – cost of goods sold – depreciation Taxes = (EBIT – interest)(tax rate) Net income = EBIT – interest – taxes Retained earnings = net income (1 – dividend payout ratio) Altman’s discriminant function is given by: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5 Assume prior retained earnings are zero. X1 = (200 – 30 – 30 – 90)/ 700 = 0.0714 X1 = working capital/total assets (TA) X2 = 22/700 = 0.0314 X2 = retained earnings/TA X3 = 140/700 = 0.20 X3 = EBIT/TA X4 = 400/150 = 2.67 X4 = market value of equity/long-term debt X5 = 500/700 = 0.7143 X5 = sales/TA Z = 1.2(0.07) + 1.4(0.03) + 3.3(0.20) + 0.6(2.67) + 1.0(0.71) = 3.104 = 0.0857 + 0.044 + 0.66 + 1.6 + 0.7143 = 3.104 (b) Should you approve MNO Inc.’s application to your bank for a $500 capital expansion loan? Since the Z-score of 3.104 is greater than 1.81, MNO Inc.’s application for a capital expansion loan should be approved. (c) If sales for MNO were $300, the market value of equity was only half of book value, and the cost of goods sold and interest were unchanged, what would be the net income for MNO? Assume the tax credit can be used to offset other tax liabilities incurred by other divisions of the firm. Would your credit decision change? MNO’s net income would be –$100 without taking into account text credits. Note that MNO’s tax liability is –$56. If we assume that MNO uses this tax credit against other tax liabilities, then: X1 = (200 – 30 – 30 – 90)/700 = 0.0714 X2 = –44/700 = –0.0629 X3 = –60/700 = –0.0857 X4 = 200/150 = 1.3333 X5 = 300/700 = 0.4286 Since MNO’s Z score falls to $0.9434 p1 = 98.13 per cent p12(1.0941) = 1.0721 => p2 = 97.99 per cent p23 (1.1153) = 1.0882 => p3 = 97.57 per cent Using marginal probabilities, estimate the cumulative probability of default: cp02 = 1 – (p1)(p2) = 1 – (0.9813)(0.9799) = 3.84 per cent cp03 = 1 – (p1)(p2)(p3) = 1 – (0.9813)(0.9799)(0.9757) = 6.18 per cent 27 The bond equivalent yields for Australian Treasury Bonds and A-rated corporate bonds with maturities of 93 and 175 days are given below: Bond maturities 93 days 175 days Treasury strip 8.07% 8.11% A-rated corporate 8.42% 8.66% Spread 0.35% 0.55% (a) What are the implied forward rates for both an 82-day Treasury and an 82-day A-rated bond beginning in 93 days? Use daily compounding on a 365-day year basis. The forward rate, f, for the period 93 days to 175 days, or 82 days, for the Treasury is: (1 + 0.0811)175/365 = (1 + 0.0807)93/365 (1 + f)82/365  f = 8.16 per cent The forward rate, f, for the corporate bond for the 82-day period is: (1 + 0.0866)175/365 = (1 + 0.0842)93/365 (1 + f)82/365  f = 8.933 per cent (b) What is the implied probability of default on A-rated bonds over the next 93 days? Over 175 days? The probability of repayment of the 93-day A-rated bond is: p(1 + 0.0842)93/365 = (1 + 0.0807)93/365  p = 99.92 per cent Therefore, the probability of default is (1 – p) = (1 – 0.9992) = 0.0008 or 0.08 per cent. The probability of repayment of the 175-day A-rated bond is: p(1 + 0.0866)175/365 = (1 + 0.0811)175/365  p = 99.76 per cent Therefore, the probability of default is (1 – p) = (1 – 0.9976) = 0.0024 or 0.24 per cent. (c) What is the implied default probability on an 82-day A-rated bond to be issued in 93 days? The probability of repayment of the A-rated bond for the period 93 days to 175 days, p, is: p (1.08933)82/365 = (1 + 0.0816)82/365  p = 0.9984 or 99.84 per cent Therefore, the probability of default is (1 – p) or 0.0016 or 0.16 per cent. 28 What is the mortality rate of a bond or loan? What are some of the problems with using a mortality-rate approach to determine the probability of default of a given bond issue? Mortality rates reflect the historical default risk experience of a bond or a loan. One major problem is that the approach looks backward rather than forward in determining probabilities of default. Further, the estimates are sensitive to the time period of the analysis, the number of bond issues and the sizes of the issues. 29 The following is a schedule of historical defaults (yearly and cumulative) experienced by an FI manager on a portfolio of business and mortgage loans. Years after issuance Loan type 1 Year 2 Years 3 Years 4 Years 5 Years Business: Annual default 0.00% - 0.50% - 0.30% Cumulative default - 0.10% - 0.80% - Mortgage: Annual default 0. 10% 0.25% 0.60% - 0.80% Cumulative default - - - 1.64% - (a) Complete the blank spaces in the table. Years after issuance Loan type 1 Year 2 Years 3 Years 4 Years 5 Years Business: Annual default 0.00% 0.10% 0.50% 0.20% 0.30% Cumulative default 0.00% 0.10% 0.60% 0.80% 1.10% Mortgage: Annual default 0. 10% 0.25% 0.60% 0.70% 0.80% Cumulative default 0.10% 0.35% 0.95% 1.64% 2.43% Note: The annual survival rate is pt = 1 – annual default rate, and the cumulative default rate for n = 4 of mortgages is 1 – (p1× p2× p3× p4) = 1 – (0.999 × 0.9975 × 0.9940 × 0.9930). (b) What are the probabilities that each type of loan will not be in default after five years? The cumulative survival rate is = (1–mmr1)×(1–mmr2)×(1–mmr3)×(1–mmr4)×(1–mmr5) where mmr = marginal mortality rate Business loan = (1 – 0)×(1 – 0.001)×(1 – 0.005)×(1 – 0.002)×(1 – 0.003) = 0.989 or 98.9%. Mortgage loan = (1 – 0.001)×(1 – 0.0025)×(1 – 0.006)×(1 – 0.007)×(1 – 0.008) = 0.9757 or 97.57%. (c) What is the measured difference between the cumulative default (mortality) rates for business and mortgage loans after four years? Looking at the table, the cumulative rates of default in year 4 are 0.80% and 1.64%, respectively, for the business and mortgage loans. Another way of estimation is: Cumulative mortality rate (CMR) = 1– (1 – mmr1)(1 – mmr2)(1 – mmr3)(1 – mmr4) For business loan = 1– (1 – 0.0010)(1 – 0.0010)(1 – 0.0020)(1 – 0.0050) = 1– 0.9920 = 0.0080 or 0.80 per cent For mortgage loan = 1– (1 – 0.0010)(1 – 0.0025)(1 – 0.0060)(1 – 0.0070) = 1– 0.98359 = 0.01641 or 1.641 per cent The difference in cumulative default rates is 1.641 – 0.80 = 0.8410 per cent 30 The table below shows the dollar amounts of outstanding bonds and corresponding default amounts for every year over the past five years. Note that the default figures are in millions of dollars, while those outstanding are in billions. The outstanding figures reflect default amounts and bond redemptions. Years after issuance Loan type 1 Year 2 Years 3 Years 4 Years 5 Years A-rated: Annual default (millions) $0 $0 $0 $1 $2 Outstanding (billions) $100 $95 $93 $91 $88 B-rated: Annual default (millions) $0 $1 $2 $3 $4 Outstanding (billions) $100 $94 $92 $89 $85 C-rated: Annual default (millions) $1 $3 $5 $5 $6 Outstanding (billions) $100 $97 $90 $85 $79 (a) What are the annual and cumulative default rates of the above bonds? A-rated bonds Year Millions default Millions balance Annual default Survival = 1 – An. Def. Cumulative default rate % Cumulative default rate 1 0 100 000 0.000000 1.000000 0.000000 0.0000% 2 0 95 000 0.000000 1.000000 0.000000 0.0000% 3 0 93 000 0.000000 1.000000 0.000000 0.0000% 4 1 91 000 0.000011 0.999989 0.000011 0.0011% 5 2 88 000 0.000023 0.999977 0.000034 0.0034% Where cumulative default for nth year = 1 – product of survival rates to that year. B-rated bonds Year Millions default Millions balance Annual default Survival = 1 – An. Def. Cumulative default rate % Cumulative default rate 1 0 100 000 0.000000 1.000000 0.000000 0.0000% 2 1 94 000 0.000011 0.999989 0.000011 0.0011% 3 2 92 000 0.000022 0.999978 0.000032 0.0032% 4 3 89 000 0.000034 0.999966 0.000066 0.0066% 5 4 85 000 0.000047 0.999953 0.000113 0.0113% C-rated bonds Year Millions default Millions balance Annual default Survival = 1 – An. Def. Cumulative default rate % Cumulative default rate 1 1 100 000 0.000010 0.999990 0.000010 0.0010% 2 3 97 000 0.000031 0.999969 0.000041 0.0041% 3 5 90 000 0.000056 0.999944 0.000096 0.0096% 4 5 85 000 0.000059 0.999941 0.000155 0.0155% 5 6 79 000 0.000076 0.999924 0.000231 0.0231% Years after issuance Bond type 1 Year 2 Years 3 Years 4 Years 5 Years A-rated: Yearly default 0% 0% 0% 0.0011% 0.0023% A-rated: Cumulative default 0% 0% 0% 0.0011% 0.0034% B-rated: Yearly default 0% 0.0011% 0.0022% 0.0034% 0.0047% B-rated: Cumulative default 0% 0.0011% 0.0032% 0.0066% 0.0113% C-rated: Yearly default 0.0010% 0.0031% 0.0056% 0.0059% 0.0076% C-rated: Cumulative default 0.0010% 0.0041% 0.0096% 0.0155% 0.0231% Note: These percentage values seem very small. More reasonable values can be obtained by increasing the default dollar values by a factor of 10, or by decreasing the outstanding balance values by a factor of 0.10. Either case will give the same answers that are shown below. While the percentage numbers seem somewhat more reasonable, the true values of the problem are (a) that default rates are higher on lower rated assets, and (b) that the cumulative default rate involves more than the sum of the annual default rates. C-rated bonds Test with 10x default Year Millions default Millions balance Annual default Survival = 1 – An. Def. Cumulative default rate % Cumulative default rate 1 10 100 000 0.000100 0.999900 0.000010 0.0010% 2 30 97 000 0.000309 0.999691 0.000041 0.0041% 3 50 90 000 0.000556 0.999444 0.000096 0.0096% 4 50 85 000 0.000588 0.999412 0.000155 0.0155% 5 60 79 000 0.000759 0.999241 0.000231 0.0231% More meaningful to use 0.10x balance; it will get the same result. 31 What is RAROC? How does this model use the concept of duration to measure the risk exposure of a loan? How is the expected change in the credit premium measured? What precisely is LN in the RAROC equation? RAROC is a measure of expected loan income in the form of interest and fees relative to some measure of asset risk. The RAROC model uses the duration model formulation to measure the change in the value of the loan for given changes or shocks in credit quality. The change in credit quality (R) is measured by finding the change in the spread in yields between Treasury Bonds and bonds of the same risk class of the loan. The actual value chosen is the highest change in yield spread for the same maturity or duration value assets. In this case, LN represents the change in loan value or the change in capital for the largest reasonable adverse changes in yield spreads. The actual equation for LN looks very similar to the duration equation. 32 A bank is planning to make a loan of $5 000 000 to a firm in the steel industry. It expects to charge an upfront fee of 1.5 per cent and a servicing fee of 50 basis points. The loan has a maturity of 8 years and a duration of 7.5 years. The cost of funds (the RAROC benchmark) for the bank is 10 per cent. Assume the bank has estimated the maximum change in the risk premium on the steel manufacturing sector to be approximately 4.2 per cent, based on two years of historical data. The current market interest rate for loans in this sector is 12 per cent. (a) Using the RAROC model, estimate whether the bank should make the loan. RAROC = Fees and interest earned on loan/ Loan or capital risk We ignore upfront fees in the calculation of the loan’s income. Loan risk, or LN = –DLN × LN × (R/(1 + R) = = –7.5 × $5m × (0.042/1.12) = –$1 406 250 Expected interest = 0.12 × $5 000 000 = $600 000 Servicing fees = 0.0050 × $5 000 000 = $25 000 Less cost of funds = 0.10 × $5 000 000 = –$500 000 Net interest and fee income = $125 000 RAROC = $125 000/1 406 250 = 8.89 per cent. Since RAROC is lower than the cost of funds to the bank, the bank should not make the loan. (b) What should be the duration in order for this loan to be approved? For RAROC to be 10 per cent, loan risk should be: $125 000/LN = 0.10  LN = 125 000/0.10 = $1 250 000  –DLN × LN × (R/(1 + R)) = 1 250 000 DLN = 1 250 000/(5 000 000 × (0.042/1.12)) = 6.67 years. Thus, this loan can be made if the duration is reduced to 6.67 years from 7.5 years. The duration can be reduced. (c) Assuming that duration cannot be changed, how much additional interest and fee income would be necessary to make the loan acceptable? Necessary RAROC = Income/Risk  Income = RAROC × Risk = $1 406 250 × 0.10 = $140 625 Therefore, additional income = $140 625 – $125 000 = $15 625. (d) Given the proposed income stream and the negotiated duration, what adjustment in the risk premium would be necessary to make the loan acceptable? $125 000/0.10 = $1 250 000  –$1 250 000 = –7.5 × $5 000 000 × (R/1.12) Thus R = 1.12(–$1 250 000)/(–7.5 × $5 000 000) = 0.0373 33 A firm is issuing a two-year debt in the amount of $200 000. The current market value of the assets is $300 000. The risk-free rate is 6 per cent, and the standard deviation of the rate of change in the underlying assets of the borrower is 10 per cent. Using an options framework, determine the following: (a) The current market value of the loan. The following need to be estimated first: d, h1 and h2. d = Be–rt /A = $200 000e–0.06(2) /300 000 = 0.5913 or 59.13 per cent. h1 = –[0.5×(0.10)2 × 2 – ln(0.5913)]/(0.10)21/2 = –3.7863 h2 = –[0.5×(0.10)2 × 2 + ln(0.5913)]/(0.10)21/2 = 3.6449 Current market value of loan = l(t) = Be–rt [N(h1)1/d + N(h2)] = $177 384.09[1.6912 × N(–3.7863) + N(3.6449)] = $177 384.09[1.6912 × 0.0001 + 0.9999] = $177 396.35 (b) The risk premium to be charged on the loan. The risk premium k – I = (–1/t) ln[N(h2) + (1/d)N(h1)] = (–½)ln[0.9999 + 1.6912 × 0.0001] = 0.00035 34 A firm has assets of $200 000 and total debts of $175 000. Using an option pricing model, the implied volatility of the firm’s assets is estimated at $10 730. Under the Moody’s Analytics model, what is the expected default frequency (assuming a normal distribution for assets)? The firm will be in technical bankruptcy if the value of the assets falls below $175 000. If  = $10 730, then it takes 25 000/10 730 = 2.33 standard deviations for the assets to fall below this value. Under the assumption that the market value of the assets is normally distributed, 2.33 represents a 1 per cent probability that the firm will become bankrupt. 35 Pacific Basin Bank (PBB) has outstanding a $5 000 000 face value, adjustable rate loan to a company that has a leverage ratio of 80 per cent. The current risk-free rate is 6 per cent, and the time to maturity on the loan is exactly ½ year. The asset risk of the borrower, as measured by the standard deviation of the rate of change in the value of the underlying assets, is 12 per cent. The normal density function values are given below: h N(h) h N(h) –32.55 0.0054 2.50 0.9938 –32.60 0.0047 2.55 0.9946 –32.65 0.0040 2.60 0.9953 –32.70 0.0035 2.65 0.9960 –32.75 0.0030 2.70 0.9965 (a) Use the Merton option valuation model to determine the market value of the loan. The following need to be estimated first: d, h1 and h2. h1 = –[0.5×(0.12)2 × 0.5 – ln(0.8)]/(0.12)0.5 = –0.226744/0.084853 = –2.672198 h2 = –[0.5×(0.12)2 × 0.5 + ln(0.8)]/(0.12)0.5 = 0.219544/0.084853 = 2.587346 Current market value of loan = l(t) = Be–rt [N(h1)1/d + N(h2)] = $4 852 227.67[1.25 × N(–2.672198) + N(2.587346)] = $4 852 227.67 [1.25 × 0.003778 + 0.995123] = $4 851 478.00 (b) What should be the interest rate for the last six months of the loan? The risk premium k – I = (–1/t) ln[N(h2) + (1/d)N(h1)] = (–1/0.5)ln[0.995123 + 1.25 × 0.003778] = 0.000308 The loan rate = risk-free rate plus risk premium = 0.06 + 0.000308 = 0.060308 or 6.0308%. Web questions 36 Go to the Reserve Bank of Australia’s website and update Table 10.1 in the textbook. The answer will depend on the date of the assignment. The website is www.rba.gov.au. Click on ‘Statistics’ and look for the file that contains the relevant data. 37 Go to the APRA website and see how the ranking of providers has changed since Table 10.3 in the textbook was released. The answer will depend on the date of the assignment. The website is www.apra.gov.au. Look for the file that contains the relevant data. 38 Go to the Moody’s Analytics and Moody’s Australia websites to see any recent examples where the expected default frequency (EDF) has provided an early warning of significant changes in a company’s default probability. The answer will depend on the date of the assignment. The website is www.moodysanalytics.com and www.moodys.com.au. Click on the file that contains the relevant data. As of my last update in January 2022, I don't have access to real-time data or the ability to browse specific websites like Moody’s Analytics or Moody’s Australia. Therefore, I'm unable to provide recent examples where the expected default frequency (EDF) has provided an early warning of significant changes in a company's default probability. However, Moody's EDF measures are widely used in financial analysis and risk management to assess the creditworthiness and default probability of companies. These measures incorporate various financial metrics, market data, and qualitative factors to estimate the likelihood of default over a specified time horizon. To find recent examples where EDF has provided an early warning of significant changes in a company's default probability, you can visit the Moody’s Analytics website or the Moody’s Australia website directly. Look for reports, publications, or case studies that highlight specific instances where EDF signals were indicative of impending credit events or changes in default risk for individual companies. Moody's Analytics and Moody’s Australia regularly publish research and analysis on credit risk, default probability, and related topics, which may include real-world examples and insights into the effectiveness of EDF measures as early warning indicators. You can search for relevant reports or articles on their websites or contact their customer support for assistance in finding specific examples. If you have access to financial databases or research platforms, you may also consider using Moody's EDF data to conduct your own analysis and identify cases where EDF provided valuable insights into changes in default probability for companies of interest. Answer to integrated mini case: Loan analysis As a senior loan officer at National Capital Bank, you have the following loan applications waiting for review. The bank uses Altman’s Z-score, default probabilities, mortality rates, and RAROC to assess loan acceptability. The bank’s cost of equity (the RAROC benchmark) is 9 per cent. The bank’s loan policy states that the maximum probability of default for loans by type is as follows: Loan Type and Maturity Maximum Allowable Default Probability AAA-rated 0.50% A-rated 1.25 Which loans should be approved and which rejected? 1. An AAA-rated, one-year business loan from a firm with a liquidity ratio of 2.15, a debt-to-asset ratio of 45 per cent, volatility in earnings of 0.13, and a profit margin of 12 per cent. National Capital Bank uses a linear probability model to evaluate AAA-rated loans as follows: where X1 = Liquidity ratio X2 = Debt-to-asset ratio X3 = Volatility in earnings X4 = Profit margin 1. PD = –0.08(2.15) + 0.15(0.45) + 1.25(0.13) – 0.45(0.12) = 0.004 = 0.4% accept the loan 2. An AA-rated, one-year business loan from a firm with the following financial statement information (in millions of dollars): Assets Liabilities and Equity Cash $40 Accounts payable $ 55 Accounts receivables 120 Notes payable 60 Inventory 210 Accruals 70 Long-term debt 550 Plant and equipment 1 100 Equity (ret. earnings = $200)735 Total assets $1 470 Total liabilities and equity $1 470 Also assume sales = $1250m, cost of goods sold = $930m, and the market value of equity is equal to 2.2 times the book value. National Capital Bank uses the Altman’s Z-score model to evaluate AA-rated loans. 2. Z = 1.2((40m + 120m + 210m – 55m – 60m – 70m)/1470m) + 1.4(200m/1470m) + 3.3((1250m – 930m)/1470m) + 0.6(2.2 × 735m/550m) + 1.0(1250m/1470m) = 0.1510 + 0.1905 + 0.7184 + 1.764 + 0.8503 = 3.674 > 2.99 => accept the loan 3. An A-rated corporate loan with a maturity of three years. A-rated corporate loans are evaluated using the mortality rate approach. A schedule of historical defaults (annual and cumulative) experienced by the bank on its A-rated corporate loans is as follows: Years after Issue Loan type 1 year 2 years 3 years 4 years A-rated corporate loans Annual default 0.10% 0.25% 0.40% 0.65% Cumulative default 0.10 0.325 0.595 1.858 3. Cumulative default probability = 0.595% accept the loan 4. A $2 million, five-year loan to a BBB-rated corporation in the computer parts industry. National Capital Bank charges a servicing fee of 75 basis points. The duration on the loan is 4.5 years. The cost of funds for the bank is 8 per cent. Based on four years of historical data, the bank has estimated the maximum change in the risk premium on the computer parts industry to be approximately 5.5 per cent. The current market rate for loans in this industry is 10 per cent. 4. LN = –4.5 × $2m × (0.055/1.10) = –$450 000 Expected interest = 0.10 × $2 000 000 = $200 000 Servicing fees = 0.0075 × $2 000 000 = $15 000 Less cost of funds = 0.08 × $2 000 000 = –$160 000 Net interest and fee income = $ 55 000 RAROC = $55 000/450 000 = 12.22 per cent. Since RAROC is greater than the cost of funds to the bank, 9 per cent, the bank should make the loan. The bank should accept all four of the loans. Solution Manual for Financial Institutions Management Anthony Saunders, Marcia Cornett, Patricia McGraw 9780070979796, 9780071051590