9. County Bank offers one-year loans with a stated rate of 9 percent but requires a compensating balance of 10 percent. What is the true cost of this loan to the borrower? How does the cost change if the compensating balance is 15 percent? If the compensating balance is 20 percent? In each case, assume origination fees and the reserve requirement are zero.
The true cost is the loan rate ÷ (1 – compensating balance rate) = 9% ÷ (1.0 – 0.1) = 10 percent. For compensating balance rates of 15 percent and 20 percent, the true cost of the loan would be 10.59 percent and 11.25 percent respectively. Note that as the compensating balance rate increases by a constant amount, the true cost of the loan increases at an increasing rate.
10. Metrobank offers one-year loans with a 9 percent stated or base rate, charges a 0.25 percent loan origination fee, imposes a 10 percent compensating balance requirement, and must pay a 6 percent reserve requirement to the Federal Reserve. The loans typically are repaid at maturity.
a. If the risk premium for a given customer is 2.5 percent, what is the simple promised interest return on the loan?
The simple promised interest return on the loan is BR + m = 0.09 + 0.025 = 0.115 or 11.5 percent.
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 percent, a reduction of 1.22 percent. Without the origination fee, the gross return would be 12.69 percent, a reduction of only 0.28 percent. Eliminating the reserve requirement would cause the gross return to increase to 13.06 percent, an increase of 0.09 percent.
18. Suppose the estimated linear probability model is PD = 0.3X1 + 0.2X2 - .05X3 + error, where X1 = 0.75 is the borrower's debt/equity ratio; X2 = 0.25 is the volatility of borrower earnings; and X3 = 0.10 is the borrower’s profit ratio.
a. What is the projected probability of default for the borrower?
PD = 0.3(.75) + 0.2(.25) - 0.05(.10) = 0.27
b. What is the projected probability of repayment if the debt/equity ratio is 2.5?
PD = 0.3(2.5) + 0.2(.25) - 0.05(.10) = 0.795
The expected probability of repayment is 1 ‑ 0.795 = 0.205.
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 0.0 or above 1.0, an occurrence that does not make economic or statistical sense.
20. MNO, Inc., a publicly traded manufacturing firm in the United States, 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 (ret. earnings = $0) 400
Total assets $700 Total liabilities and equity $700
Also assume sales = $500, cost of goods sold = $360, taxes = $56, interest payments = $40, net income = $44, the dividend payout ratio is 50 percent, 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 - Current liabilities.
Current assets = Cash + Accounts receivable + Inventories.
Current liabilities = Accounts payable + Accruals + Notes payable.
EBIT = Revenues ‑ Cost of goods sold ‑ Depreciation.
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
X1 = (20+90+90‑30‑30-90)/ 700 = .0714 X1 = Working capital/total assets (TA)
X2 = 44(1-.5) / 700 = .0314 X2 = Retained earnings/TA
X3 = (500-360) / 700 = .20 X3 = EBIT/TA
X4 = 400 / 150 = 2.67 X4 = Market value of equity/long term debt
X5 = 500 / 700 = .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
= .0857 + .044 + .66 + 1.6 + .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 2.99, ABC 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?
ABC’s net income would be -$100 without taking into account text credits. Note, that ABC's tax liability is ‑$56. If we assume that ABC uses this tax credit against other tax liabilities, then:
X1 = (20 + 90 + 90 ‑ 30 ‑ 30 ‑ 90) / 700 = .0714
X2 = ‑44 / 700 = ‑0.0629
X3 = ‑60 / 700 = ‑0.0857
X4 = 200 / 150 = 1.3333
X5 = 300 / 700 = 0.4286
Since ABC's Z‑score falls to $.9434 < 1.81, credit should be denied.
d. Would the discriminant function change for firms in different industries? Would the function be different for retail lending in different geographic sections of the country? What are the implications for the use of these types of models by FIs?
Discriminant function models are very sensitive to the weights for the different variables. Since different industries have different operating characteristics, a reasonable answer would be yes with the condition that there is no reason that the functions could not be similar for different industries. In the retail market, the demographics of the market play a big role in the value of the weights. For example, credit card companies often evaluate different models for different areas of the country. Because of the sensitivity of the models, extreme care should be taken in the process of selecting the correct sample to validate the model for use.
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 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
Lajira