Management of Depository Institutions 3505 Fall 2014
Problems:
1. A bank is planning to make a loan of $5,000,000 with duration of 7.5 years to “Jumbo Manufacturing”, a young and aggressive firm. The loan rate is 12% and the servicing fee is 50 basis points. The bank estimates that with a probability of 95%, the risk premium on the loan will not increase by more than 4.2%. The average cost of funds for the bank is 10 percent. The bank manager wants to use the RAROC approach to make a decision on approval/rejection of the loan:
a. What is RAROC? Explain the concept theoretically.
b. How does this model use the concept of duration to measure the credit risk of a loan?
c. How is the expected change in the credit premium of the
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Downward sloping.
Borrow short, lend long: Borrow for 2 years lend for 4.5 years: DL = 2 years, DA = 4.5 years
E = -[DA-DL x k] A [R/(1+R)] where, DL = 2 yrs R = -.01 k=1
E= {-(4.5025-2x1) (975)/1.0975} R
E= -(2.5025) (975)/1.0975 R = -2223.18 R.
This is a line between E and R.
Multiple Choice Questions
1. An FI has financial assets of $800 and equity of $50. If the duration of assets is 1.21 years and the duration of all liabilities is 0.25 years, what is the leverage-adjusted duration gap? a. 0.9000 years. b. 0.9600 years. c. 0.9756 years. d. 0.8844 years. e. Cannot be determined.
A= 800, E =50 DA =1.21, DL = .25. LADG = {1.21-.25 x 750/800}=1.21 -.23 = .98
2. Calculate the duration of a two-year corporate bond paying 6 percent interest annually, selling at par. Principal of $20M is due at the end of two years. a. 2 years. b. 1.91 years. c. 1.94 years. d. 1.49 years. e. 1.75 years.
M=2, R =6%, F =20M, P =20M. Cash flows= 1.2 and 21.2.
D =[1.2/1.06 + 21.2/(1.06)2]/20 =[1.13 +18.87x2]/20=38.87/20 =1.94
3. A $1,000 six-year Eurobond has an 8 percent coupon, is selling at par, and contracts to make annual payments of interest. The duration of this bond is 4.99 years. What will be the new price using the duration model if interest rates increase to 8.5 percent? a. $23.10. b. $976.90. c. $977.23. d. $1,023.10. e. -$23.10.
F= 1000, M =6, coupon = 8%, P=1000, D =4.99. R = 50bp.
P = P
2. Now, regardless of your answer to Question 1, assume that the 5-year bond selling for $800.00, the 15-year bond is selling for $865.49, and the 25-year bond is selling for $1,320.00.
The fixed cost is assumed that Larry has discovered the other fixed cost incurred. The total investment is $800,000. The worst case scenario assumes that Larry got a total line of credit from the bank in the amount of $400,000 and invested $400,000 from other source. The Notes payable – short term and the long-term debt is (11.8 + 3.7) = 15.5 % from Table F in the handout. The Loan interest and payment per year is ($400,000 * 0.155)= $62,000. The Income data from Table F indicates that there is a 0.4% of all other expenses net out of the total sales which equals to $109,908 (5,700,666 gallons * $4.82 *0.4%) .
A bond with an annual coupon of $70 and originally sold at par for $1,000. The current market interest rate (yield to maturity) is 8%. This bond will sell at _______. Assuming no change in market interest rates, the bond will present the holder with capital ________ as it matures.
The 442 restored their honor. They returned home heros of war and were looked at differently by all Americans, not as aliens, but as United States citizens. They became the most decorated combat team in U.S. history and freed their families from internment camps restoring honor. “The 100th Battalion/442nd RCT, in just over one year, compiled an astonishing combat record. But this segregated unit, almost entirely comprised of Japanese Americans, suffered an equally remarkable number, about 800, killed or missing in action. They won seven Distinguished Unit Citations, including one awarded personally by President Harry Truman… Over 4,000 Purple Hearts, 29 Distinguished Service Crosses, 588 Silver Stars, and more than 4,000 Bronze
You work in marketing for a company that produces work boots. Quality control has sent you a memo detailing the length of time before the boots wear out under heavy use. They find that the boots wear out in an average of 208 days, but the exact amount of time varies, following a normal distribution with a standard
A case challenging a statute as violating a person's rights under the U. S. Constitution.
* b.Assume the firm’s stock now sells for $20 per share. The company wants to sell some 20-year, $1,000 par value bonds with interest paid annually. Each bond will have attached 50 warrants, each exercisable into 1 share of stock at an exercise price of $25. The firm’s straight bonds yield 12%. Assume that each warrant will have a market value of $3 when the stock sells at $20. What coupon interest rate, and dollar coupon, must the company set on the bonds with warrants if they are to clear the market? (Hint: The convertible bond should have an initial price of $1,000.)
b. b = bU (1 + (1-T)(D/S)) At 40 percent debt: bL = 0.87 (1 + 0.6(40%/60%)) = 1.218 rS = 6 + 1.218(4) = 10.872% = wd rd(1-T) + wcers =
∆P/P = –D*(∆y) D* = D/(1 + y) = 7/1.073 = 6.52 ∆P/P = –D*(∆y) = –6.52(–0.09%) = .59% New price = $1,073(1.0059) = $1,079.33 Learning Objective: 11-02 Compute the duration of bonds; and use duration to measure interest rate sensitivity.
Peoples had accumulated assets of $556m. These assets were funded by short term consumer deposits, consisting largely of 3-month fixed rate savings certificates. These savings certificates were highly affected by interest rate fluctuations. The long term loans provided to people generate interest earnings which are do not increase or decrease with the interest rate fluctuations. Therefore, there was a mismatch between the interest rates earned by the bank and the interest rates that it had to give
2. Forecast the firm’s financial statements for 2002 and 2003. What will be the external financing requirements of the firm in those years? Can the firm repay its loan within a reasonable period? In order to forecast the financial statements of 2002 and 2003, the following assumptions need to be made. The growth of sales is 15%, same as 2001, which is estimated by managers. The rate of production costs and expenses per sales is constant to 50%. Administration and selling expenses is the average of last 4 years. The depreciation is $7.8 million per year, which is calculated by $54.6 million divided by 7 years. Tax rate is 24.5%, which is provided. The dividend is $2 million per year only when the company makes profits. Therefore, we assume that there will be no dividend in 2003. Gross PPE will be $27.3 million (54.6/2) per year. We also assume there is no more long term debt, because any funds need in the case are short term debt, it keeps at $18.2 million. According to the forecast, Star River needs external financing approximately $94 million and $107 million in 2002 and 2003, respectively. In order to analysis if the company can repay the debt, we need to know the interest coverage ratio, current ratio and D/E ratio. The interest coverage ratios through the forecast were 1.23 and 0.87 respectively, which is the danger signal to the managers, because in 2003, the profits even not
Natalie’s grandmother has decided to charge interest of 6% on the note payable extended on November 16. The loan plus interest is to be repaid in 24 months. (Assume that half a month of interest accrued during November.)
b. Generate a graph or table showing how the bond’s present value changes for semi-annually compounded interest rates between 1% and 15%.
2. The discount rate for this bond would be 0.70%. I started with an appropriate discount rate to derive my bond purchase price, since I would not purchase a bond without finding out ahead of time what a good price should be.
(0.94,0) 0.85(0.94) + 0.65(0) = $0.799 3) Linear Programing Model Decision Variables: Let a = Automobile Loans Let f = Furniture Loans Let o = Other Secured Loans Let s = Signature Loans Let r = Risk-free Securities Objective Function: Maximize Z = 0.8a + 0.1f + 0.11o + 0.12s + 0.9r where Z =