Homework 6_Bank Management

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Kent State University *

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56068

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Finance

Date

Jan 9, 2024

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4

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1 Homework 6 of FIN 46068/56068 (Due Date: December 8, 2023) Chapter 12 1. A DI has assets of $10 million consisting of $1 million in cash and $9 million in loans. The DI has core deposits of $6 million, subordinated debt of $2 million, and equity of $2 million. Increases in interest rates are expected to cause a net drain of $2 million in core deposits over the year? a. The average cost of deposits is 6 percent and the average yield on loans is 8 percent. The DI decides to reduce its loan portfolio to offset this expected decline in deposits. What will be the cost of the stored liquidity strategy and the size of the DI after the implementation of this strategy? Assuming that the decrease in loans is offset by an equal decrease in deposits, the cost of the drain = (0.08 – 0.06) x $2 million = $40,000. The average size of the firm will be $8 million after the drain. b. If the interest cost of issuing new short-term debt is expected to be 7.5 percent, what would be the cost of offsetting the expected deposit drain with purchased liquidity management strategy? Cost of the drain = (0.075 – 0.06) x $2 million = $30,000. 2. A DI has $10 million in T-bills, a $5 million line of credit to borrow in the repo market, and $5 million in excess cash reserves (above reserve requirements) with the Fed. The DI currently has borrowed $6 million in fed funds and $2 million from the Fed discount window to meet seasonal demands. a. What is the DI’s total available (sources of) liquidity? $10 + $5 + $5 = $20 million b. What is the DI’s current total uses of liquidity? $6 + $2 = $8 million. c. What is the net liquidity of the DI? The DI’s net liquidity is $12 million.
2 d. What conclusions can you derive from the result? The net liquidity of $12 million suggests that the DI can withstand unexpected withdrawals of $12 million without having to reduce its less liquid assets at fire-sale prices. 3. A DI has the following assets in its portfolio: $20 million in cash reserves with the Fed, $20 million in T-bills, and $50 million in mortgage loans. If the assets need to be liquidated at short notice, the DI will receive only 99 percent of the fair market value of the T-bills and 90 percent of the fair market value of the mortgage loans. Estimate the liquidity index using the above information. I = (20/100)(1.00/1.00) + (20/100)(0.99/1.00) + (50/100)(0.90/1.00) + (10/100)(1/1.00) = 0.848 4. Conglomerate Corporation has acquired Acme Corporation. To help finance the takeover, Conglomerate will liquidate the overfunded portion of Acme’s pension fund. The face values and current and one-year future liquidation values of the assets that will be liquidated are given below: Liquidation Values Asset Face Value t = 0 t = 1 year IBM stock $10,000 $9,900 $10,500 GE bonds 5,000 4,000 4,500 Treasury securities 15,000 13,000 14,000 Calculate the 1-year liquidity index for these securities. I = (0.333)(9900/10,500) + (0.167)(4,00/4,500) + (0.5)(13,000/14,000) = 0.927 5. Plainbank has $10 million in cash and equivalents, $30 million in loans, and $15 in core deposits. a. Calculate the financing gap. $30 million - $15 million = $15 million b. What is the financing requirement? $15 million + $10 million = $25 m
3 Chapter Sixteen 3. Contingent Bank has the following balance sheet in market value terms (in millions of dollars): Assets Liabilities and Equity Cash $20 Deposits $220 Mortgages 220 Equity 20 Total assets $240 Total liabilities and equity $240 In addition, the bank has contingent assets with $100 million market value and contingent liabilities with $80 million market value. What is the true stockholder net worth? What does the term contingent mean? First, contingent means subject to chance. Hence contingent liabilities and assets are those that can arise in the future, but we cannot add them to the balance sheet because there is uncertainty involved. Stockholder net worth= 340-300= $40million 10. A FI has issued a one-year loan commitment of $2 million for an up-front fee of 25 basis points. The back-end fee on the unused portion of the commitment is 10 basis points. The FI requires a compensating balance of 5 percent as demand deposits. The FI’s cost of funds is 6 percent, the interest rate on the loan is 10 percent, and reserve requirements on demand deposits are 8 percent. The customer is expected to draw down 80 percent of the commitment at the beginning of the year. a. What is the expected return on the loan without taking future values into consideration? Up-front fees = 0.0025 x $2,000,000= $ 5,000 Interest income = 0.10 x $1,600,000= 160,000 Back-end fee = 0.0010 x $400,000= 400 Total = $165,400 $1,600,000-80,000+6,400= $1,526,400 Expected rate of return= $165,400/$1,525,400= 10.836%
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4 b. What is the expected return using future values? That is, the net fee and interest income are evaluated at the end of the year when the loan is due? 5,000*1.06= $5,300 Expected return= 165,700/1,526,400= 10.8556% c. How is the expected return in part (b) affected if the reserve requirements on demand deposits are zero? Expected Return= $165,700/$1,520,000 = 10.90%. d. How is the expected return in part (b) affected if compensating balances are paid a nominal interest rate of 5 percent? 0.05 x $80,000 = $4,000 Expected return = $161,700/1,526,400 = 10.5936% e. What is the expected return using future values but with the compensating balance placed in certificates of deposit that have an interest rate of 5.5 percent and no reserve requirements, rather than in demand deposits? $1,600,000 x 0.055= $88,000, and the expected return is $77,700/$1,600,000 = 4.8563%