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# fins3630 solution - 6 An F1 is planning to issue \$100...

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Unformatted text preview: 6. An F1 is planning to issue \$100 million in commercial loans. The F1 will finance the loans by issuing demand deposits. a. What is the minimum capital required by the Basle accord? The minimum capital required on commercial loans = \$100 x 1.0 x 0.08 = \$8 million. b. What is the minimum amount of demand deposits needed to fund this loan assuming there is a 10 percent average reserve requirement on demand deposits? Since there is an interaction between the demand deposits and cash reserves held, the answer requires solving the following, assuming the \$8 is funded by equity and the reserve requirements are kept as cash: \$100 + (0.10 x DD) = DD + 8 2) DD = 92/9 = \$102.22 c. Show a simple balance sheet with total assets, total liabilities, and equity if this is the only project funded by the bank. Assets Liabilities Cash \$10.22 Demand deposits \$102.22 Loan 100.00 Equity 8.00 Total 110.22 110.22 d. How does this balance sheet differ from Table 28—1? Why? The example in Table 28-1 assumes that the capital ratio is only 4 percent, since the loans are residential mortgages. Thus, because the loans in this problem are commercial loans, the bank must keep a full 8 percent risk-based capital ratio and the balance sheet is \$0.44 less than the Table 28—1 example. In effect, although the capital is higher, the reserve requirement tax is lower. 10. Consider the mortgage pass—through example presented in Table 28—3 and Figure 28—2. The total monthly payment by the borrowers reﬂecting a 12 percent mortgage rate is \$1,028,612.60. The payment passed through to the ultimate investors reﬂecting an 11.5 percent return is \$990,291.43. Who receives the difference in these two payments? How are the shares determined? The difference in the two payments (438,321.17) goes to the mortgage—service—provider and to GNMA for the insurance premium. If the total fee is 50 basis points, and GNMA receives 6 basis points for the insurance premium, GNMA would receive 12 percent (6/50) of the difference (\$4,598.54) in the two payments, and the mortgage service provider would receive 88 percent (44/50) of the difference (\$33,722.63) in the two payments. 11. Consider a GNMA mortgage pool with principal of \$20 million. The maturity is 30 years with a monthly mortgage payment of 10 percent per annum. Assume no prepayments. a. What is the monthly mortgage payment (100 percent amortizing) on the pool of mortgages? The monthly mortgage payment, R, is (the monthly interest rate is .10/ 12 = .00833): = PVAn=360,k=0,8333*(R) 2) R = b. If the GNMA insurance fee is 6 basis points and the servicing fee is 44 basis points, what is the yield on the GNMA pass—through? The GNMA's annual interest rate is 0.10 — 0.0044 — 0.0006 = 9.5 percent. The monthly interest rate is 0.095/ 12 = 0.0079167 or 0.79167 percent. 0. What is the monthly payment on the GNMA in part (b)? The monthly GNMA payment, R, is: \$20m = PVAn=360, k=0.79167%*R :> R = \$168,170.84 d. Calculate the first monthly servicing fee paid to the originating banks. The first monthly servicing fee, R, is (the monthly fee rate is .44%/ 12 = .0367%): R = (.000367)\$20m = \$7,340 e. Calculate the first monthly insurance fee paid to GNMA. The first monthly insurance payment, R, is (monthly insurance rate is .06%/12 = .005%): R = (.00005)\$20m = \$1,000 18. If 150 \$200,000 mortgages are expected to be prepaid in three years and the remaining 150 \$200,000 mortgages in a \$60 million 15-year mortgage pool are to be prepaid in four years, what is the weighted-average life of the mortgage pool? Mortgages are fully amortized with mortgage coupon rates set at 10 percent to be paid annually. The annual mortgage payment is \$60 million = PVAn=150,k=10%*R :> R = \$7,888,426.61. Annual mortgage payments, with no prepayments, can be decomposed into principal and interest payments: Interest Principal Remaining m Balance Payment Payment Payment Principal 1 \$60.000 \$7.888 \$6.000 \$1.888 \$58.112 2 58.112 7.888 5.811 2.077 56.034 3 56.034 7.888 5.603 2.285 53.749 4 53.749 7.888 5.375 2.513 51.236 The first year's interest is \$6 million (0.10 X \$60 million). Deducting this from the first year's mortgage payment yields a principal payment of \$1,888,426.61 at the end of the first year, and an outstanding principal \$58,111,573.39. The second year's interest payment is 0.10 X \$58,111,573.39 = \$5,8111,157.34. Deducting this from the annual mortgage payment yields a second annual principal payment of \$2,077,269.27, for a principal outstanding of \$56,034,304.12. The third year's regular interest payment is \$5.603 million. Deducting this from the annual mortgage payment yields a third annual principal payment of \$2.285 million for a principal outstanding of \$53,749,307.92. The principal outstanding at the end of the fourth year, without prepayments, is \$51,235,812.10. However, at the end of the third year, half of the mortgages in the mortgage pool are completely prepaid. That is, at the end of the third year, an additional principal payment of 50% x \$53,749,307.92 = \$26,874,653.96 is received for a remaining outstanding principal balance of \$26.875 million. The total third year principal payment is therefore \$29.16 million = the regular principal payment of \$2.285 million plus an extra payment of \$26.875 million. The fourth year annual interest payment is 10% x \$26.875 million = \$2.687 million, leaving a regular fourth year principal payment of \$7.888 million — \$2.687 million = \$5,200,961.21. This end—of—fourth—year principal payment would have left an outstanding principal balance of \$21,673,692.75, which is paid in full at the end of the year. Fourth year principal payments total \$26.875 million = \$5.201 million, plus \$21.674 million. Prepayments alter the annual cash ﬂows for years 3 and 4 as follows: m Balance Payment Interest Principal Balance 3 56.034 7.888 5.603 29.160 26.875 4 26.875 7.888 2.687 26.875 0 Calculating the weighted average life: Time Expected Principal Payments Time x Principal 1 1.888 1.888 2 2.077 4.154 3 29.160 87.48 4 268—75 M 60.000 201.022 WAL = 201.022/60 = 3.35 years 19. A bank originates a pool of 500 30-year mortgages, each averaging \$150,000 with an annual mortgage coupon rate of 8 percent. Assume that the GNMA credit risk insurance fee is 6 basis points and that the bank's servicing fee is 19 basis points. a. What is the present value of the mortgage pool? PV = \$500 x \$150,000 = \$75 million b. What is the monthly mortgage payment? There are 360 monthly mortgage payments (30 years x 12 months). Monthly mortgage payments are \$75,000,000 = PVAn=360, k=0.6667%*R :> R = \$550,323.43. 0. For the first two payments, what portion is interest and what portion is principal repayment? For the first monthly payment, the monthly interest is 0.08/12 x \$75 million = \$500,000. Therefore, for the first monthly mortgage payment, \$50,323.43 is repayment of principal. For the second monthly payment, the principal outstanding is \$75m — \$50,323.43 = \$74,949,676.57. The monthly interest payment is \$499,664.51. The principal payment in the second month is \$550,323.43 — \$499,664.51 = \$50,658.92. d. What are the expected monthly cash ﬂows to GNMA bondholders? The GNMA bond rate is 0.08 — (6 + 19) basis points = 7.75 percent. GNMA bondholders receive monthly payments of \$75m = PVAn=360, k=0.0775/12*R :> R = \$537,309.18. e. What is the present value of the GNMA pass—through bonds? Assume that the risk— adjusted market annual rate of return is 8 percent compounded monthly. The discount yield is 8 percent annually, compounded monthly. The present value of the GNMA pass-through bonds is PV = \$537,309.18*PVA n:360, #056677, = \$73,226,373.05. f. Would actual cash ﬂows to GNMA bondholders deviate from expected cash ﬂows as in part (d)? Why or why not? Actual payments will equal expected payments if and only if no prepayments are made. If any mortgages are prepaid as a result of refinancing or homeowner mobility, then the monthly payments will change. In the month in which prepayments are made, monthly payments will increase to reﬂect the principal repayments. In all subsequent months, monthly payments will decline to reﬂect the lower face value of the pass-through bonds. g. What are the expected monthly cash ﬂows for the bank and GNMA? GNMA and the originating bank share the difference between the monthly mortgage payments and the GNMA pass—through payments \$550,323.43 — \$537,309.18 = \$13,014.25. The originating bank gets 19 out of the 25 basis points (or 76 percent) for a payment of \$9,890.83 monthly. GNMA receives the remaining 6 basis points (or 24 percent) for a payment of \$3,123.42. h. If all of the mortgages in the pool are completely prepaid at the end of the second month, what is the pool's weighted—average life? Hint: Use your answer to part c. Time Expected Principal Payments Time x Principal 1 mo. \$50,323.43 \$50,323.43 2 mo. \$74,949,676.57 \$149,899,353.10 \$75,000,000.00 \$149,949,676.53 WAL = (149,949,676.53/75 million) = 1.9993 months The principal payment in the first month is \$50,323.43. If the loan is paid off after month two, the principal payment in month two is \$75 million - \$50,323.43 = \$74,949,676.57. i. What is the price of the GNMA pass-through security if its weighted-average life is equal to your solution for part (h)? Assume no change in market interest rates. The GNMA with a weighted average life of 1.9993 months has only two cash ﬂows. The first month's cash ﬂow is \$537,309.18. The second month's cash ﬂow is \$537,309.18 plus the extra principal repayment of \$74,899,017.65 = \$75,436,326.83. The present value of the GNMA is PV = [\$537,309.18/(l.006667)] + [\$75,436,326.83/(l.006667)2] = \$74,974,229.44, where the monthly discount rate is l + (.08/ 12). j. What is the price of the GNMA pass-through with a weighted-average life equal to your solution for part (h) if market yields decline by 50 basis points? Market yields decline 50 basis points, to 7.5 percent per annum compounded monthly. The present value of the GNMA is PV = [\$537,309.18/(1.00625)] + [\$75,436,326.83/(1.00625)2] = \$75,036,111.70, where the monthly discount rate is .075/ 12. ...
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fins3630 solution - 6 An F1 is planning to issue \$100...

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