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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 281 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 riskbased 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 15year mortgage pool are to be
prepaid in four years, what is the weightedaverage 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 30year 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 passthrough 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 passthrough 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 passthrough security if its weightedaverage
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 passthrough with a weightedaverage 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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