Suppose a $10,000 of 10% fixed rate mortgages have been pooled as security for a
ID: 2799965 • Letter: S
Question
Suppose a $10,000 of 10% fixed rate mortgages have been pooled as security for an issue of 10 pass-through securities. The mortgages have 3 years to maturity. The pass-through will carry a pass- through rate of 9% and a servicing fee of 1%. Consider the following prepayment assumptions for the pass-through: The following information pertains to next FOUR questions Suppose a $10,000 of 10% fixed rate mortgages have been pooled as security for an issue of 10 pass-through securities. The mortgages have 3 years to maturity. The pass-through will carry a pass- through rate of 9% and a servicing fee of 1% Consider the following prepayment assumptions for the pass-through: Pass-through A Pass-through B No prepayment throughout the entire term of the mortagages. 50% of the outstanding pool balance is expected to be id at the end of year 2. 10. If the market interest rate for the pass-through is 5%, the market value of each pass-through A is nearest: a) $1056 b) $1066 c) $1076 d) $1086 e) $1096 Sample 4, Tse 11. If the market interest rate for the pass-through remains at 58 the market value of pass-through B is nearest: a) $1064 b) $1074 c) $1084 d) $1094 e) $1104 12. If the market interest rate increases to 15%, then the difference in price between B and A is nearest: a) 11.77 b) 12.77 c) 13.77 d) 14.77 e) 15.77Explanation / Answer
We will first calculate the EMI on the mortgage using the below formulae:
Monthly Payment = P * [(r * (1+r)n)/((1+r)n - 1)] where P is the mortgage loan amount ($ 10000.00), r is the interest rate (10%) and n is the term. Since in this case the term is 3 years and mortgage payment are monthly, the tenure and rate shall be adjusted by 12. Hence r shall be 10%/12 and n shall 36. This will give us monthly payment of $322.67. Out of this 9% interest shall be for pass through holders ans balance 1% shall be service fee.
We can segregate the interest portion and cash flows of the Pass Through Holders (PTC) A as below in excel:
1,061.29
Hence the option (b) is the nearest answer.
To calculate the value of PTC B, where 50% of mortgage is expected to be prepaid at the end of Year 2, we can simulate the payment stream in excel as below and calculate the present value at 5% and value comes to $ 1057.71
Hence the option (a) is the nearest to answer at $ 1064
If the market rates increase to 15%, the value of PTC A shall become $ 916.98 and PTC B shall be $ 921.22; hence the option (a) is the nearest answer.
Month Mortgage Amount Interest Charged @ 10% Monthly Mortgage Payment Residual Mortgage Loan Amount Interest for PTC holders @ 9% Cash Flow PTC A Discount @ 5% 1.00 10,000.00 83.33 322.67 9,760.66 75.00 314.34 313.03 2.00 9,760.66 81.34 322.67 9,519.33 73.20 314.54 311.93 3.00 9,519.33 79.33 322.67 9,275.99 71.39 314.74 310.84 4.00 9,275.99 77.30 322.67 9,030.62 69.57 314.94 309.75 5.00 9,030.62 75.26 322.67 8,783.21 67.73 315.14 308.66 6.00 8,783.21 73.19 322.67 8,533.73 65.87 315.35 307.58 7.00 8,533.73 71.11 322.67 8,282.17 64.00 315.56 306.51 8.00 8,282.17 69.02 322.67 8,028.52 62.12 315.77 305.44 9.00 8,028.52 66.90 322.67 7,772.76 60.21 315.98 304.37 10.00 7,772.76 64.77 322.67 7,514.86 58.30 316.19 303.31 11.00 7,514.86 62.62 322.67 7,254.81 56.36 316.41 302.26 12.00 7,254.81 60.46 322.67 6,992.60 54.41 316.62 301.21 13.00 6,992.60 58.27 322.67 6,728.20 52.44 316.84 300.17 14.00 6,728.20 56.07 322.67 6,461.60 50.46 317.06 299.13 15.00 6,461.60 53.85 322.67 6,192.78 48.46 317.29 298.10 16.00 6,192.78 51.61 322.67 5,921.71 46.45 317.51 297.07 17.00 5,921.71 49.35 322.67 5,648.39 44.41 317.74 296.05 18.00 5,648.39 47.07 322.67 5,372.79 42.36 317.96 295.03 19.00 5,372.79 44.77 322.67 5,094.89 40.30 318.19 294.02 20.00 5,094.89 42.46 322.67 4,814.68 38.21 318.42 293.02 21.00 4,814.68 40.12 322.67 4,532.13 36.11 318.66 292.01 22.00 4,532.13 37.77 322.67 4,247.23 33.99 318.89 291.02 23.00 4,247.23 35.39 322.67 3,959.95 31.85 319.13 290.02 24.00 3,959.95 33.00 322.67 3,670.28 29.70 319.37 289.04 25.00 3,670.28 30.59 322.67 3,378.20 27.53 319.61 288.06 26.00 3,378.20 28.15 322.67 3,083.68 25.34 319.85 287.08 27.00 3,083.68 25.70 322.67 2,786.71 23.13 320.10 286.11 28.00 2,786.71 23.22 322.67 2,487.26 20.90 320.35 285.14 29.00 2,487.26 20.73 322.67 2,185.32 18.65 320.60 284.18 30.00 2,185.32 18.21 322.67 1,880.86 16.39 320.85 283.22 31.00 1,880.86 15.67 322.67 1,573.86 14.11 321.10 282.27 32.00 1,573.86 13.12 322.67 1,264.31 11.80 321.36 281.32 33.00 1,264.31 10.54 322.67 952.17 9.48 321.62 280.38 34.00 952.17 7.93 322.67 637.44 7.14 321.88 279.44 35.00 637.44 5.31 322.67 320.08 4.78 322.14 278.51 36.00 320.08 2.67 322.67 0.08 2.40 322.40 277.58 Discounted Cash Stream Value 10,612.88 Value Per Pass Through Bond (PTC) A - divide above value by 101,061.29
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.