
Explanation:
To find the internal rate of return (IRR) for the equity holders, we need to identify the cash flows associated with the equity tranche from the table (column 10, Equity Flow) and set the net present value (NPV) to zero:
$0.820$$0.565$$0.310$$0.055$$6.101$The IRR is the discount rate that solves the following equation:
Using a financial calculator or testing the given options, let's test 11.44% ():
Sum of PVs = $0.7358 + 0.4549 + 0.2241 + 0.0357 + 3.5516 \approx 5.00215.00` (within rounding differences).
Thus, the internal rate of return (IRR) is nearest to 11.44%.
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313.3. The following structure is identical to Malz's<sup>12</sup> three-tier securitization structure, with one difference: the scenario reflects an assumption that the annual default is 3.0%. To remind of Malz structure:
$95.0 million = $85.0 million senior + $10.0 million mezzanine$5.0 mi| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Defaults | |||||||||||
| t | Annual | Cum'l | Survived | Loan Interest | Excess Spread | Over-collateral | Recovery | OC + Recovery | Equity Flow | Results | OC a/c |
| d(t) | |||||||||||
| 0 | (5.00) | ||||||||||
| 1 | 3.0 | 3.0 | 97.0 | $8.245 | $2.570 | $1.750 | $1.200 | $2.950 | $0.820 | Y | $2.950 |
| 2 | 3.0 | 6.0 | 94.0 | 7.990 | 2.315 | 1.750 | 1.200 | 2.950 | 0.565 | Y | 6.048 |
| 3 | 3.0 | 9.0 | 91.0 | 7.735 | 2.060 | 1.750 | 1.200 | 2.950 | 0.310 | Y | 9.300 |
| 4 | 3.0 | 12.0 | 88.0 | 7.480 | 1.805 | 1.750 | 1.200 | 2.950 | 0.055 | Y | 12.715 |
| 5 | 3.0 | 15.0 | 85.0 | 92.225 | 1.200 | 6.101 | 13.351 |
Total terminal avai funds = L(5) + R(5) + OC a/c (final) 106.776
Owed to bond tranches 100.675
Equity terminal cash flow 6.101
Note: except for defaults/survive, all amounts in $millions
(Source: Allan Malz, Financial Risk Management: Models, History, and Institutions (Hoboken, NJ: John Wiley & Sons, 2011))
Which is nearest to the internal rate of return (IRR) for the equity holders?
A
-33.3%
B
2.09%
C
11.44%
D
56.25%