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Explanation:
To determine the correct recommendation, we need to calculate the RAROC and the Adjusted RAROC (ARAROC) for the SMBL division.
1. Calculate Net Income (After-Tax):
$150 million = $18.00 million$6.00 million$1.25 million$1506.30` million$120 million = $2.40 millionPre-tax Income = Revenue - Interest Costs - Operating Costs - EL + Income from Risk Capital
= $18.00 - $6.00 - $1.25 - $6.30 + $2.40 = $6.85 million
Taxes = 30% × $6.85 million = $2.055 million
Net After-Tax Income = $6.85 - $2.055 = $4.795 million
2. Calculate RAROC:
(Note: Since RAROC 3.9958% < Hurdle rate 4.6%, the division is underperforming relative to the company's baseline expectation).
3. Calculate Adjusted RAROC (ARAROC): Using the standard adjustment formula:
(Alternative ARAROC formulation: . Both methods yield a value significantly below the required threshold).
4. Conclusion: Because the Adjusted RAROC (1.848%) is less than the risk-free rate (2.0%), and is far below the market risk premium ( = 6% - 2% = 4%), the division is effectively destroying shareholder value. Thus, the bank should close down the SMBL division, which matches statement C.
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Q.38 Smart Bank (SB) recently launched a successful takeover of AC Bank. After post-acquisition analysis, senior management at SB strongly feels some of the AC’s business lines do not justify their huge capital allocations. Of key concern is AC’s Small and Medium Businesses Lending Division (SMBL), which has a Loan portfolio worth $150 million. The division relies heavily on deposits to satisfy its funding needs. After extensively analyzing the division’s credit risk, analysts at SB determine that the probability of default is 7% and the loss given default is 60%. What’s more, the exposure at default is 100% of the loan exposure. Senior management requests a review of SMBL’s capital allocation in an attempt to establish exactly how efficient the division is in its use of funds compared to other divisions. The bank applies a 1-year horizon to measure the parameters outlined in the exhibit below:
| Item | Value |
|---|---|
| SMBL division | |
| Economic capital | $120 million |
| Operating direct costs | $1.25 million |
| Interest costs | $6 million |
| Cost of debt capital | 5% |
| Return on risk capital | 2% |
| Return on the loan portfolio | 12% |
| Further Details | |
| Hurdle rate | 4.6% |
| Equity market return | 6% |
| Risk-free rate | 2% |
| Equity beta | 1.08 |
| Effective tax rate | 30% |
Assume that the effective tax rate and hurdle rate span all business lines, there are no transfers, and that correlations between the various divisions are the same. Furthermore, all divisions have a mandate to maximize shareholder wealth. Which of the following recommendations of SB’s analysts would be correct?
A
Keep the SMBL division because the adjusted RAROC is greater than the risk-free rate
B
Keep the SMBL division because RAROC is greater than the hurdle rate
C
Close down the SMBL division because the adjusted RAROC is less than the risk-free rate
D
Close down the SMBL division because adjusted RAROC is greater than the hurdle rate