
Explanation:
First, calculate the Expected Net Income for the SMBL division:
$150m = $6.30m$150m = $18.00m$120m = $2.40m$1.25m$6.00mPre-tax Income = Revenues + Return on risk capital - Operating direct costs - Interest costs - Expected Loss
Pre-tax Income = 18.00 + 2.40 - 1.25 - 6.00 - 6.30 = $6.85m
After-tax Net Income = Pre-tax Income × (1 - Effective tax rate)
After-tax Net Income = 6.85 × (1 - 0.30) = $4.795m
Next, compute RAROC: RAROC = After-tax Net Income / Economic Capital = 4.795 / 120 = 3.996%
To evaluate whether the division creates shareholder value considering its systematic risk, calculate the Adjusted RAROC: Adjusted RAROC = (RAROC - Risk-free rate) / Equity beta Adjusted RAROC = (3.996% - 2.0%) / 1.08 = 1.848%
Since the Adjusted RAROC (1.848%) is less than the risk-free rate (2.0%) (and also falls well below the market risk premium required to create shareholder value), the division destroys value. Hence, the analysts should recommend closing down the SMBL division. This accurately matches option 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