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FRM Part II · FRM Exam Part II · Capital Structure in Banks

A bank's Corporate unit has net income after expected losses of 60 million, and is allocated economic capital of 400 million. The bank's cost of equity (hurdle rate) is 12%. Capital earns a risk-free return of 3% that is credited to the unit, adding to income in a RAROC calculation. Using RAROC = (net income after expected loss + return on allocated capital) / economic capital, what are RAROC and the economic value added (RAROC minus hurdle, times capital)?

RAROC is 18% and EVA is 24 million. The 3% credit on 400 million of capital adds 12 million to the 60 million income, giving 72 million over 400 million capital. Excess over the 12% hurdle is 6%, times 400 million, equals 24 million.

  1. ARAROC 18.0%; EVA 24 millionCorrect
  2. BRAROC 15.0%; EVA 12 million
  3. CRAROC 15.0%; EVA 60 million
  4. DRAROC 18.0%; EVA 72 million

Explanation

Return on capital = 3% x 400 = 12 million. Numerator = 60 + 12 = 72 million. RAROC = 72/400 = 18%. EVA = (18% - 12%) x 400 = 24 million. Ignoring the capital benefit gives 15% and 12 million; 72 million confuses the numerator with EVA.

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