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Answer: USD -225.4 million
## Calculation Explanation **Step 1: Calculate the equity loss** - Initial equity assets: USD 350 million - Loss of 50%: 350 × 0.50 = USD 175 million loss **Step 2: Calculate the change in liability value due to interest rate decline** - Liabilities: USD 180 million - Modified duration: 14 - Yield decline: 2% - Change in liability value = -Duration × ΔYield × Liability Value - Change = -14 × (-0.02) × 180 = -14 × (-0.02) × 180 = 0.28 × 180 = USD 50.4 million increase **Step 3: Calculate the change in surplus** - Initial surplus = Assets - Liabilities = 350 - 180 = USD 170 million - New assets = 350 - 175 = USD 175 million - New liabilities = 180 + 50.4 = USD 230.4 million - New surplus = 175 - 230.4 = USD -55.4 million - Change in surplus = New surplus - Initial surplus = -55.4 - 170 = USD -225.4 million **Step 4: Verify the calculation** - Change in surplus = Change in assets - Change in liabilities - Change in assets = -175 million (equity loss) - Change in liabilities = +50.4 million (due to interest rate decline) - Change in surplus = -175 - 50.4 = USD -225.4 million Therefore, the correct answer is USD -225.4 million (Option C).
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At the end of 2007, Chad & Co.'s pension had USD 350 million worth of assets that were fully invested in equities and USD 180 million in fixed-income liabilities with a modified duration of 14. In 2008, the wide spread effects of the subprime crisis hit the pension fund, causing its investment in equities to loss 50% of their market value. In addition, the immediate response from the government – cutting interest rates – to salvage the situation, caused bond yields to decline by 2%. What was the change in the pension fund's surplus in 2008?
A
USD -55.4 million
B
USD -124.6 million
C
USD -225.4 million
D
USD -230.4 million
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