Question29 Assume that the exchange rate was AU$1.25/US$1 at 31/12/2006. One year later the exchange rate changed to AU$1/US$1. The rate of return in terms of US$ on the US$ assets was 10% from 12/31/2006 to 12/31/2007. What was the effective rate of return in terms of AU$ earned by this FI on the US$ assets? Select one alternative: a. -12% b. -10% c. +8% d. +10% e. +20% ResetMaximum marks: 3 Flag question undefined

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BlackTom AI · Accepted Answer

To analyze the problem, we first restate the given numbers and what needs to be compared.

- At 31/12/2006, the exchange rate is AU$1.25 per US$1. This means 1 USD costs 1.25 AU$. If the FI starts with US$1 of assets, the AU$ outlay is 1.25 AU$.
- One year later, the rate is AU$1 per US$1, i.e., 1 USD costs 1.00 AU$. The US$ assets earn 10% in USD terms over the year, so the ending value in USD is 1 × (1 + 0.10) = 1.10 USD.
- We want the effective rate of return in AU$ earned by the FI on the US$ assets, i.e., the growth of the AU$ value of the investment from initial AU$ outlay to the AU$ value at the end.

Now we evaluate each option and explain the reasoning behind it.

Option a: -12%
- Initial AU$ outlay: 1.25 AU$ for 1 USD.
- End value in AU$: 1.10 USD × 1.00 AU$/USD = 1.10 AU$.
- AU$ return: 1.10 − 1.25 = −0.15 AU$.
- Percentage return in AU$: (−0.15) / 1.25 = −0.12 = −12%.
- This matches the math above, so this option is consistent with the data.

Option b: -10%
- A −10% AU$ return would imply ending AU$ value of 1.25 × (1 − 0.10) = 1.125 AU$.
- However, the actual end value in AU$ is 1.10 AU$, not 1.125 AU$.
- Therefore this option misstates the outcome.

Option c: +8%
- An 8% gain would give an end AU$ value of 1.25 × 1.08 = 1.35 AU$ if computing from the same initial outlay, which is far from the actual end value of 1.10 AU$.
- This contradicts the given USD return and exchange-rate movement.

Option d: +10%
- A 10% AU$ gain would correspond to an end value of 1.25 × 1.10 = 1.375 AU$, again not matching the actual 1.10 AU$ end value.
- The USD return of 10% together with the depreciating AU$ value per USD leads to a loss in AU$ terms, not a gain.

Option e: +20%
- A 20% AU$ gain implies an end value of 1.25 × 1.20 = 1.50 AU$, which is clearly inconsistent with the end value determined from the USD return and the end exchange rate.

In summary, the only option that aligns with: (i) USD assets growing by 10%, and (ii) the change in AU$ per US$ from 1.25 to 1.00, is a negative AU$ return of −12%. The reasoning shows how the currency depreciation against the AU$ affects the AU$ value of USD-denominated assets, producing a loss in AU$ terms despite a positive USD return.

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