OZ Bank in Australia borrows from local capital market and invests in one-year U.S. treasury bond. The interest rate in Australia is 5% per annum. And the yield to maturity of the invested U.S. treasury bond is 10% per annum. Currently, the spot exchange rate is AU$1.1 per US$. What will be the NET return in local currency (AU$) of this investment to the bank if the exchange rate falls to AU$1 per US$ in one year? (round to the nearest 2nd decimal)

Question

BlackTom AI · Accepted Answer

To begin, restate the scenario and the numbers involved to keep track of cash flows clearly. OZ Bank borrows 1.10 AU$ (the amount needed to invest in 1 US$ at the current spot of 1.1 AU$/US$) and uses it to buy 1.00 US$ worth of a one-year US Treasury, which yields 10% over the year. The spot exchange rate today is AU$1.10 per US$, and at the end of the year the rate falls to AU$1.00 per US$.

First, determine the dollar cash inflow from the US bond in USD terms. An investment of 1.00 USD at a 10% yield grows to 1.00 × (1 + 0.10) = 1.10 USD after one year.

Second, convert that USD payoff back to Australian dollars using the expected future exchange rate. If the rate falls to AU$1.00 per US$, then 1.10 USD equals 1.10 × 1.00 = 1.10 AU$.

Third, figure out the loan repayment in AU$. The bank borrowed 1.10 AU$ at 5% interest, so the amount owed after one year is 1.10 × (1 + 0.05) = 1.155 AU$.

Fourth, compute the net AU$ cash flow at year end by subtracting the AU$ loan repayment from the AU$ payoff from the investment: 1.10 AU$ − 1.155 AU$ = −0.055 AU$.

Fifth, assess the net return relative to the initial AU$ investment. The initial investment in AU$ was 1.10, so the return rate is −0.055 / 1.10 = −0.05, i.e., −5.00%.

Putting it together, the calculated net return in AU$ is −0.055 AU$, which corresponds to a −5.00% return when rounded to two decimals. Among the given options, this matches the option that shows −5.00%.

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