pmond, are you set with this one?
Sometimes I look at the CFAI answers and think they’re so elegant but other times I look at them and they just make my head hurt.
I easily get confused with currencies so I find it a lot easier to convert to the relevant currencies and work with actual loan and interest amounts than work with present value factors - although, I readily agree that working w/ factors is quicker (assuming I don’t get confused). However, you’ve got it straight in your head now is what’s important.
Here’s how I approached the question:
I figured out how many HK$ I would need to convert to get 25,000,000 euros. You know how to do this, it’s simply 25,000,000E x 11.42HK/E (the exchange rate at inception) = 285,500,000 HK.
Then I figured out what the quarterly interest payments would be in each currency. In euros, it’s 25,000,000E x 2.32%/4 = 145,000E per quarter In HKD, its’ 285,500,000 HK x 1.84%/4 = 1,313,300 per quarter.
Then I calculated the PV factors for Euribor & Hibor based on the rates in Exhibit 2.
Then I figured out the PV of the interest & principal in euros (the euro loan), and the PV of the interest & principal in HK$ (the Hong Kong dollar loan)
Then I converted the PV of the euro loan back into HK$ given the exchange rate 45 days later and compared it to the PV of the HK loan I calculated in step 4)
I didn’t come up with exact answer of HK$35,402,000 but it was pretty darn close.