The current level of real estate prices in Moscow seem to be on a reasonable lev

Question

The current level of real estate prices in Moscow seem to be on a reasonable level now and you consider that this is just the right time to step into the market. You have noticed a nice apartment in the Leninsky Prospekt close to the city centre. The price for the apartment is $1.50 million. However, due to tax reasons you could buy that apartment only after 6 months. Currently you have sufficient funds deposited in a bank in Cypros (in euros). The annual yield on a bank deposit is 2.6%. Another option would be to convert a certain amount into dollars and deposit these funds into another bank with the annual yield of 1.5%. The spot exchange rate is 1.1741 EUR/USD (see the quote conventions from the lecture slides) and the 6m forward rate is quoted with premium equal to 95 basis points. So, you have two options of how to pay for the apartment:

a) Invest enough dollars for dollar deposit already today and hedge your exchange rate exposure in this way

b) Buy a forward contract for buying dollars against euros in six months (and continue to deposit euros)

Questions:

Try to show with calculations, which option has the lowest present value cost for you in euros?

Compute the correct forward rate implied by the interest rates.

Explanation / Answer

Price of the department= 1.5 million or say 1500000

Spot Rate 1 euro= 1.1741$ (Direct quote of Euro)

Spot Rate via direct quote of 1 USD =1/1.1741   = .8517 USD per Euro

Equivalent amount for apartment in Euros = (1500000*.8517) =1277550

So we have 1277550 Euros in our Cypros bank

Six Month forward rate = Spot rate + Premium =1.1741+.0095= 1.1836 USD for one Euro

Six month forward rate of 1 USD = 1/1.1836= .8449 Euro

Option A: Invest in Dollar in USA

Interest Rate in USA = 1.5%

Rate of apartment=1500000

Amount need to be deposited    = 1500000/periodic interest for 6 months

                                                          =1500000/ 1+ (.015*6/12)

                                                          =1488834 USD

Equivalent Euros needed at present = 1488834*Spot rate of USD via indirect quote

                                                                  = 1488834* .8517 = 1268040 EUROS

We need to withdraw this amount from Cypros bank

Remaining balance in Cypros= 1277550-1268040= 9510euros

we earn interest @ 2.6 % Per annumon this remaining amount and balance at 6 months end will be:

9510+9510*(2.6*6/12)% =9634Euros

Total amount spent is 1268040 and remaining amount is 9634

Option B

Euro balance at the end of 6 months = 1277550 + interest

                                                                   = 1277550 + 1277550*(2.6*6/12)%

                                                                   = 1294158 Euros

We have taken a forward contract at 1 USD= .8449 Euro

Equivalent Euros for payment of apartment = 1500000*.8449

                                                                               =1267350 Euros

Remaining balance in Cypron bank (1294158-1267350) = 26808 Euros

Conclusion: Select option B

Correct forward rate using interest rates

Forward Rate= Spot rate * (1+Periodic interest home/1+periodic interest foreign)

                       = 1.1741 * (1.0075/1.013)

Forward rate =1.1677 USD per Euro

Dollar will be at premium because interest rate in USA is lower

Thanks

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