Question

Surfboards U.S.A. is expanding its operations to Australia. The current indirect exchange rate is 1.45. The discount rate in the U.S. for the project is 14% and the company has forecasted the following Australian dollars (in millions) for the expansion project:

Year 0	Year 1	Year 2	Year 3	Year 4
A-$30	A$5	A$9	A$16	A$20

     What is the NPV of the project given the risk free rate of interest in each country as shown below?

	1 year	2 years	3 years	4 years
U.S. Risk Free Rate	0.137%	0.275%	0.397%	0.606%
Australia Risk Free Rate	2.93%	2.96%	3.06%	3.24%

Answer 1

NOTE: The NPV of the Project can be calculated by converting A$ project cash flow into USD at the exchange rate prevailing at the time of the cash flow. To project the exchange rate at each such time one needs to use the interest parity equation to determine expected exchange rates at the end of Year 1, Year 2, Year 3 and Year 4.

Initial Investment in A $ = A$ 30 and Current Exchange Rate = A$ 1.45 / $

Initial Investment in $ = I ($) = 30 / 1.45 = $20.6897 million

Year 1: US Risk-Free Rate = 0.137% and Australian Risk-Free Rate = 2.93 %. Prevalent Exchange Rate = 1.45 x [(1.0293) / (1.00137)] = $ 1.49044

Year 1 Cash Flow in A $ = A $ 5 and Year 1 Cash Flow in USD = 5 / 1.49044 = $ 3.35471 million

Year 2: US Risk-Free Rate = 0.275% and Australian Risk-Free Rate = 2.96 %. Prevalent Exchange Rate = 1.45 x [(1.0296) / (1.00275)]^(2) = $ 1.52869

Year 2 Cash Flow in A $ = A $ 9 and Year 2 Cash Flow in USD = 9 / 1.52869 = $ 5.88739 million

Year 3: US Risk-Free Rate = 0.397 % and Australian Risk-Free Rate = 3.06 %. Prevalent Exchange Rate = 1.45 x [(1.0306) / (1.00397)]^(3) = $ 1.56847

Year 3 Cash Flow in A $ = A $ 16 and Year 3 Cash Flow in USD = 16 / 1.56847 = $ 10.201 million

Year 4: US Risk-Free Rate = 0.606 % and Australian Risk-Free Rate = 3.24 %. Prevalent Exchange Rate = 1.45 x [(1.0324) / (1.00606)]^(4) = $ 1.60792

Year 4 Cash Flow in A $ = A $ 20 and Year 4 Cash Flow in USD = 20 / 1.60792 = $ 12.4384 million

USD Discount Rate = 14 %

Total Present Value of USD Cash Flows = PV($) = [3.35471 / 1.14] + [5.88739 / (1.14)^(2)] + [10.201/(1.14)^(3)] + [12.4384 / (1.14)^(4)] = $ 21.7228 million

Project NPV = PV($) - I($) = 21.7228 - 20.6897 = $ 1.03317 million