You work for an Australian firm that is considering a foreign investment in the U.S. The investment yields expected after-tax US dollar (USD) cash flows (in millions) as follows:[table]
Year 0 (initial investment) | Year 1 | Year 2 | Year 3
USD -500 | USD 300 | USD 300 | USD 300
[/table]Expected inflation is 20% in Australia and 44% in the U.S. for the next 3 years. Assume that the international parity conditions hold. Required returns for projects in this risk class are 20% in Australia; and 25% in the U.S. The spot exchange rate is AUD1.728/USD. USD -500 million at Year 0 means that the initial investment is USD 500 million. Estimate the project NPV itself (project perspective) in USD.Answer it in a unit of million USD with two decimal places, if your answer is USD 12.34 million, answer 12.34.

Question

You work for an Australian firm that is considering a foreign investment in the U.S. The investment yields expected after-tax US dollar (USD) cash flows (in millions) as follows:[table]
Year 0 (initial investment) | Year 1 | Year 2 | Year 3
USD -500 | USD 300 | USD 300 | USD 300
[/table]Expected inflation is 20% in Australia and 44% in the U.S. for the next 3 years. Assume that the international parity conditions hold. Required returns for projects in this risk class are 20% in Australia; and 25% in the U.S. The spot exchange rate is AUD1.728/USD. USD -500 million at Year 0 means that the initial investment is USD 500 million. Estimate the project NPV itself (project perspective) in USD.Answer it in a unit of million USD with two decimal places, if your answer is USD 12.34 million, answer 12.34.

BlackTom AI · Accepted Answer

We begin by restating the problem: an Australian firm considers a U.S. investment with cash flows in USD: Year 0 = -500 (USD million), Years 1–3 = +300 each year. Inflation is 20% in Australia and 44% in the U.S. for the next 3 years, with PPP holding.

First, determine how to evaluate the project from the project perspective in USD. Since the required return specified (project class risk) is 25% in the U.S. and the cash flows are already denominated in USD, the straightforward approach is to discount USD cash flows at the USD discount rate of 25%.

Option A (or the approach adjusted for USD cash flows) would be to compute NPV in USD directly:
- Year 0 cash flow: -500 (USD million).
- Year 1 PV: 300 / (1.25) = 240.00
- Year 2 PV: 300 / (1.25^2) = 300 / 1.5625 = 192.00
- Year 3 PV: 300 / (1.25^3) = 300 / 1.953125 ≈ 153.60

Next, sum the present values of the inflows and subtract the initial outlay:
- PV of inflows = 240.00 + 192.00 + 153.60 = 585.60
- NPV (USD) = 585.60 − 500.00 = 85.60 (USD million)

This calculation yields an NPV of +85.60 USD million when evaluated purely in USD terms with a 25% discount rate.

Now, consider the additional information about inflation and PPP. The problem provides expected inflation in Australia and the U.S. and the spot rate AUD/USD. Relative PPP suggests the expected future exchange rates could be influenced by the inflation differential, which would be relevant if we were converting USD cash flows to AUD for an AUD-based NPV or for a project valuation in AUD terms. The PPP forecast would imply changes in the AUD/USD rate over years 1–3, potentially changing the AUD value of USD cash flows if we were doing an AUD-terms analysis. In other words:
- If we were asked to report the NPV in AUD, we would convert each USD cash flow to AUD using the expected future exchange rates (based on PPP): S1 ≈ S0 × (1+π_AUS)/(1+π_US) = 1.728 × (1.20/1.44) ≈ 1.44 AUD/USD, and similarly for years 2 and 3, then discount at Australian rates or adjust accordingly. However, since the question explicitly asks for the NPV in USD, these PPP-derived exchange-rate movements do not affect the NPV calculation in USD terms.

To recap: the USD-denominated NPV calculation uses only the USD cash flows and the USD discount rate of 25%. The result of 85.60 is the project’s NPV in USD. If you were to report in AUD, you would perform an additional set of conversions using the expected exchange rates from PPP and then discount using Australian cost of capital, which could yield a different AUD-NPV value.

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