Suppose you are evaluating a proposed expansion of an existing subsidiary located in France. The cost of the expansion would be € 2 million. The cash flows are expected to be € 0.9 million a year for the next three years. The dollar required return is 10 percent per year, and the current spot exchange rate for Euros is € 0.5. The risk-free rate in the United States is 5 percent, and the risk-free rate in “Euro-land” is 7 percent.
Using home currency and foreign currency approach decide whether the expansion should made or not on the basis of NPV
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Suppose you are evaluating a proposed expansion of an existing subsidiary located in France. The cost of the expansion would be € 2 million. The cash flows are expected to be € 0.9 million a year for the next three years. The dollar required return is 10 percent per year, and the current spot exchange rate for Euros is € 0.5. The risk-free rate in the United States is 5 percent, and the risk-free rate in “Euro-land” is 7 percent.
Using home currency and foreign currency approach decide whether the expansion should made or not on the basis of NPV
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IT SELF
To determine whether the expansion should be made or not based on the Net Present Value (NPV), we need to calculate the NPV using both the home currency and foreign currency approach.
1. Home Currency Approach:
In the home currency approach, we convert all cash flows to the home currency (in this case, US dollars) using the spot exchange rate.
Step 1: Calculate the present value of each cash flow in euros.
- Year 1: PV1 = € 0.9 million / (1 + 7%) = € 0.840 million
- Year 2: PV2 = € 0.9 million / (1 + 7%)^2 = € 0.785 million
- Year 3: PV3 = € 0.9 million / (1 + 7%)^3 = € 0.733 million
Step 2: Convert the present value of each cash flow to US dollars using the spot exchange rate (€ 0.5 = $1).
- Year 1: PV1 ($) = € 0.840 million × $0.5 = $420,000
- Year 2: PV2 ($) = € 0.785 million × $0.5 = $392,500
- Year 3: PV3 ($) = € 0.733 million × $0.5 = $366,500
Step 3: Calculate the NPV in US dollars by subtracting the initial investment.
- NPV ($) = ($420,000 + $392,500 + $366,500) - € 2 million = -$820,000
2. Foreign Currency Approach:
In the foreign currency approach, we discount the cash flows using the foreign risk-free rate.
Step 1: Calculate the present value of each cash flow in euros using the foreign risk-free rate.
- Year 1: PV1 = € 0.9 million / (1 + 7%) = € 0.840 million
- Year 2: PV2 = € 0.9 million / (1 + 7%)^2 = € 0.785 million
- Year 3: PV3 = € 0.9 million / (1 + 7%)^3 = € 0.733 million
Step 2: Calculate the NPV in euros by subtracting the initial investment in euros.
- NPV (€) = (€ 0.840 million + € 0.785 million + € 0.733 million) - € 2 million = -€ 0.642 million
To decide whether the expansion should be made or not based on NPV:
- In the home currency approach, the NPV is -$820,000, indicating a negative value. Hence, the expansion should not be made.
- In the foreign currency approach, the NPV is -€0.642 million, also representing a negative value. Therefore, based on both approaches, the expansion should not be made.