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.
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.
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accountant
To evaluate the proposed expansion of the subsidiary located in France, we need to calculate the net present value (NPV) of the cash flows taking into account the cost of the expansion, the expected cash flows, and the required return.
Step 1: Convert the cost of the expansion from Euros to Dollars.
Given:
Cost of expansion = € 2 million
Spot exchange rate = € 0.5
To convert Euros to Dollars, we multiply the amount in Euros by the exchange rate:
Cost of expansion in Dollars = € 2 million * € 0.5 = $1 million
Step 2: Calculate the present value of the expected cash flows.
Given:
Expected cash flows = € 0.9 million per year for the next three years
Required return in Dollars = 10 percent per year
To calculate the present value of the cash flows, we need to discount each cash flow by the required return in Dollars:
PV of cash flows = Σ (Cash flow / (1 + Required return)^t)
Where:
Cash flow = € 0.9 million
Required return = 10 percent
t = year (1, 2, 3)
PV of cash flows = (€ 0.9 million / (1 + 0.1)^1) + (€ 0.9 million / (1 + 0.1)^2) + (€ 0.9 million / (1 + 0.1)^3)
PV of cash flows = (€ 0.9 million / 1.1) + (€ 0.9 million / 1.21) + (€ 0.9 million / 1.331)
Step 3: Convert the present value of cash flows from Euros to Dollars.
Given:
Spot exchange rate = € 0.5
To convert Euros to Dollars, we multiply the amount in Euros by the exchange rate:
PV of cash flows in Dollars = PV of cash flows * € 0.5
Step 4: Calculate the net present value (NPV).
Given:
Cost of expansion in Dollars = $1 million
The NPV of the project is calculated by subtracting the cost of the expansion from the present value of the cash flows:
NPV = PV of cash flows in Dollars - Cost of expansion in Dollars
If the NPV is positive, it means the project is expected to generate more value than its cost and is considered a good investment. If the NPV is negative, it means the project is expected to generate less value than its cost and is not recommended.
So, to find the NPV, compute the PV of cash flows in Dollars as described in step 3 and subtract the cost of expansion in Dollars.