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.
is there a question somewhere in there?
To evaluate the proposed expansion of the subsidiary located in France, we can use the Net Present Value (NPV) method to determine if the project is financially viable. The NPV takes into account the initial investment, expected cash flows, and the required return.
Step 1: Calculate the present value of the expected cash flows.
- As the cash flows are in Euros, we need to convert them to US dollars using the current spot exchange rate of €0.5 per dollar.
- The cash flows are expected to be €0.9 million for the next three years, so the present value of each cash flow can be calculated as follows:
Year 1: PV1 = €0.9 million / (1 + 7%) = €0.8411 million
Year 2: PV2 = €0.9 million / (1 + 7%)^2 = €0.7856 million
Year 3: PV3 = €0.9 million / (1 + 7%)^3 = €0.7347 million
Step 2: Calculate the present value of the initial investment.
- The cost of the expansion is €2 million, which needs to be converted to US dollars using the current spot exchange rate.
- PV(initial investment) = €2 million * €0.5 / (1 + 5%) = €0.9524 million
Step 3: Calculate the net present value (NPV).
- NPV = sum of present values of cash flows - present value of initial investment
- NPV = PV1 + PV2 + PV3 - PV(initial investment)
- NPV = €0.8411 million + €0.7856 million + €0.7347 million - €0.9524 million
Step 4: Determine the viability of the project.
- If the NPV is positive, the project is financially viable and creates value for the company.
- If the NPV is negative, the project is not financially viable and may result in losses for the company.
- If the NPV is zero, the project is considered to break even.
By calculating the NPV, you can determine whether the proposed expansion of the subsidiary in France is a financially viable investment.
To evaluate the proposed expansion of the subsidiary in France, we need to calculate the net present value (NPV) of the project. NPV is a financial metric that measures the profitability of an investment by comparing the present value of its expected cash flows with the initial investment cost.
To calculate the NPV, we need to convert the cash flows from Euros to Dollars using the spot exchange rate and then discount them back to the present value using the required return rate. Here are the steps to calculate the NPV:
1. Calculate the present value factor for each year using the required return rate. The formula to calculate the present value factor is (1 + required return rate)^(number of years). In this case, the required return rate is 10 percent and the project is expected to generate cash flows for three years. So the present value factors for each year would be:
- Year 1: (1 + 10%)^1 = 1.1
- Year 2: (1 + 10%)^2 = 1.21
- Year 3: (1 + 10%)^3 = 1.331
2. Convert the cash flows from Euros to Dollars using the spot exchange rate. The spot exchange rate is given as € 0.5 per Dollar. So, the cash flows in Dollars would be:
- Year 1: € 0.9 million * € 0.5 per Dollar = $ 0.45 million
- Year 2: € 0.9 million * € 0.5 per Dollar = $ 0.45 million
- Year 3: € 0.9 million * € 0.5 per Dollar = $ 0.45 million
3. Calculate the present value of each cash flow by multiplying it with the corresponding present value factor. The present values in Dollars would be:
- Year 1: $ 0.45 million * 1.1 = $ 0.495 million
- Year 2: $ 0.45 million * 1.21 = $ 0.5445 million
- Year 3: $ 0.45 million * 1.331 = $ 0.59895 million
4. Calculate the sum of the present values to get the total present value of the cash flows. In this case, the total present value of the cash flows would be:
Total PV = $ 0.495 million + $ 0.5445 million + $ 0.59895 million
5. Subtract the initial investment cost from the total present value to get the net present value (NPV). The initial investment cost is given as € 2 million. To convert Euros to Dollars, multiply it by the spot exchange rate. So, the initial investment cost in Dollars would be:
- € 2 million * € 0.5 per Dollar = $ 1 million
NPV = Total PV - Initial Investment Cost
Finally, compare the calculated NPV with zero. If the NPV is positive, it indicates that the project is expected to generate a positive return and should be considered. If the NPV is negative, it indicates that the project is expected to generate a negative return and may not be worthwhile.
Note: The risk-free rates in the United States and Euro-land are mentioned in the question but are not used in the calculation of NPV.