Lakonishok Equipment has an investment opportunity in Europe. The project costs

Question

Lakonishok Equipment has an investment opportunity in Europe. The project costs €15 million and is expected to produce cash flows of €2.8 million in Year 1, €3.4 million in Year 2, and €3.9 million in Year 3. The current spot exchange rate is $1.43 / €; and the current risk-free rate in the United States is 2.9 percent, compared to that in Europe of 2.2 percent. The appropriate discount rate for the project is estimated to be 11 percent, the U.S. cost of capital for the company. In addition, the subsidiary can be sold at the end of three years for an estimated €9.8 million. Use the exact form of interest rate parity in calculating the expected spot rates. What is the NPV of the project in U.S. dollars? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16. Enter your answer in dollars, not in millions, e.g., 1,234,567.) NPV $ Enter your answer in dollars, not in millions, e.g., 1,234,567.

Explanation / Answer

Step 1: Calculate Expected Spot Rates for Year 1 to Year 3

The expected spot rates for Year 1 to Year 3 have been calculated as follows:

Expected Spot Rate (Year 1) = (Risk Free Rate in US/Risk Free Rate in Europe)^(Years)*(Current Spot Exchange Rate) = (1.029/1.022)^1*(1.43/€) = 1.4397945205/€

Expected Spot Rate (Year 2) = (Risk Free Rate in US/Risk Free Rate in Europe)^(Years)*(Current Spot Exchange Rate) = (1.029/1.022)^2*(1.43/€) = 1.4496561269/€

Expected Spot Rate (Year 3) = (Risk Free Rate in US/Risk Free Rate in Europe)^(Years)*(Current Spot Exchange Rate) = (1.029/1.022)^3*(1.43/€) = 1.4595852784/€

_______

Step 2: Calculate Cash Flows in Dollars For Each Year with the Use of Expected Spot Rates

The cash flows for year have been calculated as follows:

Cash Flow Year 0 = -€15,000,000*1.43/€ = -$21,450,000

Cash Flow Year 1 = €2,800,000*1.4397945205/€ = $4,031,424.66

Cash Flow Year 2 = €3,400,000*1.4496561269/€ = $4,928,830.83

Cash Flow Year 3 = €(3,900,000 + 9,800,000)*1.4595852784/€ = $19,996,318

_______

Step 3: Calculate NPV

NPV is the difference between the present value of cash inflows and present value of cash outflows. It can be calculated with the use of following formula:

NPV = Cash Flow Year 0 + Cash Flow Year 1/(1+Discount Rate)^1 + Cash Flow Year 2/(1+Discount Rate)^2 + Cash Flow Year 3/(1+Discount Rate)^3

Using the values calculated above and informationg provided in the question, we get,

NPV = -21,450,000 + 4,031,424.66/(1+11%)^1 + 4,928,830.83/(1+11%)^2 + 19,996,318/(1+11%)^3 = $803,399.16 (answer)

Notes:

There can be a slight difference in answer on account of rounding off values.

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