Question

Company X has an investment opportunity in Europe. the project costs €15,500,000 and is expected to produce cash flows of €4,100,000 in year 1, €5,100,000 in year 2, and €5,500,000 in year 3. the current spot exchange rate is $.73/€ and the current risk-free rate in the united states is 3.1 percent, compared to that in euroland of 2.2 percent. the appropriate discount rate for the project is estimated to be 10 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 €10,000,000.

what is the npv of the project in u.s. dollars?
a) $4,200,000
b) $2,300,000
c) $3,400,000
d) $5,100,000

Answer 1

The NPV of the investment opportunity for Company X in U.S. dollars, after converting and discounting the cash flows and sale price, is approximately $2.9 million, making the closest provided choice (b) $2,300,000. Therefore, the correct option is b) $2,300,000.

Step-by-step explanation:

To calculate the Net Present Value (NPV) of the investment in U.S. dollars, we need to: convert future cash flows from euros to dollars, discount those cash flows to their present value at the 10 percent discount rate, and then sum up these discounted cash flows along with the discounted value of the estimated sale price of the subsidiary at the end of year 3.

Here's the step-by-step calculation:

• 
  
• Year 1 cash flow: €4,100,000 * $.73/ € = $2,993,000
• 
  
• Year 2 cash flow: €5,100,000 * $.73/ € = $3,723,000
• 
  
• Year 3 cash flow (including sale): (€5,500,000 + €10,000,000) * $.73/ € = $11,285,000
• 
  
• Discounted year 1 cash flow: $2,993,000 / (1 + 0.10)^1 = $2,720,909
• 
  
• Discounted year 2 cash flow: $3,723,000 / (1 + 0.10)^2 = $3,081,818
• 
  
• Discounted year 3 cash flow: $11,285,000 / (1 + 0.10)^3 = $8,433,577

Summing up the discounted cash flows:

$2,720,909 + $3,081,818 + $8,433,577 = $14,236,304

Now, subtract the project cost (already in U.S. dollars) from the sum of the discounted cash flows:

$14,236,304 - $11,335,000 (cost converted at $.73/ €)= $2,901,304

The NPV of the project in U.S. dollars is approximately $2.9 million, so the closest answer choice provided is (b) $2,300,000.