Question

The Strik-it-Rich Gold Mining Company is a U.S. multinational firms and considering investing in a project in Germany.  The cost of the investment project is €100 million. This cost occurs at the beginning of the year. The returning cash flow of this project is €120 million. Assume the returning cash flows happen at the end of the year. The firm’s cost of capital in the U.S. is 10%. The current exchange rate is S₀($/€)= $1.20/€. Strik-it-Rich’s management is, however, concerned with the possibility that the exchange rate may change quit a bit because of the potential withdrawal of the United Kingdom from the European Union. The firm estimates that the exchange rate at the end of the year could either be S₀($/€)= $1.00 or S₀($/€)= $1.40.

-find the net present value (NPV) of this project in U.S. dollars, if S₀($/€)is still $1.20/€ at the end of the year.

- find the net present value (NPV) of this project in U.S. dollars, if S₀($/€)is $1.00/€ or $1.40/€ at the end of the year.

- There are one-year call options on the exchange rates with the exercise price ofS($/€)= $1.20/€. The price paid to buy the call option contracts is $0.01 million for purchasing 1 million U.S. dollars. Please find the NPV if the mining company use call options.

- Instead of using call option contracts, the mining company can also use the real option. The exchange rate should become clear within a year. If the company has the option to delay this expansion plan for a year, please find the NPV after the company delays the expansion. Assume the exchange rate would not change in the next year.

Answer 1

Initial investment (in $ terms) = C₀ = €100 million x S₀ = €100 million x  $1.20/€ = $ 120 mn

Cash flows in year 1 (in $ terms) = C₁ = €120 million x S₁

The firm’s cost of capital in the U.S. is 10% = R

Find the net present value (NPV) of this project in U.S. dollars, if S₀($/€)is still $1.20/€ at the end of the year.

C₁ = 120 x 1.20 = $ 144 mn

NPV = - C₀ + C₁ / (1 + R) = -120 + 144 / (1 + 10%) = $ 10.91 mn

Find the net present value (NPV) of this project in U.S. dollars, if S₀($/€)is $1.00/€ or $1.40/€ at the end of the year.

When S₁ = $1.00/€

C₁ = 120 x 1.00 = $ 120 mn

NPV = - C₀ + C₁ / (1 + R) = -120 + 120 / (1 + 10%) = - $ 10.91 mn

When S₁ = $1.40/€ ​​​​​​​

C₁ = 120 x 1.40 = $ 168 mn

NPV = - C₀ + C₁ / (1 + R) = -120 + 168 / (1 + 10%) = $ 32.73 mn

There are one-year call options on the exchange rates with the exercise price ofS ($/€)= $1.20/€. The price paid to buy the call option contracts is $0.01 million for purchasing 1 million U.S. dollars. Please find the NPV if the mining company use call options.

The NPV in this case will be NPV as calculated in the first part - cost of purchasing the call options = $ 10.91 - Price of one call option contract x Number of contracts required = $ 10.91 - 0.01 x 120 = $ 9.71 mn