Question

A French firm is considering selling its line of laundry machines in the U.K. The business risk will be identical to the firm's existing line of business in the euro zone, the cost of capital in the euro zone is i€ = 10%. The expected inflation rate over the next two years in the U.K. is 3% per year and 2% per year in the euro zone. The spot exchange rates are $1.80 = £1.00 and $1.15 = €1.00. The pound sterling denominated cash flows are as follows: CF0= -200,000 Pounds CF1= 50000 Pounds CF2= 200000 Pounds What is the NPV of this project in Euros? Note: This is a French firm investing in UK. Please make sure that you convert the exchange rates into the Euro/Pound rate.

Answer 1

We will project the cash flows in pounds, then convert them into Euros.

Spot rate, (Euro/Pound rate) E0 = $1.80/ £1.00 x €1.00 / $1.15 = €1.5652 / £

E1 = E0 x (1 + i_Euro) / (1 + i_pound) = €1.5652 / £ x (1 + 2%) / (1 + 3%) = €1.5500 / £

E1 = E1 x (1 + i_Euro) / (1 + i_pound) = €1.5500 / £ x (1 + 2%) / (1 + 3%) = € 1.5350 / £

a M 49 Year, n 50 Cash flows in £ 51 Exchange rate (€/ £) 52 Cash flows in € 53 cost of capital in the euro 54 NPV N Linkage с E |CXE 0 1 2 -200,000.00 50,000.00 200,000.00 1.5652 1.5500 1.5350 -313,043.48 77,501.06 306,994.47 10% 11,126.47 '=NPV(053,P52:252)+052

Hence, NPV in Euros =  € 11,126.47