Question

A firm has borrowed $100m by selling bonds in the US on which it pays a fixed coupon rate. This money was used to build a plant in Germany and all the sales from this plant are in Euros. The firm is facing currency risk because if Euro depreciates then the amount received in $ will go down. So the firm decides to enter into a currency swap with a notional principal of $100m. The swap will be for 2 years with fixed rate payments being exchanged on days 180,360,540 and 720.

You also have the following information: S₀ = $1.20/€.

Term (days)                $ Rate (r^$)       € Rate (r^€)      

180                              3.50%              2.80%

360                              3.60%              3.00%

540                              3.80%              3.40%

720                              3.90%              3.50%

a. Calculate the fixed coupon rate for the dollar and Euro.

b. Calculate the expected cash flows on days 180, 360, 540 and 720 in dollar terms.

c. Calculate the PV of the CFs calculated in b.

Answer 1

AMOUNT BORROWED IN US = $ 100

So 180 days payment principal with interest=100*(1+(3.50%*180/360))=101.75$

360 days   payment principal with interest=100*(1+3.60%) =103.60$

540 days   payment principal with interest=100*(3.80%*540/360) =105.70$

720 days   payment principal with interest=100*(3.90%*720/360) =107.80$

Then convert the same ( whtat we are paying in US) and deposit in Germany

So 180 days deposit principal with interest=101.75/1.20*(2.80%*180/360)=85.9786 £

360 days   depositt principal with interest=103.60/1.20*(1+3%) =88.40£

540 days   payment principal with interest=105.70*(3.40%*540/360) =92.519£

720 days   payment principal with interest=107.80/1.20*(3.5%*720/360) =95.30

a) Fxed cupon rate of $= 7.80% ( the cumulative percentage of 720 days)

Fixed cupon rate of £= 12.40% ( the cumulative percentage of 720 days)

b)

Expected cash flow 180 days =(85.9786*1.20)-101.75=1.42$

360 days=( 88.40*1.20 -103.60=2.48$

540 days =(92.519*1.2-105.7=5.32$

720 days =(95.30*1.20-107.80)=6.56$

c