Question

Mainz GmbH, a German importing firm anticipates receiving ¥189.3 million in 6 months.
Mainz’s management team is worried about the course of the ¥/€ exchange rate over the next 6
months and decides to hedge. The current spot and forward rates are S0=125 ¥/€ and Ft=6 months = 121
¥/€. The €-interest rate is 0.36% and the ¥-interest rate is 0.28%.

a) Compute the € cash flow to Mainz GmbH if it hedges its position using the forward market.
b) Compute the € cash flow to Mainz GmbH if it hedges its position using the money market.
c) Which of the two above hedges is best for Mainz GmbH.?
Alternatively, Mainz GmbH is contemplating the use of an options hedge. Sanwa bank is offering to
Mainz GmbH the following options:
i) Call option on ¥189.3 million at K=125 ¥/€, with a 3.8% premium (price as a percent
of current spot rate).
ii) Put option on ¥189.3 million at K=125 ¥/€, with a 3.15% premium (price as a percent
of current spot rate).
d) Which one is the right option to choose? What is the upfront cost of the option hedge?
e) Compute the break-even rate between the options hedge and the better one of the forward
and money market hedges. How does the break-even rate help you decide on which hedge to use?

Answer 1

(a)

1	Hedge using Forward Contract
	Receivable	¥         189,300,000.00
	Forward Rate	¥                          121.00
	Receivable in Forward Contract		€             1,564,462.81

(b)

2	Hedge via Money Market Hedge
	Receivable	¥         189,300,000.00
	(A) Today Borrow Money equivelent to ¥ 189,300,000 after 6-Months including interest	¥         189,035,350.51
	( ¥ 189,300,000 /1.0014)
	Exchange rate (Spot)	¥                          125.00
	Money received in $	€              1,512,282.80
	Interest on above Invest in @0.36% for 6-months	€                      2,722.11	€                  (49,457.90)
	Receivable in Money Market Hedge		€              1,515,004.91

(c)

Forward Contract hedge is best for mainz GmbH as the extra inflow received in this hedge is € 49,457.90 ( €1,564,462.81 - € 1,515,004.91)

(d)

Put option is right option to choose as the mainz GmbH want to sell ¥ and buy €.

Upfront cost of the option hedge is option premium

Option Premium = Spot Rate x 3.15% = ¥ 125 x 3.15% = ¥3.9375 or in € = ¥3.9375/¥125 (Spot rate) = €0.0315

So upfront cost of option hedge is €0.0315 for every ¥ 125 received or for every ¥ = €0.000252 (€0.0315/125)

(Here interest cost on option premium ignored)

(e)

Here better one is Forward contract hedge.

Break-even rate : Between option hedge and forward rate (Means receipt in both hedge should be same.

So here assume that spot rate after 6-month is 'z'

So,

Receipt in forward rate = Receipt in Option rate

€1,564,462.81 = (Receivable x Spot rate after 6-Month) - Total Option premium

€1,564,462.81 = (¥189,300,000 x z) - (¥189,300,000 x €0.000252)

Here total premium = Receivable x option cost per ¥ (as calculated in (d) )

€1,564,462.81 = (189300000z) - €47,703.60

189300000z = €1,612,166.41

z = €0.0085165 per ¥ or say ¥117.42/€

This B.E.P. help to decide which hedge is better, If mainz GmbH is expect that spot rate after 6-Month is more than ¥117.42/€ then forward rate is better and if expect that spot rate after 6-month is less than ¥117.42/€ then option hedge is better, as it will increase the cash inflow.