Question

Mini Case: Richard May’s Options It is Tuesday afternoon, February 14, 2012. Richard May, Assistant Treasurer at American Digital Graphics (ADG), sits in his office on the thirty-fourth floor of the building that dominates Rockefeller Plaza’s west perimeter. “I must get this hedging memo done,” thinks May, “and get out of here. Foreign exchange options? I had better get the story straight before someone in the Finance Committee starts asking questions.”

Before we delve any further into Richard May’s musings, let us learn a bit about ADG. ADG is a $12 billion sales company engaged in the development, manufacture, and marketing of microprocessorbased equipment. Although thirty percent of the firm’s sales are currently abroad, the firm has full-fledged manufacturing facilities in only three foreign countries, Germany, Canada, and Brazil. An assembly plant in Singapore exists primarily to solder Japanese semiconductor chips onto circuit boards and to screw these into Brazilian-made boxes for shipment to the United States, Canada, and Germany. The German subsidiary has developed half of its sales to France and the United Kingdom, billing in euros. The Hamburg office has automatic permission to repatriate €3 million by September 15th (in 214 days). Meanwhile, the firm has an agreement to buy 300,000 RAM chips at ¥8000 each semi-annually, and it is this payment that will fall due on June 10th (in 117 days).

Richard May is in his Rockefeller Center office, he has been printing spot, forward and currency options and futures quotations from the company’s Bloomberg terminal. Looking at these prices, Richard realizes that he can work out how much the euro or yen would have to change to make the option worthwhile. Richard makes a mental note that ADG can typically borrow in the Eurocurrency market. “I’ll attach these numbers to my memo,” mutters May, but the truth is he has yet to come to grips with the real question, which is when are currency options a better mean of hedging exchange risk for an international firm than traditional forward exchange contracts or future’s contracts.

Please assist Mr. May in his analysis of currency hedging for his report to ADG’s Finance Committee. (use 360 days in 1 year in the calculation)

a. For the future receivables, calculate the receiving from each of the forward, money market, and option hedging

b. For the future payables, calculate the receiving from each of the forward, money market, and option hedging

c. Calculate the breakeven exchange rate between forward and option hedging.

Relevant market data:

The current spot exchange rate S0=$1.3088/€ 7-month forward exchange rate F7-month=$1.3090/€ Dollar 1-year lending interest rate = 0.78% and euro 1-year borrowing interest rate = 2.40%. The strike price for put option on the euro = $1.3100 The put option premium = $0.0509/€ .

The current spot exchange rate S0=$0.01274/¥ 4-month forward exchange rate F4-month=$0.01274/¥ Dollar 1-year borrowing interest rate = 0.62% and yen 1-year lending interest rate = 0.18%. The strike price for call option on the yen = $.0127/¥ The call option premium = $0.000311/¥

Answer 1

ADG’s euro receivable
ADG has a €3,000,000 receivable in 214 days on September 15th. To assess alternative ways of hedging, the following data are relevant: The current spot exchange rate (S)=$1.3088/€, 7-month forward exchange rate (F)=$1.3090, the dollar interest rate (bid)=0.78% and euro interest rate (ask)=1.40%; the put option on the euro with the strike (exercise) price of $1.31 selling for a premium of 5.09 cents per euro. Here we consider and compare three alternative hedging methods as in our discussions in the textbook: Forward, money market, and option hedges. Hedging with futures is often inconvenient due to the standardized maturities and contract size and also possibly thin trading.

▪ Forward hedge

If ADG chooses to use forward contract, it just needs to sell its euro receivable at today’s forward exchange. ADG then is assured of receiving a guaranteed dollar amount of $3,927,000 on September 15th: (€3,000,000) ($1.3090/€) = $3,927,000.

▪ Money market hedge

If ADG decides to use money market hedging, it first needs to borrow the present value (PV) of its euro receivable at 2.40% interest rate (=1.40%+1.0%):

PV = (€3,000,000) / (1+0.024(214/360)) = 3,000,000 / 1.01427 = €2,957,802.

It then would convert €2,957,802 at today’s spot exchange rate of $1.3088/€ into $3,871,171. If ADG invests this dollar amount at the dollar interest rate till September 15th, the future value (FV) of the investment will be:

FV = ($3,871,171) (1+0.0078 (214/360) ) = $3,889,121.

▪ Option hedge

If ADG chooses to hedge its euro receivable using currency options, it can purchase put options on three million euros with a $1.31 strike price at the premium of 5.09 cents per euro. This means that the firm has to spend the option cost upfront. The option costs, including the time value of money, would be: 153,408 = (€3,000,000) ($0.0509) [1+0.0078 (214/360) ]. If the future spot exchange rate turns out to be less than the strike price, i.e., if the euro becomes cheaper than the option strike price ($1.31), ADG will simply exercise its put option and exchange its euro receivable at the strike price, collect $3,776,592 (net of option costs), which is the guaranteed minimum net dollar proceeds: (€3,000,000) ($1.31) - $153,408 = $3,776,592. If the euro becomes stronger than the strike price, the firm will simply let its put option expire and convert its euro receivable at the future spot exchange rate.

As can be seen from the following graph, forward hedging dominates money market hedging. If the future spot rate exceeds the indifference rate, S* = $1.36, option hedging becomes preferable; otherwise, forward hedging is preferable.
Dollar receipt from euro receivable hedging alternatives

ADG’s yen payable
ADG has a ¥2,400 million payable in 4 months. The relevant market data include: The current spot exchange rate of $0.01274/¥, four-month forward exchange rate of $0.01274/¥, four-month call option on yen with the strike price set at 127 cents for 100 yen that is selling for 3.11 cents per 100 yen. ADG’s borrowing interest rate in dollars is 0.62%, while lending interest rate in yen is 0.18%.

▪ Forward hedge

If ADG decides to use forward contract to hedge its yen payable, it just needs to purchase the yen payable amount forward at today forward exchange rate. The dollar cost of doing so will be $30,576,000 = (¥2,400,000,000) ($0.01274/¥).
▪ Money market hedge

Money market hedging would require borrowing the PV of the yen payable in dollars, $30,558,123.50 = [(¥2,400,000,000)/(1+0.0018(117/360)] ($0.01274), and converting the dollar amount borrowed into yen and invest for four months at the yen interest rate to receive,

¥2,400,000,000 = ($30,558,123.50/$0.01274/¥)(1+0.0018(117/360)). When ADG receives the maturity value of the yen investment, it will use the yen amount to make payment to Matsumerda. Lastly, in four month, ADG will pay back the dollar loan: $30,719,012 = ($30,558,123.50) (1+0.0162(117/360)).
▪ Option hedge

In the case of hedging with option, ADG will need to buy call option on its yen payable. If ADG decides to buy options with strike price set at $0.0127 per dollar trading for 3.11 cents per 100 yens, the option cost (including the time value of money) will be,

$747,783 = (¥2,400,000,000)($0.000311)[1+0.0057(117/360)]

= ($746,400)(1.0018525)

If the yen appreciates beyond the strike price of the call option, K=$0.0127/¥, ADG will simply exercise its option and the max dollar cost of securing the yen payable amount will be,

$31,227,783 = (¥2,400,000,000)($0.0127/¥) + $747,783.

As can be seen from the graph below, forward hedge dominates money market hedge as the dollar cost will be always lower with forward hedge than with money market hedge. If the exchange rate becomes lower than the indifference rate, S*=$0.0124, call option hedge would be preferable; otherwise, forward hedge would be preferable. The indifference rate can be identified from solving the following equation for S*: 30,576,000 = (2,400,000,000) S* +747,783.

Dollar cost from yen payable hedging alternatives