Question

You are the CFO of the Spade Music Company (HMC), a US-based musical instruments manufacturer. You have just made a huge sale to a British Music Festival company of GBP 2.5M worth of instruments. This money will be paid in GBP in 90 days and there is a FX risk attached to this transaction.

Given the information below, please determine what your choices are for managing this risk, be sure to consider all possible ways. Use a 360-day year basis, and determine the value on day 90 (when the payment will occur). Use the rates provided below, the bid/ask spread does not need to be considered for this problem.

Spot	GBP/USD	1.0875
Forward (90 Day)	GBP/USD	1.0772
Forecast Rate	GBP/USD	1.0735	in 90 days
Cost of Capital	10%
	Borrow	Invest
US Rates	4.0%	2.0%
UK Rates	7.0%	5.0%

Put Option Available @ 1.075 for a 1.25% premium. Minimal Acceptable Margin (USD) is 2.6 million.

Please provide all available decision choices and show calculations in details.

Answer 1

There are four scenarios possible in the above case:

(A) No Hedge

(B) Forward Cover

(C) Money Market Operation

(D) Currency Options

Now, let us calculate the payoff in each scenario:

(A) Do Nothing. All positions remaining uncovered. Receive GBP 2.5 Mn at the end of 90 days.

Forecast Rate = GBP 1.0735/ USD

Hence Payoff = GBP 2.5 Mn * 1.0735 = USD 2,683,750

(B) Forward Cover. Lock in a Forex Rate for the contract period. Hedge against any fluctuation whatsoever.

Buy Currency Forward at day 0 @ GBP 1.0772/ USD

We may ignore forward charges in the absence of information relating to it.

Payoff on Day 90 = GBP 2.5 Mn * 1.0772 = USD 2,693,000

(C) Money Market Operation.

Borrow GBP 2.5 Mn on Day 0 (including Interest). Convert and Invest in dollars. On Day 90, receive GBP 2.5 Mn from the customer and pay off borrowing plus interest.

Amount of Borrowing = GBP 2.5 Mn * (1/(1+(0.07 * 90/ 360))

Amount of Borrowing = GBP 2.5 Mn * 0.9828

Amount of Borrowing = GBP 2,457,000

Convert to USD using spot rate of GBP 1.0875/ USD

USD Received on conversion = USD 2,671,987.50

Investment Income at 2% for 90 days = USD 2,671,987.50 * 0.02 * 90/ 360

Investment Income = USD 13,359.94

Net Payoff = USD 2,671,987.50 + USD 13,359.94

Net Payoff = USD 2,685,347.44

(D) Currency Options

Buy a Put option at GBP 1.075/ USD

Margin Requirement = GBP 2.5 Mn * 1.0875 (Spot Rate) = USD 2,718,750

Hence, USD 2,600,000 will be covered position and the balance USD 118,750 would be uncovered position (i.e., GBP 2,390,804.60 is covered and GBP 109,195.40 is uncovered)

Premium cost = USD 2,600,000 * 1.25% = USD 32,500

Cost of Capital = Opportunity cost of Funds usage = USD 32,500 * 10% * 90/ 360 = USD 812.50

On Day 90, Forecast Rate = GBP 1.0735/ USD

Hence, Spade Music Company would exercise the put option and receive USD 2,570,114.95 (GBP 2,390,804.60 * 1.075) and convert the rest to USD at Forecast Rates (i.e.,) GBP 1.0735/ USD.

Money received from conversion = USD 117,221.26

Total Payoff = USD 2,570,114.95 + USD 117,221.26 – USD 32,500 – USD 812.50

Net Payoff = USD 2,654,023.71

Comparing the payoff from all the alternatives

(A) USD 2,683,750

(B) USD 2,693,000

(C) USD 2,685,347.44

(D) USD 2,654,023.71

Hence, the company should choose the forward cover option to maximize its returns.