Question

1. You have just landed a job with a prestigious venture capital firm and will be making a great salary in the Spring. Your recent ambition to own a nice Rolex Watch will now be possible. You find that the watch is currently priced at $50,000 for a limited time and you won’t have access to your huge $100,000 signing bonus until 4 months from now. Although you do not have the cash to buy the watch, the dealer doesn’t want to lose a sure sale. He is therefore willing to quote you a guaranteed price for the watch 4 months from now if agree to purchase the watch today.   The reason he is willing to do that is because he can book the sale for accounting purposes today as long as the deal is signed and both parties are obligated to the transaction.
2. 1. a. If the dealer quotes you a price of $54,000 (and is willing to buy or sell forward at this price), is there an opportunity to make a zero investment profit and if so how would you specifically do so and how much would the profit would you make? Assume that you could borrow or lend from a bank at the 12% mentioned in part a) above.
   2. b. If the appropriate borrowing rate for a Rolex loan is 12%, what price does he quote today to transact 4 months from now? Assume that any borrowing or investing associated with the Rolex transaction must be related to the 12% loan rather than at the risk-free rate. Also assume that the dealer’s spot and forward prices are good for buying or selling at those prices.

Answer 1

Given - Cost of Rolex Watch Today = $50,000

Signing Bonus Available 4 months from Today =$ 100,000

a) Calculation of zero investment profit

Since the quoted price by the seller 4 months from now is $54,000 (both for selling or buying the watch), we can make a zero investment profit by buying the Rolex Watch today for $50,000 today and selling it after 4 months to the watch dealer at his quoted price of $54,000. However, since we cannot use our bonus till 4 months, we can borrow $50,000 today from bank for 4 months at 12% interest rate per annum.

Workings are as under -

Step 1 - Borrow $50,000 from bank at 12% p.a. interest rate

Step 2 - Purchase Rolex Watch today from the dealer at $50,000

Step 3 - Sell the Rolex Watch to the dealer for $54,000 after 4 months.

Step 4 - Repay bank loan with interest for 4 months which comes out to be $52,000.

($50,000 + ($50,000 x 12/100 x 4/12)) = $50,000 + $2,000 = $52,000

Zero Investment Profit Earned = $54,000 - $52,000 = $2,000

b) Calculation of price to be quoted today by the dealer to transact 4 months from now.

Current price of Rolex $50,000

Value of amount if invested for 4 months from now at 12%p.a. will be $52,030

Future value of Amount Invested = (Amount Invested + Interest for 4 months at 12% p.a.)

Interest per month = 12/(100 x 12) = 0.01

Monthly Compounding = 50,000(1+0.01)(1+0.01)(1+0.01)(1+0.01)

(50000×1.01×1.01×1.01×1.01)

= 52,030 approx

This implies that the future value of Rolex is $52,030 at 12% Interest rate is $52,030

If the dealer wants to buy the Rolex after 4 months from now, he must quote a price of $52,030 or below to earn a profit

If the dealer wants to sell the Rolex after 4 months from now, he must quote a price of $52,030 or above to earn a profit