# Five short problems on derivatives, swaps, warrants

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1. Coffman & Tony Inc. can borrow at 13 percent in the long-term capital market (fixed rate) or can borrow at London Interbank offer rate (LIBOR) plus 75 basis points in the Eurodollar market. Jim & Pfeiffenberger Inc. can borrow at 12 percent in the capital market long term (fixed) or can borrow at LIBOR plus 50 basis points. Show a plain vanilla swap arrangement.

2. Swap/cap/floor parity involves creating a zero cost collar such that cap premium equals the floor premium. You are looking at a $50, non-dividend-paying stock, with a risk-free rate at 5 percent. What strike price would make the one-year call premium equal to the one-year put premium.

3. A swap dealer notes the following spot interest rates:

6 months 5.55 percent

12 months 5.75 percent

18 months 5.95 percent

24 months 6.10 percent

Determine the equilibrium swap price on a semiannual payment, two-year swap.

4. A speculator buys July corn futures contract at $2.18/bushel and simultaneously writes a July 220 corn futures call option at 8 cents. Calculate the speculator's combined gain or loss if the price of corn rises to 235 and the option is exercised.

5. One hundred shares of a stock are purchased for $45 per share. Simultaneously, a 5-year warrant on the same company is sold short at $8. The warrant permits the purchase of 100 shares of stock from the company at $55. Over the next 5 years, a total of $2.50 in dividends is received on each share. What is your profit or loss if, at the end of the warrant's life, the stock price is $60.

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1. Coffman & Tony Inc. can borrow at 13 percent in the long-term capital market (fixed rate) or can borrow at London Interbank offer rate (LIBOR) plus 75 basis points in the Eurodollar market. Jim & Pfeiffenberger Inc. can borrow at 12 percent in the capital market long term (fixed) or can borrow at LIBOR plus 50 basis points. Show a plain vanilla swap arrangement.

In the fixed rate market, Jim & Pfeiffenberger Inc ("J&P") has an advantage of 100 basis points over Coffman & Tony Inc. ("C&T") (12% versus 13%). In the floating rate market, it has an advantage of only 25 bps (Libor + 50 versus Libor + 75). Therefore, J&P has a comparative advantage in the fixed rate market and C&T has a comparative advantage in the floating rate market. So J&P should issue debt at 12% fixed rate and C&T should issue debt at Libor + 75. Let's see now a vanilla swap arrangement that will benefit both parties:

J&P agrees to pay the Libor (floating) rate to C&T. C&T, on the other hand, agrees to pay a 12% fixed rate to J&P.

That's a vanilla swap arrangement, and it benefits both parties. J&P receives 12% from C&T (from the swap), and then pays 12% to its creditors (recall we said it issued debt at the fixed rate). It also pays the Libor rate to C&T (from ...

#### Solution Summary

This post explains five problems on Swaps and derivatives. It could be used as a good practice for the students preparing for exams for financial derivatives.