Principles of Corporate Finance_ 12th Edition

688 Part Eight Risk Management

bre44380_ch26_673-706.indd 688 09/30/15 12:09 PM

The dealer is quoting a rate for five-year swaps of 6% against LIBOR.^26 This figure is

sometimes quoted as a spread over the yield on U.S. Treasuries. For example, if the yield on

five-year Treasury notes is 5.25%, the swap spread is .75%.

The first payment on the swap occurs at the end of year 1 and is based on the starting

LIBOR rate of 5%.^27 The dealer (who pays floating) owes the bank 5% of $66.67 million,

while the bank (which pays fixed) owes the dealer $4 million (6% of $66.67 million). The

bank therefore makes a net payment to the dealer of 4 − (.05 × 66.67) = $.67 million:

Bank 0.05 × $66.67 = $3.33 Counterparty

Bank $4 Counterparty

Bank Net = $0.67 Counterparty

The second payment is based on LIBOR at year 1. Suppose it increases to 6%. Then the net

payment is zero:

Bank 0.06 × $66.67 = $4 Counterparty

Bank $4 Counterparty

Bank Net = 0 Counterparty

The third payment depends on LIBOR at year 2, and so on.

The notional value of this swap is $66.67 million. The fixed and floating interest rates

are multiplied by the notional amount to calculate dollar amounts of fixed and floating

interest. But the notional value vastly overstates the economic value of the swap. At creation the

economic value of the swap is zero because the NPV of the cash flows to each counterparty is

Year

0 1 2 3 4 5

Homemade swap:

1. Borrow $66.67 at 6%
   fixed rate +66.67 − 4 − 4 − 4 − 4 −(4 + 66.67)


2. Lend $66.67 at LIBOR
   floating rate

−66.67 +0.05 × 66.67 + LIBOR 1

× 66.67

+ LIBOR 2

× 66.67

+ LIBOR 3

× 66.67

+ LIBOR 4

× 66.67 + 66.67

Net cash flow 0 − 4 − 4 − 4 − 4 − 4

+0.05 × 66.67 + LIBOR 1

× 66.67

+ LIBOR 2

× 66.67

+ LIBOR 3

× 66.67

+ LIBOR 4

× 66.67

Standard fixed-to-floating swap:

Net cash flow (^0) − 4 − 4 − 4 − 4 − 4
+0.05 × 66.67 + LIBOR 1
× 66.67

• LIBOR 2
  × 66.67


• LIBOR 3
  × 66.67


• LIBOR 4
  × 66.67
  ❱ TABLE 26.3^ The top panel shows the cash flows in millions of dollars to a homemade fixed-to-floating
  interest rate swap. The bottom panel shows the cash flows to a standard swap transaction.
  (^27) More commonly, interest rate swaps are based on three-month LIBOR and involve quarterly cash payments.
  (^26) Notice that the swap rate always refers to the interest rate on the fixed leg of the swap. Rates are generally quoted against LIBOR,
  though dealers will also be prepared to quote rates against other short-term debt.