# Bond Prices

Present value explains why the price of bonds on the bond exchange falls when interest rates rise and rises when interest rates fall. A bond is a contract. At the beginning of the contract, the lender pays a specified amount, usually \$1000 or a multiple of \$1000, to the borrower. The bond specifies when the \$1000 will be paid back, how much will be paid as interest each year, and all other terms of the agreement. A bond issued in 1983, due in 2003, and paying \$130 a year interest (a coupon rate of 13%) had the stream of payments illustrated in the table below. If the market rate of interest equaled 13%, the 1983 value of the Get column would equal \$1000.

 What a Bond Does Year Give Get 1983 \$1000 \$0 1984 0 \$130 1985 0 \$130 1986 0 \$130 ... ... ... ... ... ... 2001 0 \$130 2002 0 \$130 2003 0 \$1130

If the lender decides that he no longer wants to hold this bond, he cannot demand payment from the borrower because the contract does not give the owner of the bond the right to payment on demand. But he can sell it to someone else, and the price of this sale need not be \$1000. If market interest rates have risen since the original purchase of the bond, the present value of future payments in the Get column will drop, and so will the value of the bond. Another way of seeing this principle is to realize that if the market interest rate rises to 15%, there will be borrowers selling contracts for \$1000 that pay \$150 each year until the maturity of the bond (when the contract ends). It would be foolish to pay \$1000 to buy a contract that pays only \$130 a year.

The notion of present value may seem dry to someone who has never owned a bond or made business decisions. But for many corporate financiers, and for those who have money invested in bonds, it is a notion that provides a lot of excitement—both joy and woe—in their lives.

The notion of rational consumers leads to an important concept called consumers' surplus.